Creating InferenceData#
InferenceData is the central data format for ArviZ. InferenceData itself is just a container that maintains references to one or more xarray.Datasets. See the InferenceData structure specification here. For more on xarray, you can get the details here. Below are various ways to generate an InferenceData object.
import arviz as az
import numpy as np
From 1D numpy array#
size = 100
dataset = az.convert_to_inference_data(np.random.randn(size))
dataset
arviz.InferenceData
-
- chain: 1
- draw: 100
- chain(chain)int640
array([0])
- draw(draw)int640 1 2 3 4 5 6 ... 94 95 96 97 98 99
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99])
- x(chain, draw)float640.1579 -1.096 ... 0.2098 -0.8789
array([[ 0.15786879, -1.09617856, -1.14186804, 0.36890996, -0.00480893, -0.26640545, -0.22589345, 0.36226862, -0.1637468 , 0.9463602 , -0.16037895, -0.47217036, -0.32559551, 0.02146089, -1.1951687 , -0.55566732, -1.58659649, 1.22081265, -1.08665849, -0.7958125 , 0.65958937, 0.27969403, -0.17490678, -1.24356584, -0.1324672 , 0.36716036, -0.36945927, 0.52743292, 1.55669984, -1.55496202, -0.23208698, 0.3184957 , 1.89373564, 1.50685094, 0.06062807, 0.03812133, -1.50142131, -0.51704982, 0.00602984, -0.0113514 , -0.88565062, 2.62424394, -0.61801463, -2.50243202, -2.15975804, 1.67773991, 0.2355224 , -0.46748378, 0.93796441, 1.22928386, -0.10454738, -1.16191922, 2.0844819 , 1.14643675, -1.2708001 , -1.20772303, 1.30867462, -1.41595009, 0.39046395, -1.75340487, -0.63020928, 0.54330999, 0.82563864, -0.29676448, 0.39695874, -0.43591367, 0.33793442, -0.28370068, 0.87123748, 0.78362023, 0.80684138, -0.28939298, 0.15943827, 0.02084011, -1.17347054, 2.08937644, -0.05675786, 0.02685161, 0.18905682, 0.86255176, 0.43466604, -0.50953183, -4.12647035, -1.28030692, -0.92458282, 0.31344078, -0.76004658, -0.93271076, 0.3004889 , 1.37911025, -0.20649192, 0.49806992, 1.21242756, 1.2386684 , 0.9563797 , 0.74242753, 1.97889055, -1.38845611, 0.20983583, -0.87888212]])
- created_at :
- 2021-02-13T14:34:09.064078
- arviz_version :
- 0.11.1
<xarray.Dataset> Dimensions: (chain: 1, draw: 100) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 2 3 4 5 6 7 8 9 ... 90 91 92 93 94 95 96 97 98 99 Data variables: x (chain, draw) float64 0.1579 -1.096 -1.142 ... 0.2098 -0.8789 Attributes: created_at: 2021-02-13T14:34:09.064078 arviz_version: 0.11.1xarray.Dataset
From nD numpy array#
shape = (1, 2, 3, 4, 5)
dataset = az.convert_to_inference_data(np.random.randn(*shape))
dataset
arviz.InferenceData
-
- chain: 1
- draw: 2
- x_dim_0: 3
- x_dim_1: 4
- x_dim_2: 5
- chain(chain)int640
array([0])
- draw(draw)int640 1
array([0, 1])
- x_dim_0(x_dim_0)int640 1 2
array([0, 1, 2])
- x_dim_1(x_dim_1)int640 1 2 3
array([0, 1, 2, 3])
- x_dim_2(x_dim_2)int640 1 2 3 4
array([0, 1, 2, 3, 4])
- x(chain, draw, x_dim_0, x_dim_1, x_dim_2)float64-0.08403 1.102 ... -0.5577 -0.5846
array([[[[[-0.08403065, 1.1017712 , 1.62302046, 1.39574141, 1.901956 ], [ 0.61743317, 0.64286807, 1.65556641, 0.35500703, 1.35779885], [-2.07848838, -0.29836442, -0.85049063, 0.73218157, -1.44790928], [-0.45602564, -0.61318067, -1.40920883, 0.51587317, 1.32186021]], [[ 0.63302553, 0.73647764, -0.09351366, 0.56765985, 1.76398645], [-0.84039966, 0.65844108, -0.69561599, 2.45493478, 0.67689617], [ 0.29668126, -1.61519616, -0.6773996 , -1.6269603 , 2.48250982], [ 1.85530246, -0.86730015, 2.78300975, 0.04338923, 0.06634155]], [[ 0.13229749, 0.38531945, 1.76259904, 0.41885034, 2.89667167], ... [-0.47604491, 0.50072873, -0.52789957, 1.17294914, -1.67759066]], [[-0.31814332, 0.19096605, -0.22101215, -2.28617523, -1.62671503], [-0.39575603, 0.51917412, -1.78458713, 1.94001721, -0.2580746 ], [-1.44927599, -0.7534741 , 0.65399302, -1.10388202, 1.17203129], [-1.30190085, 1.49935812, -0.0981464 , 0.47667323, 0.31247077]], [[ 0.14913867, -1.25433089, 1.24156086, -0.49093126, 1.24566456], [ 0.91544263, -1.62292738, -1.07362398, -0.65013752, 1.19963122], [ 0.39388328, -0.89078638, 0.13971883, 0.33744372, 1.06058924], [-0.63608906, 0.13908276, -1.48103522, -0.55767142, -0.58462068]]]]])
- created_at :
- 2021-02-13T14:34:09.909620
- arviz_version :
- 0.11.1
<xarray.Dataset> Dimensions: (chain: 1, draw: 2, x_dim_0: 3, x_dim_1: 4, x_dim_2: 5) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 * x_dim_0 (x_dim_0) int64 0 1 2 * x_dim_1 (x_dim_1) int64 0 1 2 3 * x_dim_2 (x_dim_2) int64 0 1 2 3 4 Data variables: x (chain, draw, x_dim_0, x_dim_1, x_dim_2) float64 -0.08403 ... -0... Attributes: created_at: 2021-02-13T14:34:09.909620 arviz_version: 0.11.1xarray.Dataset
From a dictionary#
datadict = {
"a": np.random.randn(100),
"b": np.random.randn(1, 100, 10),
"c": np.random.randn(1, 100, 3, 4),
}
dataset = az.convert_to_inference_data(datadict)
dataset
arviz.InferenceData
-
- b_dim_0: 10
- c_dim_0: 3
- c_dim_1: 4
- chain: 1
- draw: 100
- chain(chain)int640
array([0])
- draw(draw)int640 1 2 3 4 5 6 ... 94 95 96 97 98 99
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]) - b_dim_0(b_dim_0)int640 1 2 3 4 5 6 7 8 9
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
- c_dim_0(c_dim_0)int640 1 2
array([0, 1, 2])
- c_dim_1(c_dim_1)int640 1 2 3
array([0, 1, 2, 3])
- a(chain, draw)float64-2.135 -0.2855 ... 0.004506 -0.6005
array([[-2.13544683, -0.28549645, -0.22264909, -0.93293274, -0.70340885, -1.6431039 , 1.12579702, -0.07256171, -0.94842639, -0.97520597, -0.97121903, 1.55988844, 0.16842664, 1.20203192, -1.451998 , 1.1034488 , 0.30540674, -0.9740496 , 0.99117123, -0.02244417, 0.21356687, 0.1782902 , -0.2357763 , 1.89391712, 0.05707509, 0.14578992, -0.10872117, -0.16515133, 1.45943019, 0.464367 , 2.24189297, -0.98596886, 0.18449422, -0.53079197, -0.78859255, 1.93031216, -0.93846074, 0.59057879, -0.54179058, 1.03929777, -0.47815684, -1.00029637, 0.25930499, -1.08620067, 0.10544712, -0.33510953, 2.7918108 , -0.48445729, 1.35519298, -1.07978766, 1.2403764 , -0.48409421, -0.29797492, 1.74034758, 0.26002921, -1.60571308, 2.08458728, -0.18937691, -0.73170727, 1.22968393, 0.44830485, 0.88102682, -1.4087653 , 0.82006584, 0.01361757, -0.68680755, -2.12192547, 0.48157838, -0.99493753, -1.1710843 , -0.00324472, -0.34669479, 0.75617941, 0.13809252, -0.00293795, 1.54383557, 0.75466282, 0.70882703, -0.76888358, 0.88078721, -0.98875811, -0.66684028, -0.17737408, -0.19195556, -0.52677063, -0.3035301 , 0.33827756, -1.21031729, -0.66538835, 1.24311501, -0.30734044, -1.13224426, -0.23575202, 0.74078858, 0.45278921, 1.40622741, -0.68259759, 0.16404416, 0.00450633, -0.60046321]]) - b(chain, draw, b_dim_0)float642.316 -1.102 ... 2.333 0.08732
array([[[ 2.31594064e+00, -1.10239464e+00, -9.20590630e-02, -1.00067395e+00, -1.00982365e-01, 3.12551977e-01, 1.30889742e-01, 1.01067763e+00, -1.93728644e+00, -1.96631559e+00], [ 2.88912815e-01, 8.64017095e-01, -4.15148499e-01, -1.52566003e+00, 7.65670834e-01, -1.24231992e+00, -1.57352946e-01, 2.13860180e-01, 3.64663713e-01, -2.73271702e-01], [-8.25991982e-01, 1.84076957e+00, 1.08514639e+00, -7.08543063e-01, -2.00597994e-01, 4.02011481e-01, -2.23579981e+00, -1.15752412e+00, -4.43020640e-01, 1.39158209e+00], [ 2.12319852e-01, 1.57386014e-01, -2.80671862e-01, -9.28866866e-01, -6.99740772e-01, -5.80207944e-01, 8.39600405e-02, -3.95043366e-01, 5.60529521e-01, 1.96818442e-01], [ 9.31745987e-02, -1.76612249e+00, 1.26661338e+00, -8.41517795e-01, -1.09134025e+00, 1.21106377e+00, -5.89417432e-02, 4.90687025e-01, -1.45992378e+00, 1.10820280e+00], ... [ 4.03376765e-01, 9.42158780e-01, 1.86929928e-01, 3.19502814e-01, -1.52896559e+00, 9.65853447e-02, -5.83760878e-01, 2.32820817e-01, 6.85423182e-01, -9.65070463e-01], [ 3.89276446e-02, -5.24983298e-01, 8.76155496e-01, 1.04176946e+00, -2.85950102e-01, -7.23899820e-01, 2.79438377e-01, -6.63992916e-01, -2.59889488e-01, 8.53932257e-01], [-5.84313907e-01, 1.16472351e+00, 1.54747379e+00, 4.25130441e-01, -1.12248710e+00, 5.99760270e-01, -9.37162916e-01, 7.98654999e-01, -2.03388722e-01, -1.37138445e-01], [-9.58500168e-01, -2.15828236e-01, -2.20728934e-02, -3.64141198e-01, 2.74506372e-01, 5.47167487e-01, 1.50047521e+00, -1.52031173e+00, -5.09673590e-01, -1.17376898e+00], [-1.47383906e+00, 6.66256624e-01, 7.81715878e-01, 1.88467870e-01, 1.13442069e+00, -1.85172363e+00, 7.40123308e-01, 1.26232317e+00, 2.33276361e+00, 8.73152677e-02]]]) - c(chain, draw, c_dim_0, c_dim_1)float64-0.3045 0.1427 ... -0.6531 0.5698
array([[[[-3.04502571e-01, 1.42737459e-01, -9.71657962e-02, -8.93188910e-01], [ 3.04563145e-01, 5.24937448e-04, -1.09452361e+00, -1.35199712e+00], [ 4.12119313e-01, -8.82643195e-01, -7.04691324e-01, -1.25075637e+00]], [[-5.52101365e-01, 1.11897936e+00, 2.58616801e-01, -4.08383300e-02], [-1.72855282e+00, -1.44721457e+00, 1.94643245e+00, 4.32584013e-01], [-3.94882193e-01, 7.70659226e-01, -1.61441696e+00, -1.72500340e+00]], [[-3.40557372e-01, 1.49244307e+00, -8.79396841e-01, 6.19749682e-01], [ 5.86304569e-02, -1.29708098e+00, -8.91758881e-01, 8.60487195e-01], [-6.46215644e-01, -1.24231084e+00, 1.02951259e-01, -1.14116359e+00]], ... [[-2.51927923e-01, 4.86355686e-01, 1.02337110e-01, -3.91983265e-01], [-3.16304455e-01, -9.77624093e-01, 7.47037624e-01, 1.47022330e+00], [ 2.75938704e+00, -1.45844332e+00, 6.05000304e-01, -1.09534187e+00]], [[ 1.32989709e+00, -1.48206442e-01, 1.41643986e+00, 3.21362235e-01], [ 7.14366149e-01, -8.96126440e-01, 1.25597256e+00, 1.47682789e-01], [ 5.90506409e-01, -7.26727058e-01, 4.73393503e-01, -7.49608085e-01]], [[-4.48031599e-01, 1.30492399e+00, -8.19654000e-02, -6.30742208e-01], [ 6.57215837e-01, -4.16781732e-01, 1.76999107e+00, 2.95505700e-01], [-1.46068664e-01, -1.72669102e+00, -6.53139048e-01, 5.69801286e-01]]]])
- created_at :
- 2021-02-13T14:34:10.676263
- arviz_version :
- 0.11.1
<xarray.Dataset> Dimensions: (b_dim_0: 10, c_dim_0: 3, c_dim_1: 4, chain: 1, draw: 100) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 2 3 4 5 6 7 8 9 ... 90 91 92 93 94 95 96 97 98 99 * b_dim_0 (b_dim_0) int64 0 1 2 3 4 5 6 7 8 9 * c_dim_0 (c_dim_0) int64 0 1 2 * c_dim_1 (c_dim_1) int64 0 1 2 3 Data variables: a (chain, draw) float64 -2.135 -0.2855 -0.2226 ... 0.004506 -0.6005 b (chain, draw, b_dim_0) float64 2.316 -1.102 ... 2.333 0.08732 c (chain, draw, c_dim_0, c_dim_1) float64 -0.3045 0.1427 ... 0.5698 Attributes: created_at: 2021-02-13T14:34:10.676263 arviz_version: 0.11.1xarray.Dataset
From dictionary with coords and dims#
datadict = {
"a": np.random.randn(100),
"b": np.random.randn(1, 100, 10),
"c": np.random.randn(1, 100, 3, 4),
}
coords = {"c1": np.arange(3), "c2": np.arange(4), "b1": np.arange(10)}
dims = {"b": ["b1"], "c": ["c1", "c2"]}
dataset = az.convert_to_inference_data(datadict, coords=coords, dims=dims)
dataset
arviz.InferenceData
-
- b1: 10
- c1: 3
- c2: 4
- chain: 1
- draw: 100
- chain(chain)int640
array([0])
- draw(draw)int640 1 2 3 4 5 6 ... 94 95 96 97 98 99
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]) - b1(b1)int640 1 2 3 4 5 6 7 8 9
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
- c1(c1)int640 1 2
array([0, 1, 2])
- c2(c2)int640 1 2 3
array([0, 1, 2, 3])
- a(chain, draw)float640.1803 0.5852 ... -0.05 1.146
array([[ 0.18025798, 0.58521032, -0.18510602, 0.29572838, -0.4678021 , 1.05480259, 1.28168388, 0.28121633, 1.28831772, -0.9405371 , -0.01534311, 2.06181243, 0.24717768, 0.92023114, -0.20417784, 0.40450326, -1.81281575, 0.32930736, 1.37936813, -1.045988 , -1.17985161, 1.52358934, 0.81251164, 1.28913742, -0.23414291, 0.02790046, 1.01011449, 0.57112459, 0.90010843, 1.45698772, -1.54781426, 0.68288115, 0.26818358, 0.27993301, 0.83487245, -0.38779835, -3.00243428, -0.83141511, 0.84487712, -0.1588264 , 0.4761695 , 0.48862562, -0.41776401, -0.42193439, 0.45713259, -1.37347751, -0.44040984, 0.43530538, -2.11459774, -0.02085076, -1.99419785, -1.6438705 , 0.3642352 , 0.16277758, -1.14936101, -0.03853989, 1.17273882, 1.24492894, -0.85045339, 0.23314687, -1.06573434, 0.12197202, -0.90605231, 1.3832725 , -0.96656837, 0.38713005, 1.43913237, 0.13171886, -0.41252912, -0.22330962, 0.66293516, 0.49838978, 1.11763287, -0.12153436, -0.95715543, 0.28567201, -1.04870722, -0.7706029 , -0.08357007, -0.97143108, -1.03133491, -0.5744688 , -0.25378889, -1.41828196, 0.15854538, 0.77810164, -0.85872318, -0.95917415, -1.10980651, 0.15896798, 0.95216139, 0.25552642, -0.03821542, 0.31519828, 0.60881462, -0.07113351, -0.50351016, 1.41964737, -0.05000121, 1.14579741]]) - b(chain, draw, b1)float640.1448 0.3689 ... 0.6358 0.3637
array([[[ 1.44768645e-01, 3.68912141e-01, -4.41145092e-01, 1.01329899e+00, -2.07608831e-01, 1.58289413e-01, 1.62900724e+00, 4.81549794e-01, 7.36543747e-01, -6.19077739e-01], [-9.64115527e-01, -7.95727502e-01, 8.39260050e-01, 1.85614010e-01, 5.28028388e-01, -1.01281926e+00, 2.08883508e-01, 9.99168036e-01, 4.39771693e-01, 2.12305143e+00], [ 3.59210211e-01, 3.40273376e-01, 2.98681466e-01, -8.43803598e-01, 2.16024571e+00, -5.77565866e-01, -1.71335609e-01, -1.19055415e-01, -5.83590579e-01, -3.93990715e-01], [ 1.34295134e-01, 1.98614920e+00, -6.64298704e-01, -9.27949544e-02, 6.89743208e-01, -8.08106338e-01, 6.61251310e-01, -9.97463634e-01, -4.41736557e-01, 1.72348721e-01], [-3.97988577e-01, 1.53273089e+00, -7.91212995e-01, 2.24241430e+00, -1.59580390e+00, -2.15388666e+00, -8.10599091e-01, 2.64187178e+00, -4.07235896e-01, -8.90425685e-01], ... [ 3.07674673e-01, -1.50641692e+00, 1.73030789e+00, -1.47323923e-01, -2.16538092e-01, 1.00179747e+00, -4.65012767e-03, -8.00730253e-01, 7.95794005e-01, -1.12679215e+00], [ 1.92166661e+00, 3.11945611e-01, 8.00024301e-01, 8.95247769e-01, -5.88769922e-01, -7.67819877e-01, 1.28055926e+00, -4.62022641e-01, 4.09592181e-01, 8.32283149e-01], [-2.05812436e-01, 9.03045539e-01, 3.40563354e-01, 2.31481211e-01, 4.27513621e-01, 6.94560792e-01, 4.03242602e-01, -1.91523827e+00, -2.26753819e+00, 2.61259842e-01], [-6.19526267e-01, 2.65777755e-01, 3.12480251e-02, -1.16288163e+00, 1.04619214e+00, 1.53060008e-01, 6.51890028e-01, 1.28364550e+00, -3.16561855e-01, 2.55569983e-01], [ 3.62763197e-01, -2.32596286e-01, -1.08565195e-01, -1.02661301e+00, 2.55885867e-01, -7.11633669e-01, 2.16457106e-01, -1.43406267e-01, 6.35785896e-01, 3.63733284e-01]]]) - c(chain, draw, c1, c2)float64-0.9854 1.128 ... -0.08264 -0.1264
array([[[[-0.9853996 , 1.12752293, -1.9499529 , 0.53327689], [-1.20611327, 0.49807201, 1.69088725, 1.23112537], [-0.23287423, -1.03069988, 0.67629377, 0.01194341]], [[-2.8234039 , -1.11843694, -0.62971856, -0.83978545], [ 0.7580245 , 2.99053767, 0.7134701 , 1.79643044], [ 1.31332094, 0.46178798, -1.05648389, -0.37917092]], [[-0.06346469, 1.04674024, 0.58744707, -0.76578695], [ 0.04049516, 0.02051111, 0.99117427, 0.30782594], [ 0.49078966, -1.17610465, 0.08032067, 0.24485989]], ..., [[ 0.55327319, 0.54893173, -0.82879398, -2.70989554], [ 0.38160275, -1.85099807, 0.89347682, -0.15399947], [ 1.12543953, -0.06551779, -1.4420331 , 0.34254678]], [[ 0.46316553, -0.25416657, -2.12689551, -0.74543099], [ 0.3510827 , 1.34503713, 0.33211332, -0.00794034], [-0.62564394, 1.57612706, -0.47899028, -0.95268644]], [[ 0.71415433, -0.90717209, -0.34649499, 1.19899274], [-1.18767475, 0.07201166, -0.3339749 , 0.30002289], [-0.77867416, -0.28337606, -0.08264274, -0.1263899 ]]]])
- created_at :
- 2021-02-13T14:34:11.561406
- arviz_version :
- 0.11.1
<xarray.Dataset> Dimensions: (b1: 10, c1: 3, c2: 4, chain: 1, draw: 100) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 2 3 4 5 6 7 8 9 ... 90 91 92 93 94 95 96 97 98 99 * b1 (b1) int64 0 1 2 3 4 5 6 7 8 9 * c1 (c1) int64 0 1 2 * c2 (c2) int64 0 1 2 3 Data variables: a (chain, draw) float64 0.1803 0.5852 -0.1851 ... 1.42 -0.05 1.146 b (chain, draw, b1) float64 0.1448 0.3689 -0.4411 ... 0.6358 0.3637 c (chain, draw, c1, c2) float64 -0.9854 1.128 ... -0.08264 -0.1264 Attributes: created_at: 2021-02-13T14:34:11.561406 arviz_version: 0.11.1xarray.Dataset
From Dataframe#
import pandas as pd
import xarray as xr
data = np.random.rand(100, 2)
df = pd.DataFrame({"a": data[:, 0], "b": data[:, 1]})
df["chain"] = 0
df["draw"] = np.arange(len(df), dtype=int)
df = df.set_index(["chain", "draw"])
xdata = xr.Dataset.from_dataframe(df)
dataset = az.InferenceData(posterior=xdata)
dataset
arviz.InferenceData
-
- chain: 1
- draw: 100
- chain(chain)int640
array([0])
- draw(draw)int640 1 2 3 4 5 6 ... 94 95 96 97 98 99
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99])
- a(chain, draw)float640.174 0.5209 ... 0.7712 0.7085
array([[0.17399969, 0.5208888 , 0.78073958, 0.81270859, 0.8326313 , 0.69481359, 0.4527345 , 0.04006563, 0.77150224, 0.16863518, 0.68034228, 0.86157851, 0.96612157, 0.69838848, 0.7405653 , 0.40183901, 0.93158215, 0.57381034, 0.03965956, 0.24734419, 0.29724078, 0.9013152 , 0.57675347, 0.40654378, 0.69854638, 0.09837131, 0.21214115, 0.1279704 , 0.55363704, 0.12164797, 0.65484205, 0.49855299, 0.582182 , 0.40784308, 0.35231303, 0.5077159 , 0.75960323, 0.01040058, 0.09464055, 0.23224409, 0.20540761, 0.92500228, 0.68019656, 0.17963035, 0.31480531, 0.192919 , 0.29010568, 0.27310427, 0.51541579, 0.75374609, 0.44719811, 0.47072294, 0.94771935, 0.60403158, 0.27252951, 0.54313015, 0.73418615, 0.61183258, 0.58393097, 0.75639231, 0.87383449, 0.28687463, 0.57651506, 0.99342533, 0.30465784, 0.09122743, 0.64509912, 0.16049284, 0.56583453, 0.57754649, 0.66636619, 0.84445723, 0.79335418, 0.60991439, 0.26558104, 0.5107463 , 0.33189211, 0.0483592 , 0.01859405, 0.98429866, 0.90619961, 0.25960695, 0.94647809, 0.09666915, 0.41470572, 0.2318206 , 0.84605472, 0.04214555, 0.44629552, 0.0779919 , 0.33989361, 0.55105841, 0.11240351, 0.32139337, 0.60258537, 0.65662102, 0.92479269, 0.32653733, 0.77124998, 0.70845848]]) - b(chain, draw)float640.2623 0.7124 ... 0.7347 0.2066
array([[0.26233205, 0.71237734, 0.40614189, 0.157799 , 0.30508373, 0.43105906, 0.70338858, 0.9934347 , 0.62548769, 0.573906 , 0.18520596, 0.0185891 , 0.51231002, 0.34795437, 0.78205858, 0.64245918, 0.92387104, 0.55519649, 0.14265756, 0.10061876, 0.57597563, 0.26250029, 0.86924449, 0.49315196, 0.49264495, 0.11063183, 0.31925675, 0.65678517, 0.21526201, 0.87798507, 0.55008982, 0.84317132, 0.46329765, 0.82825291, 0.81930421, 0.54645579, 0.32158564, 0.03518231, 0.53148206, 0.56233558, 0.54699573, 0.57645566, 0.82334312, 0.5028602 , 0.65316495, 0.81334273, 0.19176257, 0.00114957, 0.52653155, 0.7395968 , 0.44507712, 0.80512889, 0.65411647, 0.1615548 , 0.61605705, 0.06003412, 0.73053819, 0.6909904 , 0.62895864, 0.84121641, 0.75035995, 0.30656108, 0.18868098, 0.32532067, 0.3747053 , 0.25471167, 0.6967188 , 0.30872236, 0.39623998, 0.45088483, 0.69392015, 0.3753773 , 0.54683931, 0.46712367, 0.69873646, 0.96662166, 0.59242308, 0.69475848, 0.76610687, 0.6491353 , 0.05237508, 0.17393994, 0.77190906, 0.67008818, 0.98883783, 0.83755151, 0.72336427, 0.84498439, 0.43565136, 0.89425368, 0.65094689, 0.98856566, 0.0738281 , 0.40562204, 0.98279899, 0.10461026, 0.56767586, 0.84467041, 0.73472178, 0.20655504]])
<xarray.Dataset> Dimensions: (chain: 1, draw: 100) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 2 3 4 5 6 7 8 9 ... 90 91 92 93 94 95 96 97 98 99 Data variables: a (chain, draw) float64 0.174 0.5209 0.7807 ... 0.3265 0.7712 0.7085 b (chain, draw) float64 0.2623 0.7124 0.4061 ... 0.8447 0.7347 0.2066xarray.Dataset
From PyMC3#
with pm.Model() as model:
mu = pm.Normal("mu", mu=0, sd=5)
tau = pm.HalfCauchy("tau", beta=5)
theta_tilde = pm.Normal("theta_tilde", mu=0, sd=1, shape=eight_school_data["J"])
theta = pm.Deterministic("theta", mu + tau * theta_tilde)
pm.Normal("obs", mu=theta, sd=eight_school_data["sigma"], observed=eight_school_data["y"])
trace = pm.sample(draws, chains=chains)
prior = pm.sample_prior_predictive()
posterior_predictive = pm.sample_posterior_predictive(trace)
pm_data = az.from_pymc3(
trace=trace,
prior=prior,
posterior_predictive=posterior_predictive,
coords={"school": np.arange(eight_school_data["J"])},
dims={"theta": ["school"], "theta_tilde": ["school"]},
)
pm_data
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [theta_tilde, tau, mu]
100.00% [2000/2000 00:02<00:00 Sampling 2 chains, 3 divergences]
There were 3 divergences after tuning. Increase `target_accept` or reparameterize.
100.00% [1000/1000 00:01<00:00]
arviz.InferenceData
-
- chain: 2
- draw: 500
- school: 8
- chain(chain)int640 1
array([0, 1])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- mu(chain, draw)float646.638 4.791 5.564 ... 5.818 2.299
array([[ 6.63799683e+00, 4.79134072e+00, 5.56424218e+00, 5.57420954e+00, 3.22669739e+00, 4.09925197e+00, 6.77486926e+00, 7.78605439e+00, -2.52944163e-01, 6.61229871e+00, 4.18502958e+00, 1.76376618e+00, 4.62694426e+00, 3.50036596e+00, 3.05630576e+00, 6.62692262e+00, 4.14235573e+00, 6.16275502e+00, 6.22938258e+00, 6.15304590e+00, 3.22079869e+00, 7.23136829e-01, 7.23136829e-01, 5.34538848e+00, 2.39661416e+00, 3.69046096e+00, 2.48955251e+00, 7.46552620e+00, 9.03574415e+00, 6.72969686e+00, 6.34335555e+00, 4.04220266e+00, 2.19778203e+00, 1.37076499e-02, 1.74828963e+00, 7.67516122e+00, 7.67516122e+00, 6.85639862e+00, 4.64813775e+00, 2.65791301e+00, 5.01452937e+00, 1.83039053e+00, 1.78045535e+00, 2.17111590e+00, 2.00686198e+00, 5.41209154e+00, 4.34875837e+00, 4.91332931e+00, 3.53930002e+00, 7.51604256e+00, 7.19161274e+00, 2.03515930e+00, 9.42214963e+00, 7.09555156e+00, 1.93087165e+00, 5.59001258e+00, 7.17291829e+00, 5.13261847e+00, 5.86915693e+00, 2.57897255e+00, 6.61818370e+00, 1.39310780e+00, 3.59564785e+00, 4.32735112e+00, 7.85800197e+00, 1.60693679e+00, 5.56027445e+00, 7.71824903e+00, 7.52958298e+00, 2.17221759e+00, 2.61447368e+00, 1.35683982e+01, 9.20871183e-02, 3.19997426e+00, 4.76437822e+00, 5.54460105e+00, 6.67417392e+00, 5.16285638e+00, -8.19217157e-01, 1.26674178e+01, -5.89391857e-01, -5.89391857e-01, -2.70426811e+00, 9.43770323e+00, 1.01234303e+01, 1.54012544e+00, 1.75412845e+00, 4.47119156e+00, 4.97567517e+00, 1.84977782e+00, 6.91461195e+00, 6.60657308e+00, 3.56008090e-01, 6.93045204e+00, -1.25531329e-01, -1.25531329e-01, 6.39259731e-01, 7.94587362e+00, 2.63018477e+00, 5.63533128e+00, 3.86413926e+00, 4.56795589e+00, 9.47234622e+00, 2.10143003e+00, 6.41839518e+00, 3.83593844e+00, 8.59218468e+00, 2.27599500e+00, 1.03086797e+01, 9.70552286e+00, 8.29190773e+00, 7.70075129e-01, 7.70075129e-01, -1.80722476e+00, 1.27386142e+01, 1.10855042e+01, -1.83874233e+00, 5.03200899e+00, 3.79758372e+00, 3.21167374e+00, 4.00223089e+00, 5.59012552e+00, 4.42937022e-01, 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array([[[-0.32529772, -0.61651454, -0.1667071 , ..., 1.03328716, 2.1823746 , 0.47316842], [ 2.02958114, 1.38140157, 0.75320748, ..., -0.76415401, -0.26376613, 2.59527651], [-1.29974382, -0.93838206, -1.66930843, ..., 0.45610521, 1.16510883, -1.90862339], ..., [ 0.76405243, 1.57497136, -0.19382101, ..., -0.90719718, 0.13818502, -0.53287742], [-0.01956823, -0.44742285, 0.22391893, ..., 1.26672305, 1.48674961, 0.59971362], [-1.31647166, 0.85301164, 0.48705457, ..., 1.10464535, -0.20971009, 0.16073751]], [[ 0.39528795, 2.42188047, -0.63226669, ..., -1.08800486, -1.18916527, -1.15738863], [-1.14188208, 1.13112039, 0.07025925, ..., -0.71775304, 0.42484354, 0.43962524], [ 0.71622022, -1.36901772, 0.34158932, ..., 1.14499937, -0.08757469, -1.25347347], ..., [ 0.18628521, 1.50088211, -0.65171658, ..., 0.48396343, 0.77830976, -0.36442883], [ 0.86143906, -1.5081053 , 0.16205563, ..., -1.43705565, -0.382151 , -0.01870404], [ 0.70965545, 1.59856161, -0.47552168, ..., 0.91627404, 1.22218512, 0.29782471]]]) - tau(chain, draw)float643.1 1.632 1.529 ... 2.741 4.724
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False False
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False]]) - depth(chain, draw)int643 3 3 3 3 3 3 3 ... 3 3 3 3 3 3 3 3
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- created_at :
- 2020-06-10T18:19:23.335024
- arviz_version :
- 0.8.3
- inference_library :
- pymc3
- inference_library_version :
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xarray.Dataset -
- chain: 1
- draw: 500
- school: 8
- chain(chain)int640
array([0])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- tau_log__(chain, draw)float641.706 2.102 -0.9025 ... 3.191 3.0
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-2.44972579, 3.57249281, 2.9723942 , 3.75687405, 5.63509009, -0.21011503, 0.46972604, 1.54744965, 3.04382219, 0.2551527 , 2.33588406, 1.71926505, 2.61660087, 0.72918814, 5.45802459, -1.17878783, 2.09894824, 2.02709688, 1.03242723, 3.71406849, 2.91980202, -0.87215908, 1.84922519, 2.06389569, 1.51474805, 1.82651549, -0.98556942, 1.88015217, 1.86588563, 2.19522154, 0.90610739, 0.12818577, 2.6526049 , -0.34089079, 0.5623638 , 1.17314998, 1.07607117, 3.45167634, 2.07764134, -2.25318032, 1.57445238, 5.17363495, 1.67180101, 1.51730549, 3.60385835, 1.21391414, 4.88465051, 1.34819836, 2.07995028, 1.9411707 , 0.8344764 , 0.53314648, 0.95237139, 2.70993294, 0.25197114, 0.68954274, 2.10559803, 1.46707996, 0.38024107, 3.6718587 , -0.27665213, 1.42949829, -1.62354754, 1.42518566, -1.06680294, 0.79928264, 0.51339205, 1.66846884, 3.79669344, 1.39648667, 1.48479347, -0.15476104, 1.9127241 , 1.2560361 , 0.58643927, 1.6832115 , 2.0844959 , 0.27473111, 1.98730803, 1.73073339, 2.39902852, 1.25603917, 2.13876395, 0.70809256, 0.38677292, 1.12534926, 3.49333425, 5.51480037, 2.27937884, 2.19669492, 1.07241914, 1.29741512, 3.6515715 , 2.20619041, -1.01632301, -1.00972668, -0.13866914, 1.58748499, 4.16389488, 1.47806225, 2.18470271, 2.17287451, 0.35138308, -0.08737636, 3.75533117, 2.12592275, 1.61577535, -0.08719834, -3.74146033, -1.36428267, -5.40154713, 1.85700736, 0.32336021, 1.9426761 , 3.56852419, 1.55354747, 0.97723259, -0.13230045, 1.5765091 , 1.28410518, 1.00776594, 2.02259487, 1.21227949, 0.62992772, 3.05016949, 0.35337658, 0.40199874, 1.48527419, 2.64238791, 0.43196549, 0.10784032, 1.70192077, 2.28243656, 2.03935257, 0.61773816, 0.86907984, -0.76778866, 1.94899872, -0.02152823, -2.29418832, 2.37588713, 1.63970504, 1.19798191, 4.58844073, 2.6773426 , 4.52417613, 0.32385163, 1.97589555, 0.5072283 , -1.26472421, 2.06191531, 0.84805248, 3.71899798, 3.85586477, 1.27418696, -1.66429176, 2.89621868, 0.5836731 , 2.42453699, 2.83891664, -0.10785864, 4.878018 , 7.05836481, 4.95169144, 0.66509645, 0.88350777, 2.27091977, -0.70442498, 0.61656012, 1.18896414, 2.97898156, 2.52738653, 1.25978368, 3.6986964 , 3.52576019, 3.52752708, 4.35818753, -0.09883578, 1.86856041, -1.38208987, 3.10093326, 1.75405802, 5.07287701, 4.1858028 , 3.15839962, 1.25920842, 2.07146588, 1.11480582, 2.82629916, 1.09979417, 0.40300613, -0.99749685, 1.75980059, 2.72177195, 2.58293073, 1.05452379, 0.26683768, -0.08899415, 1.8233168 , 1.25087499, 0.51544631, 1.71713821, -0.07991098, 1.04087024, 1.92818799, -0.35251242, 2.77931855, 1.26470085, 1.39402269, 1.69576834, 2.69417672, 1.35947815, 1.28346478, 0.97858565, 2.01678674, 2.77387222, 1.22566557, 2.8065254 , 2.39601751, 2.79108204, 3.22977667, 2.34095033, 1.21336144, 2.65564027, 0.85456707, 2.84012414, 1.32798643, 0.71154812, 3.49958034, -0.45660104, 1.81603681, 1.96863298, 3.10477242, 0.02468627, 0.6817256 , 3.54044187, 3.26327222, 1.65833051, 1.42266403, 1.18580882, 3.200757 , 2.84417962, 2.09119768, 0.01526257, 1.78042628, 1.67860247, 0.53106916, 2.20371117, 2.16164611, 0.75287014, 1.77576973, 2.20152037, 3.19102252, 2.9998979 ]]) - tau(chain, draw)float645.507 8.185 0.4056 ... 24.31 20.08
array([[5.50686275e+00, 8.18498929e+00, 4.05560437e-01, 1.30457567e+01, 1.64504830e+01, 2.69962919e+00, 2.01269022e+01, 8.99097276e-01, 1.87625645e+00, 4.40620548e+00, 8.75700183e+00, 2.43239497e+00, 1.44189180e+00, 1.76826038e+01, 6.59324864e-02, 1.38897985e+01, 2.96988714e+00, 8.59686709e-01, 4.54883689e+00, 3.08040285e+00, 8.18501327e+00, 9.65243249e+00, 7.83833691e+00, 3.75150607e+00, 3.98325370e+00, 7.42502229e+00, 9.52694584e-01, 1.22156659e+00, 1.09420480e+00, 3.72055864e+01, 3.73287963e-01, 8.53960826e+00, 9.45041492e+01, 1.75767299e+00, 8.06157503e+00, 6.14265162e+00, 7.02672777e+00, 6.96026860e+00, 2.87512835e+01, 2.05550166e+01, 3.77273632e+00, 8.79722240e+00, 1.69188711e+00, 1.25566346e+00, 8.17259137e+00, 1.82778393e+01, 3.99297764e+00, 3.80219282e+00, 2.36415060e+00, 1.83460476e+01, 4.99244772e+01, 1.40951424e+01, 1.33904739e+01, 4.73324937e+00, 8.23979948e-01, 1.85632561e+00, 1.06323880e+00, 3.06079899e+00, 2.50876515e+01, 1.70800873e+01, 5.94768225e+01, 3.88743982e-01, 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1.68828643e+01, 3.00354774e+00, 1.49631606e+00, 3.68801452e-01, 5.81127847e+00, 1.52072448e+01, 1.32358722e+01, 2.87060781e+00, 1.30582847e+00, 9.14850928e-01, 6.19236323e+00, 3.49339832e+00, 1.67438563e+00, 5.56856956e+00, 9.23198526e-01, 2.83168019e+00, 6.87703770e+00, 7.02919842e-01, 1.61080403e+01, 3.54203298e+00, 4.03103308e+00, 5.45083242e+00, 1.47933347e+01, 3.89416062e+00, 3.60912292e+00, 2.66069043e+00, 7.51414121e+00, 1.60205492e+01, 3.40643254e+00, 1.65523055e+01, 1.09793640e+01, 1.62986461e+01, 2.52740118e+01, 1.03911068e+01, 3.36477616e+00, 1.42340968e+01, 2.35035662e+00, 1.71178905e+01, 3.77343764e+00, 2.03714255e+00, 3.31015576e+01, 6.33433007e-01, 6.14744658e+00, 7.16088069e+00, 2.23041424e+01, 1.02499349e+00, 1.97728679e+00, 3.44821524e+01, 2.61349166e+01, 5.25053778e+00, 4.14815656e+00, 3.27333328e+00, 2.45511084e+01, 1.71874526e+01, 8.09460414e+00, 1.01537964e+00, 5.93238476e+00, 5.35806269e+00, 1.70074971e+00, 9.05856906e+00, 8.68542308e+00, 2.12308484e+00, 5.90482450e+00, 9.03874533e+00, 2.43132755e+01, 2.00834863e+01]]) - mu(chain, draw)float64-0.1979 3.452 ... -15.29 -7.206
array([[-1.97924571e-01, 3.45176103e+00, 3.66898018e+00, -1.02743940e+01, 4.25360730e+00, -2.02111574e+00, 4.99512893e+00, -4.89951797e+00, 2.93259999e+00, 3.14718356e+00, 1.27127831e-02, -5.89109961e+00, -3.95595294e+00, 7.20764616e+00, -1.13762985e+01, -2.64993320e+00, 4.63740279e+00, -2.61164777e+00, -4.92404586e+00, -5.32221786e-01, -7.24192440e+00, -2.84180113e+00, -5.93344391e-01, -9.75138109e+00, 1.48560255e-01, -4.42832119e-01, -1.52289735e+00, 6.52718424e+00, -4.55815233e+00, 8.03345649e+00, -1.25949421e+00, 4.09944512e+00, -2.85912239e+00, -3.12320344e-01, -1.25621514e+00, 2.68736028e+00, -2.19802764e+00, 4.40315543e+00, 9.20349072e+00, -3.84608588e+00, -2.21098734e+00, 7.98896705e+00, -2.56405874e+00, -7.55191977e+00, -3.66256916e+00, -1.93900442e+00, 1.22065841e+00, 1.71740829e+00, 8.21454272e+00, 1.92083009e+00, -4.55360166e+00, 2.24412248e+00, -2.13959890e+00, 9.43831952e+00, 9.61207333e+00, -3.95567894e+00, -4.81381220e+00, -4.39614559e+00, -1.56718278e+00, -5.36653851e+00, 1.92902328e+00, -5.46437773e+00, -8.28278477e-01, -2.15915746e+00, -5.48922909e+00, 1.13661423e+00, 2.09137433e+00, -2.54786877e+00, -2.65724057e+00, 2.05729726e+00, -1.61402241e-01, -2.83105628e+00, 5.37481879e+00, -7.79670411e+00, 1.23781801e+00, -1.05330598e+01, -4.50752694e+00, -8.14796386e+00, -4.70073053e+00, 3.80565742e+00, 5.50567267e+00, 4.16868852e-01, -2.35527277e+00, -8.36613464e+00, -7.13115096e-01, 1.43720177e+00, -6.10898476e+00, -8.81174187e-01, -7.00294828e+00, -6.25292261e+00, -3.70662453e-01, 5.97140466e-01, 1.69662795e+00, 6.36365353e+00, 1.95191457e+00, -4.14199908e-01, -9.02638518e+00, 5.15984968e+00, -4.09147662e+00, -5.23406237e+00, -6.09587492e+00, -4.65743036e+00, 4.33676745e+00, -9.91340056e+00, 2.83535062e+00, 4.70713637e+00, -6.33033245e+00, -2.19378021e+00, 5.86431705e+00, 3.46673670e+00, -2.43746040e+00, 1.68730344e+00, 3.60685353e+00, 2.88654746e+00, -3.15878724e-01, 1.62471781e+00, 3.35119982e+00, 4.63666452e-01, 7.87306500e-01, -9.24725008e-01, -3.38194013e+00, 4.52134311e+00, -2.26543848e-01, -3.44352266e+00, 1.72719800e+00, 2.39885986e+00, -6.50678946e+00, -7.56880421e+00, -5.30732847e+00, -5.17096376e+00, -1.94421141e+00, -6.93298928e-01, -1.52396072e+00, -5.60458995e-02, 4.94155671e+00, -1.07948739e+00, -1.69029823e+00, 1.84554371e+00, 6.38458750e-01, -8.40430815e+00, -3.73774329e+00, 3.07278534e+00, 2.05623948e-01, -5.27314592e-01, 6.15851493e-01, -6.35782747e+00, 1.05558401e+00, -4.61172554e-01, 2.74970370e+00, -1.11008096e+00, -1.06719737e+00, -1.25335382e+00, -1.05161094e+01, -2.79222678e+00, -2.61743694e+00, 1.06859928e+01, 4.17430844e+00, -8.61940068e+00, 6.62649786e+00, -3.77297366e+00, -4.79928278e+00, 2.11312406e+00, 3.82841892e+00, 1.65150718e+01, 1.28827753e+00, 7.69045233e+00, 4.32595573e+00, 5.67468866e+00, -4.26950865e+00, 1.42134184e+01, -3.02203250e+00, 7.88690400e+00, 4.70002602e+00, 1.22227407e+01, -9.17601028e+00, -4.89870159e+00, 3.69229719e+00, -7.05443646e+00, 3.16827030e+00, 5.92829164e+00, 6.32853189e-01, -4.97531523e+00, 5.35110233e+00, 4.84398026e+00, -1.30950889e+00, 3.10966847e+00, 5.19944573e+00, -4.09236633e+00, -1.51532902e+00, 2.07513611e+00, 1.17597066e+00, -1.32898956e+00, -6.41614907e+00, -7.89735147e+00, 1.50822033e+00, 4.09212007e+00, 2.47951153e+00, -1.63800121e+00, -1.86176988e+00, -2.52168837e+00, -6.64242059e+00, -1.02397782e+01, -4.54425137e+00, 2.62436848e+00, 1.22193671e+00, -9.38962033e+00, -1.10203324e+00, -7.05103435e+00, -4.46289833e+00, 5.25312798e+00, -3.56515665e+00, 1.26120037e+00, 4.75885172e+00, -2.50167965e+00, 3.80542944e+00, 3.01167210e+00, 2.70345411e+00, 5.73690638e+00, -4.54935671e+00, -6.43236445e+00, 7.41097905e+00, 1.35900623e+00, 5.04012320e-01, -3.15086965e-01, 1.64858689e+00, -2.06980294e+00, -8.59024295e+00, -4.97349172e-01, -1.80382620e+00, 1.17371261e+01, 2.15827083e+00, 2.22745215e+00, -1.20855349e+00, -2.44807351e+00, -9.87085690e+00, -1.34467216e+00, -5.81848641e+00, 3.96936369e+00, 6.03001020e+00, 2.48189062e+00, -3.39454396e+00, 8.02506367e+00, -1.08853432e+01, -5.95905160e+00, 5.62999973e+00, -1.33903618e+00, 2.43456328e-01, 7.46115585e+00, 7.25904503e+00, 5.91408176e+00, -8.78687142e+00, -6.51018263e+00, -4.41948337e+00, -2.48947673e+00, -1.64088207e+00, 6.20255356e+00, -9.17992329e+00, 3.82492982e+00, 2.63842026e+00, -4.17331044e+00, 1.75196415e+00, -5.04693689e+00, 1.35289027e+00, 7.57024645e+00, 7.42244523e-01, -8.30060584e+00, -4.41346052e+00, 2.16165760e+00, -5.26439002e+00, -6.91396918e+00, 5.37676522e-01, 4.51113679e+00, -8.02857560e-01, -2.33763106e+00, -3.14059882e+00, -3.39669533e+00, 9.30930118e-01, -5.37274114e+00, 1.77406778e+00, 4.51427847e+00, -4.11358649e+00, 3.99759043e+00, 1.53790689e+00, 3.08286549e+00, 1.96950901e+00, -2.33147685e+00, 8.35301298e+00, 3.64283230e+00, 3.93723672e+00, -1.55395905e+00, -4.08348595e+00, -1.12488433e+00, -4.94433054e+00, 1.09220685e+00, -2.96159007e+00, -3.82612120e+00, 5.71952703e+00, 2.96089980e+00, 6.57383263e+00, 3.43877847e+00, 3.23617754e+00, -3.26402642e-01, -1.83070903e+00, 2.65271223e+00, 4.20683702e+00, 6.46751652e+00, 3.60872783e-01, -8.27036082e+00, -9.63407531e+00, 3.26333096e-01, 2.43822818e+00, -7.43272899e+00, -2.69406922e+00, 3.71935806e+00, -5.18549573e+00, -4.51118195e+00, -2.09199225e+00, 5.78108487e+00, -5.89811771e+00, 3.49169444e+00, -5.05185406e+00, -1.20226878e+00, 6.53307013e+00, 4.81768620e+00, 4.17257863e+00, -3.86026668e+00, 5.58392228e+00, -4.41510369e+00, 5.57459816e-01, 2.72842246e+00, -7.78855364e+00, 5.68483356e+00, 3.29852882e+00, 9.55117660e+00, -6.27973606e+00, 1.78814651e+00, 1.39547434e+00, 7.55131835e-01, 3.65522852e-01, 4.38405961e+00, -1.68567975e+00, -8.80176186e+00, -5.19047572e+00, 4.07829465e+00, 4.29162615e+00, -1.20809055e+00, -2.34765354e+00, -6.46386071e+00, -6.03662219e-01, -4.66821357e+00, -1.43937731e-01, 1.09606189e+00, 6.30828939e+00, -1.30803069e+00, -3.03474141e+00, 3.35965967e-01, -6.33265044e+00, 3.28254564e+00, 1.37978799e+00, -2.48652438e+00, -1.84211152e+00, -8.65571630e+00, -2.90481357e+00, -5.34261854e+00, 1.34312306e+00, -2.08973719e+00, 6.18252186e+00, 4.09215122e+00, -1.48227522e+00, -9.72847583e+00, -1.06198133e+00, 8.99839205e-01, -9.42087378e-01, -1.78560508e+00, -4.11869577e+00, -1.94607602e+00, -6.34726065e+00, 5.24379982e+00, -2.23697781e+00, 3.40115386e-01, 3.73908939e+00, 4.53282894e+00, -2.28989784e+00, -6.71804450e+00, -4.63620303e-01, 1.13621798e+01, -6.37943935e+00, -2.25709706e+00, 1.65004215e+00, 4.45505702e-01, -4.29752873e+00, 3.41480439e+00, -4.48702607e+00, 5.83413204e+00, 9.06419203e+00, -2.52112835e+00, 5.00974231e+00, -7.78393797e-01, 3.36146623e+00, 4.83698962e+00, -1.05169071e+00, 3.66616293e+00, -1.67252497e+00, -3.62323547e+00, 7.80121165e+00, -3.08831078e+00, -5.43366444e+00, -3.69190337e+00, 3.04940823e+00, 4.94988152e-01, -1.56235549e+00, -1.31380093e+01, -2.68698571e-01, -7.08968310e+00, 7.25984399e+00, -7.94048679e+00, -9.01143028e+00, 2.15010800e+00, -1.39225759e+01, -1.92367776e+00, -1.05580966e+01, -5.65026775e-01, 5.79205213e+00, -1.55147165e+00, -6.97345557e+00, 3.81667571e+00, -1.17125097e+00, -8.23705763e+00, 2.03794735e+00, -1.28032492e+00, -1.10053320e+01, 6.43417469e+00, -3.93257893e+00, 5.37706754e-01, 2.38022617e+00, 6.33201935e-01, 6.87942708e+00, -4.85099290e+00, 3.03039778e+00, 4.28465279e+00, -3.74243269e+00, 5.41243454e+00, 4.19264965e+00, 3.94209299e+00, 4.19019105e-01, 9.03729243e-01, -8.47680165e-01, 5.44887897e+00, -6.64587581e+00, 2.24505549e+00, -1.62886915e+00, 6.52696615e+00, 4.65538080e+00, 2.16153384e+00, 8.01812241e+00, 8.87701558e+00, -8.82977615e-01, 7.44374430e+00, -7.26633089e-01, 5.07979280e+00, -7.77941048e+00, 5.93222518e+00, -1.22668195e+01, 1.15109144e+00, -1.05951734e+01, 1.09823498e+00, 8.38289171e+00, -5.66352195e+00, 9.02288722e+00, 6.64762146e+00, -3.59210701e+00, 5.01362305e+00, -2.18552082e+00, 8.10170049e+00, 3.35098197e+00, -3.67603554e+00, 9.50009626e-01, -2.69213521e+00, 5.97375478e+00, 9.19377263e+00, 4.00684514e+00, -5.14242881e+00, -5.04404481e+00, 6.80877591e+00, 2.08913991e+00, -3.28593673e+00, 6.94325245e+00, -2.76457961e+00, -1.44369907e-01, -3.11771191e+00, 2.59296320e+00, -1.89779512e+00, -3.00382367e+00, -1.49473069e+00, -6.88520684e+00, 5.65785904e+00, -4.92529741e-01, 4.68942995e+00, -1.52910780e+01, -7.20569740e+00]]) - theta(chain, draw, school)float64-9.888 -1.89 2.237 ... 13.34 -21.99
array([[[ -9.88782452, -1.89045271, 2.23745711, ..., 3.05783633, 4.50876933, -12.02277258], [ 12.52324972, -0.10257462, 17.90235743, ..., -6.03914366, 5.39459901, 7.07427163], [ 3.22949408, 4.20144679, 3.28459753, ..., 3.70696941, 3.39716626, 4.14062422], ..., [ 2.88020715, 6.85078948, 10.60362223, ..., -5.47622351, 2.56413578, -9.94645561], [ 10.70735593, -35.010802 , -49.8329035 , ..., -20.31738401, -42.62663544, -8.45896299], [-55.3145697 , -16.82455975, -1.67088179, ..., 18.1635401 , 13.33866153, -21.98739496]]]) - theta_tilde(chain, draw, school)float64-1.76 -0.3073 ... 1.023 -0.736
array([[[-1.75960441, -0.30734889, 0.44224485, ..., 0.59121882, 0.85469606, -2.14729303], [ 1.10830795, -0.43425049, 1.76549973, ..., -1.15955004, 0.23736598, 0.44257976], [-1.0836513 , 1.31291559, -0.94778141, ..., 0.09367097, -0.67021802, 1.16294391], ..., [-0.20016305, 0.23912163, 0.65431562, ..., -1.12467528, -0.23513155, -1.61923862], [ 1.06931022, -0.81106818, -1.42069815, ..., -0.20673093, -1.12430583, 0.28100348], [-2.39544427, -0.47894385, 0.27559038, ..., 1.26318892, 1.02294784, -0.73601253]]])
- created_at :
- 2020-06-10T18:19:23.480401
- arviz_version :
- 0.8.3
- inference_library :
- pymc3
- inference_library_version :
- 3.8
xarray.Dataset -
- chain: 1
- draw: 500
- obs_dim_0: 8
- chain(chain)int640
array([0])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- obs_dim_0(obs_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- obs(chain, draw, obs_dim_0)float64-25.31 -0.8959 ... 3.422 -20.64
array([[[-25.31078195, -0.89588955, 22.6413552 , ..., 24.13451408, 16.67999654, -30.23034528], [ 4.86375172, 11.18885402, 22.53588377, ..., -13.80804677, -5.73731196, -4.12169577], [ -1.79113884, 2.53093031, 15.8191744 , ..., 7.61230557, -4.66752285, 23.29882677], ..., [ 28.47079674, -2.79239653, 14.3904422 , ..., -12.63998944, 20.70652864, -3.05241501], [ 46.65347282, -46.95008753, -41.11688486, ..., -19.96545045, -34.31368027, -7.26684645], [-45.06736361, -5.81423829, 1.34788684, ..., 19.91178202, 3.42152391, -20.64388589]]])
- created_at :
- 2020-06-10T18:19:23.484023
- arviz_version :
- 0.8.3
- inference_library :
- pymc3
- inference_library_version :
- 3.8
xarray.Dataset -
- obs_dim_0: 8
- obs_dim_0(obs_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- obs(obs_dim_0)float6428.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
array([28., 8., -3., 7., -1., 1., 18., 12.])
- created_at :
- 2020-06-10T18:19:23.485040
- arviz_version :
- 0.8.3
- inference_library :
- pymc3
- inference_library_version :
- 3.8
xarray.Dataset
From PyStan#
import pystan
schools_code = """
data {
int<lower=0> J;
real y[J];
real<lower=0> sigma[J];
}
parameters {
real mu;
real<lower=0> tau;
real theta_tilde[J];
}
transformed parameters {
real theta[J];
for (j in 1:J)
theta[j] = mu + tau * theta_tilde[j];
}
model {
mu ~ normal(0, 5);
tau ~ cauchy(0, 5);
theta_tilde ~ normal(0, 1);
y ~ normal(theta, sigma);
}
generated quantities {
vector[J] log_lik;
vector[J] y_hat;
for (j in 1:J) {
log_lik[j] = normal_lpdf(y[j] | theta[j], sigma[j]);
y_hat[j] = normal_rng(theta[j], sigma[j]);
}
}
"""
eight_school_data = {
"J": 8,
"y": np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
"sigma": np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}
stan_model = pystan.StanModel(model_code=schools_code)
fit = stan_model.sampling(data=eight_school_data, control={"adapt_delta": 0.9})
stan_data = az.from_pystan(
posterior=fit,
posterior_predictive="y_hat",
observed_data=["y"],
log_likelihood={"y": "log_lik"},
coords={"school": np.arange(eight_school_data["J"])},
dims={
"theta": ["school"],
"y": ["school"],
"log_lik": ["school"],
"y_hat": ["school"],
"theta_tilde": ["school"],
},
)
stan_data
INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_9d743830ec4a29fb58eb4660d4b9417f NOW.
arviz.InferenceData
-
- chain: 4
- draw: 1000
- school: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- mu(chain, draw)float648.801 4.356 5.887 ... 5.811 6.163
array([[ 8.80085977, 4.35621311, 5.88747459, ..., 7.56510323, 3.75692215, 4.24241574], [ 3.88430209, 1.25503637, 8.12161043, ..., 0.77999781, 8.88447765, 2.55867698], [ 3.69774758, 5.56187344, 7.18886091, ..., 2.35104484, 7.36896537, 7.30112058], [ 4.56370867, -1.9814485 , 8.93919361, ..., -0.45859494, 5.81131473, 6.16295074]]) - tau(chain, draw)float641.079 2.76 3.322 ... 3.54 0.5714
array([[1.07873807, 2.75983947, 3.32167212, ..., 4.65835454, 5.67923053, 1.15391559], [0.68602682, 1.9898873 , 1.71348775, ..., 6.32124664, 6.49443423, 7.88054963], [6.09793056, 2.08870225, 3.01847687, ..., 0.19977493, 2.0959731 , 2.08265721], [4.80268382, 8.63940768, 7.49279334, ..., 4.94150802, 3.54035862, 0.57140337]]) - theta_tilde(chain, draw, school)float640.7707 3.4 ... 0.9492 -0.1983
array([[[ 0.77065058, 3.3999605 , 0.896277 , ..., 0.85548385, 0.56312311, -0.02336804], [-0.23856364, 1.88839417, 0.11615247, ..., 0.20239506, -0.65088377, -0.59082016], [-0.44993014, 0.3660292 , -0.85342255, ..., -0.05060912, 1.89747793, -0.29915642], ..., [-1.53738528, 0.34600749, 0.66613118, ..., -0.31358001, -0.13278535, -0.13050197], [ 0.10392075, 1.2781256 , 0.17946725, ..., 0.73474013, 1.59901667, -0.22310606], [ 0.40039 , -0.36919646, -0.41812356, ..., -0.82578604, -0.95433683, -0.70055211]], [[ 0.28550956, -1.75918566, 1.08585615, ..., -0.17260057, -0.31717858, -0.15889076], [ 1.12616284, 2.12250411, -1.22377048, ..., -0.50452776, 1.09665063, 0.62770833], [-0.82113198, 0.60950151, 0.12629451, ..., 1.18250354, 1.03982808, 0.4350411 ], ..., [-0.14425363, 0.18750333, 2.30758557, ..., 0.19605514, 0.04511098, 1.31371653], [ 0.70622565, 0.07230275, -1.80811131, ..., -0.30374127, 0.73420799, -0.89225914], [ 1.13667967, -0.62298503, 0.70894404, ..., 0.93673866, 0.83697246, 1.22364797]], [[ 1.71586288, 0.2645208 , 1.38154111, ..., 1.34611706, 0.67924247, 0.6426671 ], [-0.63375751, -0.25986361, -1.85613258, ..., -1.1958948 , 0.65731631, -0.33917202], [-0.25273764, -0.31382369, -0.34433588, ..., 1.56951567, -0.42550589, 0.13231013], ..., [-1.3109662 , 1.0167199 , 0.29096078, ..., 1.2091756 , -0.35967787, 0.28249554], [ 2.40744126, -0.73846363, -0.98632421, ..., -0.79229741, 2.01420262, 1.00171644], [ 2.25146098, 0.08915173, -0.37030215, ..., -0.75901238, 0.46540678, 0.5400871 ]], [[ 0.43838309, 0.06907241, 0.44621424, ..., -0.26691355, 1.45697414, 0.66782308], [ 1.38057301, 0.71432475, -0.92534916, ..., 0.23614769, 0.48711266, 1.27270678], [ 0.38952426, -0.18324781, 0.28926883, ..., -0.11207212, 1.06242534, -1.2021079 ], ..., [-0.57243771, 1.20324745, -2.03671137, ..., -0.31232212, 0.68695275, 0.59062609], [ 0.83778081, -0.58047982, 1.78149714, ..., -0.62379571, 1.44340525, -0.0475484 ], [ 1.5197586 , -0.90722855, 1.74266398, ..., -1.08440477, 0.94915432, -0.19832845]]]) - theta(chain, draw, school)float649.632 12.47 9.768 ... 6.705 6.05
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- created_at :
- 2020-06-10T18:20:55.257774
- arviz_version :
- 0.8.3
- inference_library :
- pystan
- inference_library_version :
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xarray.Dataset -
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- school: 8
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array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
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array([[[ 16.81606234, 11.42314561, 17.62390159, ..., 9.79825611, 17.93449592, 20.74301303], [ -2.87371409, 3.26558897, 23.16168449, ..., 5.60727737, 9.07428464, -0.29335618], [ 29.69759628, 27.78756772, 15.23144444, ..., 11.23869389, 19.64442795, 16.32327954], ..., [ 0.22658945, 14.21873048, 41.77431262, ..., 27.79849965, 8.97700113, -10.97758778], [-25.71679369, 7.54290441, 22.1185727 , ..., -1.9379867 , 24.08319264, 11.10296328], [ 29.8534142 , 19.97743567, -2.22962611, ..., -1.57819509, 2.04335776, -4.69118197]], [[ 19.34365445, -4.00444521, -16.23523472, ..., 13.94222586, 8.86119588, -2.0744115 ], [ 4.70865213, 23.04754692, 21.70862296, ..., 0.26881933, 8.3109079 , -24.0917072 ], [ 8.61267321, 5.41437255, -12.84437828, ..., 30.43257723, 1.84297616, 8.86262284], ..., [ 3.59843013, 6.09765236, 25.76124843, ..., -10.2115549 , 25.59755363, 22.36298176], [ -5.29619527, -2.95926353, -29.68418582, ..., -15.42170733, 16.63492822, 24.59769265], [ 19.98940386, 3.80606888, 42.7843385 , ..., 34.96627185, 14.25740899, -1.3367825 ]], [[ 2.14679791, 8.14117178, 21.25441028, ..., 11.52465386, 5.80097177, -10.65373129], [ -8.44034177, 7.0589406 , -18.60138882, ..., 8.82950324, 8.08712236, -6.39852626], [ 32.71773469, 8.39087771, 15.51443141, ..., 14.32087597, -1.38048653, 1.96559162], ..., [ -1.62917408, 1.07111862, 8.02957128, ..., 8.58210981, -12.75033047, 9.07205784], [ 6.81102221, 1.40270907, 47.46417874, ..., -1.49189963, 23.77214897, -32.30678056], [ -3.58688927, -9.19334261, 3.48471769, ..., 22.20224365, 22.04574534, 9.43498321]], [[ 10.88989427, 9.67031316, -19.15138861, ..., 3.89717316, 5.08967642, -3.21365656], [ 16.35385465, 23.58801269, -21.75232011, ..., 1.94421295, 0.10598705, -6.81390168], [ 16.65187106, 5.47807306, 16.66239838, ..., -10.24095255, 7.67808457, 23.32038006], ..., [ -5.39983067, 2.9583006 , 8.89615588, ..., -13.19594644, 8.22006103, -10.21126023], [ 11.9101745 , 6.81738971, 33.3703771 , ..., -3.27619529, 24.69391859, -16.79777889], [ 9.5301372 , 21.03087493, 15.88465758, ..., 1.06856218, -11.8929359 , 1.28188204]]])
- created_at :
- 2020-06-10T18:20:55.276063
- arviz_version :
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- inference_library :
- pystan
- inference_library_version :
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xarray.Dataset -
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- draw: 1000
- school: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- y(chain, draw, school)float64-4.377 -3.321 ... -3.859 -3.864
array([[[-4.37671417, -3.32136228, -4.00991469, ..., -3.63130897, -3.59060827, -3.82535415], [-4.93942464, -3.23381483, -3.80663053, ..., -3.38016268, -4.4135104 , -3.94204744], [-4.86541676, -3.22554395, -3.76307997, ..., -3.40886865, -3.3902882 , -3.88723997], ..., [-5.31936954, -3.22844943, -4.05640831, ..., -3.42449599, -3.8324183 , -3.84855419], [-4.8702312 , -3.26699562, -3.80963006, ..., -3.51526552, -3.35474935, -3.94888271], [-4.83295204, -3.30903641, -3.7807787 , ..., -3.33849472, -4.32544456, -3.92254441]], [[-4.89845162, -3.36317113, -3.80520915, ..., -3.34844607, -4.24873977, -3.91370182], [-4.9613161 , -3.25331141, -3.69799587, ..., -3.31915148, -4.28189242, -3.94846464], [-4.63380605, -3.22832122, -3.94260259, ..., -3.6626294 , -3.54930289, -3.82445749], ..., [-5.38565946, -3.4036145 , -4.35039426, ..., -3.32112717, -4.65546843, -3.82242938], [-4.09608083, -3.23069079, -3.69156654, ..., -3.46125517, -3.31601684, -3.93182941], [-4.23079124, -3.75721763, -3.93415067, ..., -3.64714778, -3.61273975, -3.80937307]], [[-4.05258656, -3.25768323, -4.13817498, ..., -3.80834974, -3.73767998, -3.83896065], [-4.88171287, -3.26595258, -3.7343962 , ..., -3.3344376 , -3.83371561, -3.88812705], [-4.66129633, -3.23698363, -3.85502957, ..., -3.81016597, -3.9530315 , -3.83934681], ..., [-5.11892722, -3.36980949, -3.74867401, ..., -3.3273148 , -4.45724293, -3.95131096], [-4.16675634, -3.24526023, -3.82613174, ..., -3.4084387 , -3.42692055, -3.81919966], [-4.19657885, -3.22284053, -3.86890841, ..., -3.40890727, -3.69484888, -3.82902314]], [[-4.63811378, -3.26971504, -3.87555205, ..., -3.33834887, -3.42882113, -3.83690906], [-4.35132448, -3.29410816, -3.786573 , ..., -3.32049494, -4.46547446, -3.82307 ], [-4.20603324, -3.22246473, -4.08019302, ..., -3.52510793, -3.22757663, -4.0340564 ], ..., [-5.80231133, -3.25309289, -3.802066 , ..., -3.35407193, -4.35614598, -3.94976063], [-4.44812188, -3.31157248, -4.13794842, ..., -3.34482905, -3.47205036, -3.8716741 ], [-4.6040653 , -3.24926418, -3.89308875, ..., -3.40213025, -3.85937479, -3.86395066]]])
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- 2020-06-10T18:20:55.272917
- arviz_version :
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- inference_library :
- pystan
- inference_library_version :
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xarray.Dataset -
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- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
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array([[0.9638465 , 1. , 0.9984371 , ..., 0.98147504, 0.97345614, 0.98142691], [0.95030784, 0.99451523, 0.99024004, ..., 0.89369662, 0.9823775 , 0.9890991 ], [0.97217182, 0.99864817, 0.94355364, ..., 0.82019929, 0.97292829, 1. ], [0.95704787, 0.97648727, 0.99909458, ..., 0.998659 , 0.9815929 , 0.6229969 ]]) - stepsize(chain, draw)float640.2764 0.2764 ... 0.2731 0.2731
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- 2020-06-10T18:20:55.267462
- arviz_version :
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- inference_library :
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- inference_library_version :
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xarray.Dataset -
- school: 8
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- y(school)float6428.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
array([28., 8., -3., 7., -1., 1., 18., 12.])
- created_at :
- 2020-06-10T18:20:55.238703
- arviz_version :
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- inference_library :
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- inference_library_version :
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xarray.Dataset
From Pyro#
import pyro
import pyro.distributions as dist
import torch
from pyro.infer import MCMC, NUTS, Predictive
pyro.enable_validation(True)
pyro.set_rng_seed(0)
draws = 500
chains = 2
eight_school_data = {
"J": 8,
"y": torch.tensor([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
"sigma": torch.tensor([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}
def model(J, sigma, y=None):
mu = pyro.sample("mu", dist.Normal(0, 5))
tau = pyro.sample("tau", dist.HalfCauchy(5))
with pyro.plate("J", J):
theta_tilde = pyro.sample("theta_tilde", dist.Normal(0, 1))
theta = mu + tau * theta_tilde
return pyro.sample("obs", dist.Normal(theta, sigma), obs=y)
nuts_kernel = NUTS(model, jit_compile=True, ignore_jit_warnings=True)
mcmc = MCMC(
nuts_kernel,
num_samples=draws,
warmup_steps=draws,
num_chains=chains,
disable_progbar=True,
)
mcmc.run(**eight_school_data)
posterior_samples = mcmc.get_samples()
posterior_predictive = Predictive(model, posterior_samples)(
eight_school_data["J"], eight_school_data["sigma"]
)
prior = Predictive(model, num_samples=500)(eight_school_data["J"], eight_school_data["sigma"])
pyro_data = az.from_pyro(
mcmc,
prior=prior,
posterior_predictive=posterior_predictive,
coords={"school": np.arange(eight_school_data["J"])},
dims={"theta": ["school"]},
)
pyro_data
arviz.InferenceData
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- theta_tilde_dim_0(theta_tilde_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
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False, False]])
- created_at :
- 2020-06-10T18:21:33.823431
- arviz_version :
- 0.8.3
- inference_library :
- pyro
- inference_library_version :
- 1.1.0
xarray.Dataset -
- chain: 1
- draw: 500
- theta_tilde_dim_0: 8
- chain(chain)int640
array([0])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- theta_tilde_dim_0(theta_tilde_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- mu(chain, draw)float321.8310521 7.369206 ... -0.07544144
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5.04449546e-01, -4.07291603e+00, 5.41869581e-01, 4.77750123e-01, -1.77831125e+00, -2.42855740e+00, 5.80212212e+00, 2.78317261e+00, -8.38098049e-01, -1.13215065e+01, 1.04781361e+01, -1.98796690e-02, -8.12773609e+00, 3.65236521e+00, 4.78217268e+00, 5.68206692e+00, 1.17952776e+00, 3.48964882e+00, -7.54414424e-02]], dtype=float32) - tau(chain, draw)float32233.58215 994.4366 ... 27.182827
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5.61358929e+00, 3.10696411e+00, 4.68212414e+00, 1.69084892e-01, 1.76831853e+00, 3.58425570e+00, 1.66552944e+01, 6.66814518e+00, 2.22552757e+01, 2.18585186e+01, 4.84984636e+00, 2.61942062e+01, 6.71889210e+00, 3.07793331e+01, 7.65414143e+00, 6.03538275e+00, 1.08152752e+01, 1.53035221e+01, 1.82176857e+01, 5.10415316e+00, 2.33483219e+01, 9.00594652e-01, 1.42888498e+01, 1.11383905e+01, 2.80002928e+00, 1.97191668e+00, 9.47514629e+00, 1.59550037e+01, 1.24129760e+00, 3.00389910e+00, 7.33918142e+00, 2.03434730e+00, 1.40971959e+00, 2.60195613e+00, 5.19892263e+00, 4.85553789e+00, 4.01490164e+00, 5.50108337e+00, 1.95370235e+01, 3.57205272e+00, 3.22123230e-01, 3.18224182e+01, 5.46338511e+00, 3.92666698e+00, 1.19204788e+01, 3.34672689e+00, 1.28777447e+01, 7.79884398e-01, 6.61139846e-01, 1.53919148e+00, 2.90023565e+00, 2.00248814e+00, 5.53505516e+00, 6.83246183e+00, 4.38924694e+00, 8.34967804e+00, 5.10579491e+00, 1.58182859e+01, 1.78390675e+01, 5.87143898e+00, 8.79881096e+00, 2.89170361e+00, 1.12620888e+01, 1.57768428e+00, 2.32329521e+01, 5.88128757e+00, 3.41677904e+00, 7.61884537e+01, 5.26621222e-01, 2.92264342e+00, 1.46880138e+00, 1.58016682e+00, 3.81652985e+01, 2.46611953e+00, 4.79778290e+00, 1.88320708e+00, 1.90092564e+00, 7.12588310e-01, 9.07944775e+00, 7.06309557e+00, 2.61442447e+00, 1.78211820e+00, 3.95346403e+00, 2.53750610e+00, 8.14840674e-01, 2.00210166e+00, 2.62024078e+01, 5.12925744e-01, 6.95824099e+00, 2.35959935e+00, 1.71262836e+00, 5.10069351e+01, 3.19263029e+00, 1.15136087e-01, 1.57397881e+01, 9.10933018e-01, 2.54393845e+01, 1.22716546e+00, 6.51532364e+00, 2.91248016e+01, 6.27013743e-02, 7.57493925e+00, 1.00060427e+00, 1.94976521e+00, 1.05164957e+01, 1.20389929e+01, 7.51705074e+00, 1.34320679e+02, 4.60176182e+00, 5.06012535e+00, 3.81312418e+00, 3.13340473e+00, 1.12241850e+01, 6.68661475e-01, 9.63961029e+00, 1.80393448e+01, 1.27726388e+00, 8.14500600e-02, 1.34037886e+01, 4.43923569e+00, 9.86487961e+00, 4.39872217e+00, 4.16832018e+00, 1.09472620e+00, 2.91746311e+01, 1.49736700e+01, 9.17174101e-01, 1.25601950e+01, 5.54890394e-01, 5.42279053e+00, 1.89136982e+00, 3.33140159e+00, 5.18533659e+00, 8.20474243e+00, 3.74159360e+00, 6.61919546e+00, 9.13305569e+00, 1.16696537e+00, 6.32780876e+01, 4.78538799e+00, 9.15983295e+00, 1.19233716e+00, 4.15419197e+00, 3.01625061e+00, 1.33225393e+01, 8.89955699e-01, 3.94315934e+00, 1.25022098e-01, 1.56112921e+00, 2.40924430e+00, 5.45164061e+00, 3.19068031e+01, 2.74245787e+00, 5.39334259e+01, 2.68976002e+01, 3.05201454e+01, 1.01681805e+00, 3.24505115e+00, 3.51270258e-01, 3.39455485e+00, 1.03448999e+00, 6.52295971e+00, 8.54770851e+00, 3.17444348e+00, 1.41029816e+01, 8.06216145e+00, 4.02719927e+00, 8.40551949e+00, 7.55664349e+00, 5.41498232e+00, 2.03295345e+01, 1.33403766e+00, 3.10369968e+00, 9.22239971e+00, 1.33640230e+00, 3.04194498e+00, 1.49802998e-01, 7.67462845e+01, 1.00229049e+00, 9.41823196e+00, 2.40813103e+01, 5.96192837e-01, 1.24422464e+01, 6.29803009e+01, 9.61070156e+00, 3.14717960e+00, 3.35008736e+01, 1.62203751e+02, 4.78771782e+00, 9.57639408e+00, 2.18938899e+00, 6.93462944e+00, 1.47582645e+01, 1.59039507e+01, 3.55825844e+01, 1.57970297e+00, 6.86061192e+00, 1.46212173e+00, 1.21917558e+00, 5.43149567e+00, 1.26152265e+00, 2.14529729e+00, 3.60484076e+00, 3.20548248e+00, 8.68775845e+00, 4.69007778e+00, 6.97661924e+00, 2.86727786e+00, 6.55940008e+00, 3.04591227e+00, 6.40091038e+00, 7.69913483e+01, 1.76605213e+00, 1.69695389e+00, 1.49314392e+02, 1.74520826e+00, 2.10937786e+00, 1.85648233e-01, 7.94631481e+00, 4.20290565e+00, 1.58578515e+00, 2.86422396e+00, 2.78503656e+00, 1.90926838e+01, 2.03964019e+00, 2.16318626e+01, 9.85763626e+01, 8.25113773e+00, 7.35772908e-01, 4.36113882e+00, 1.37380188e+02, 4.84867334e+00, 1.83547437e+00, 7.29557495e+01, 1.18845024e+01, 6.21232643e+01, 8.89026070e+00, 8.67310905e+00, 9.10755172e-02, 4.66671085e+00, 7.80379639e+01, 4.44808617e+01, 1.78106499e+01, 1.36136341e+01, 1.11453638e+01, 6.47962141e+00, 3.14819312e+00, 3.80757451e+00, 6.99266315e-01, 5.32106857e+01, 2.26561832e+00, 1.17912173e+00, 1.61539803e+01, 1.64006214e+01, 6.56036139e+00, 2.02290916e+01, 1.35110483e+01, 1.61717999e+00, 4.25558233e+00, 1.24771166e+00, 8.42467189e-01, 3.71366239e+00, 1.12391367e+01, 7.85699415e+00, 1.17313776e+01, 2.07943416e+00, 1.07938728e+01, 1.71249676e+01, 4.25358963e+00, 3.37078810e+00, 2.89949465e+00, 6.30591965e+01, 8.41671944e-01, 2.24199390e+00, 2.29184461e+00, 1.12583256e+01, 1.59082878e+00, 1.61483455e+00, 8.51412296e+00, 2.94279718e+00, 1.55814886e+00, 1.94127309e+00, 3.83025789e+00, 7.02682590e+00, 2.06390142e+00, 1.34827960e+00, 2.81168457e+02, 6.22805953e-01, 8.24851453e-01, 2.11877942e-01, 3.92178574e+01, 9.66570312e+02, 3.94462729e+00, 7.99840927e-01, 1.70189846e+00, 1.00781441e+01, 2.87433743e-01, 1.20128322e+00, 2.29061928e+01, 3.59614491e+00, 4.05278158e+00, 1.58789263e+01, 1.11763752e+00, 1.74107971e+01, 1.57513487e+00, 1.86496060e-02, 7.02734985e+01, 3.25848503e+01, 3.71071362e+00, 1.89383469e+01, 4.06730556e+00, 1.25093555e+00, 1.31658208e+00, 6.87853718e+00, 4.67559671e+00, 2.59621410e+01, 2.93781424e+00, 8.28132534e+00, 2.93957710e+00, 2.71064987e+01, 1.96016669e-01, 7.85356760e-01, 3.60274577e+00, 2.52142549e+00, 6.00418663e+00, 1.30085669e+01, 4.41197300e+00, 4.23312283e+00, 1.43678570e+00, 9.44298446e-01, 1.23984262e-01, 4.08745956e+01, 3.59652996e-01, 4.51054305e-01, 2.02281017e+01, 5.19320641e+01, 2.71144605e+00, 2.10441933e+01, 2.76381893e+01, 2.75218344e+00, 1.07174101e+01, 1.65728331e+00, 1.40117636e+01, 5.70923004e+01, 2.04354548e+00, 7.14082837e-01, 1.98984873e+00, 2.52286911e+01, 2.85708785e+00, 8.33650780e+00, 3.08708382e+00, 4.20598221e+00, 3.83560791e+01, 6.60561275e+00, 3.31780434e+00, 1.28404593e+00, 1.66767464e+01, 6.89008808e+00, 5.83668041e+00, 1.42359662e+00, 6.85395598e-02, 9.49191093e-01, 1.09593658e+01, 1.75060701e+00, 1.01909657e+01, 4.41580963e+00, 1.00245590e+01, 8.76809508e-02, 5.11244965e+00, 3.84632111e+00, 7.63232660e+00, 4.04119635e+00, 2.86264753e+00, 5.07223177e+00, 9.76756382e+00, 2.71828270e+01]], dtype=float32) - theta_tilde(chain, draw, theta_tilde_dim_0)float320.6022393 ... -0.31073767
array([[[ 0.6022393 , -0.39827886, 0.19862896, ..., -0.95424646, -1.1647658 , 0.3821102 ], [-1.497994 , 0.74775034, -0.78757095, ..., -1.6560527 , -1.613713 , -0.46137986], [-0.16146933, 0.2763805 , -0.8783446 , ..., 0.56389153, -0.01581344, -0.8957549 ], ..., [-1.1428025 , -1.1540538 , -1.0932158 , ..., 1.6082281 , -2.009276 , -0.5227252 ], [ 1.8399812 , 0.33280653, 0.45785332, ..., 1.834717 , 0.8924277 , 1.2369446 ], [-0.14975677, 0.8303282 , -0.00824529, ..., -1.6754906 , 0.26279444, -0.31073767]]], dtype=float32)
- created_at :
- 2020-06-10T18:21:33.976125
- arviz_version :
- 0.8.3
- inference_library :
- pyro
- inference_library_version :
- 1.1.0
xarray.Dataset -
- chain: 1
- draw: 500
- obs_dim_0: 8
- chain(chain)int640
array([0])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- obs_dim_0(obs_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- obs(chain, draw, obs_dim_0)float32152.4126 -104.43863 ... -19.538307
array([[[ 1.5241260e+02, -1.0443863e+02, 5.3149067e+01, ..., -2.1432968e+02, -2.7346640e+02, 9.8980553e+01], [-1.4595604e+03, 7.5740137e+02, -7.9331067e+02, ..., -1.6279233e+03, -1.6046724e+03, -4.5491840e+02], [-1.2688635e+01, -1.5242083e+01, 6.5625114e+00, ..., 7.7777863e-01, 1.3528487e+01, -4.4868240e+01], ..., [ 6.5915680e+00, -8.9369183e+00, -1.1899769e+01, ..., -1.4138508e-01, -2.4801119e+01, -1.1125523e+00], [ 1.1234647e+01, 9.1552639e+00, 1.3359819e+01, ..., 6.3331509e+00, -6.9926414e+00, 2.9034739e+01], [ 3.9082799e+00, 2.4938337e+01, 1.8535004e+01, ..., -4.8968292e+01, 1.1919480e+01, -1.9538307e+01]]], dtype=float32)
- created_at :
- 2020-06-10T18:21:34.025492
- arviz_version :
- 0.8.3
- inference_library :
- pyro
- inference_library_version :
- 1.1.0
xarray.Dataset -
- obs_dim_0: 8
- obs_dim_0(obs_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- obs(obs_dim_0)float3228.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
array([28., 8., -3., 7., -1., 1., 18., 12.], dtype=float32)
- created_at :
- 2020-06-10T18:21:34.070465
- arviz_version :
- 0.8.3
- inference_library :
- pyro
- inference_library_version :
- 1.1.0
xarray.Dataset
From emcee#
Please refer to Converting emcee objects to InferenceData for details.
From CmdStanPy#
from cmdstanpy import CmdStanModel
schools_code = """
data {
int<lower=0> J;
real y[J];
real<lower=0> sigma[J];
}
parameters {
real mu;
real<lower=0> tau;
real theta_tilde[J];
}
transformed parameters {
real theta[J];
for (j in 1:J)
theta[j] = mu + tau * theta_tilde[j];
}
model {
mu ~ normal(0, 5);
tau ~ cauchy(0, 5);
theta_tilde ~ normal(0, 1);
y ~ normal(theta, sigma);
}
generated quantities {
vector[J] log_lik;
vector[J] y_hat;
for (j in 1:J) {
log_lik[j] = normal_lpdf(y[j] | theta[j], sigma[j]);
y_hat[j] = normal_rng(theta[j], sigma[j]);
}
}
"""
with open("./eight_school.stan", "w") as f:
print(schools_code, file=f)
stan_file = "./eight_school.stan"
stan_model = CmdStanModel(stan_file=stan_file)
stan_model.compile()
eight_school_data = {
"J": 8,
"y": np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
"sigma": np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}
stan_fit = stan_model.sample(data=eight_school_data)
cmdstanpy_data = az.from_cmdstanpy(
posterior=stan_fit,
posterior_predictive="y_hat",
observed_data={"y": eight_school_data["y"]},
log_likelihood="log_lik",
coords={"school": np.arange(eight_school_data["J"])},
dims={
"theta": ["school"],
"y": ["school"],
"log_lik": ["school"],
"y_hat": ["school"],
"theta_tilde": ["school"],
},
)
cmdstanpy_data
INFO:cmdstanpy:compiling c++
INFO:cmdstanpy:compiled model file: /Users/percy/PycharmProjects/arviz/doc/notebooks/eight_school
INFO:cmdstanpy:found newer exe file, not recompiling
INFO:cmdstanpy:compiled model file: /Users/percy/PycharmProjects/arviz/doc/notebooks/eight_school
INFO:cmdstanpy:start chain 1
INFO:cmdstanpy:start chain 2
INFO:cmdstanpy:finish chain 2
INFO:cmdstanpy:start chain 3
INFO:cmdstanpy:finish chain 1
INFO:cmdstanpy:start chain 4
INFO:cmdstanpy:finish chain 3
INFO:cmdstanpy:finish chain 4
arviz.InferenceData
-
- chain: 4
- draw: 1000
- school: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- mu(chain, draw)float642.908 8.134 3.037 ... 2.672 10.06
array([[ 2.90813, 8.1337 , 3.03685, ..., 3.49247, 2.69144, 2.77848], [ 1.20098, 3.74153, 5.71236, ..., 5.38302, 1.55543, 6.85928], [ 4.5479 , 4.21596, 6.53758, ..., 1.8295 , 6.26736, -2.83281], [ 7.2998 , 7.03214, 1.5383 , ..., 3.01368, 2.67249, 10.056 ]]) - tau(chain, draw)float643.566 1.06 1.014 ... 0.5414 5.807
array([[ 3.56579 , 1.06035 , 1.0145 , ..., 0.295652 , 0.152276 , 1.27931 ], [ 3.75274 , 1.13823 , 1.8422 , ..., 8.23264 , 3.29958 , 9.06202 ], [ 0.0756374, 14.1684 , 2.65082 , ..., 1.91313 , 7.97043 , 4.03989 ], [ 0.0525536, 0.213029 , 2.08631 , ..., 0.51228 , 0.541425 , 5.80725 ]]) - theta_tilde(chain, draw, school)float641.911 0.3988 ... 1.757 0.5014
array([[[ 1.91055 , 0.398843 , -0.206331 , ..., -1.11405 , 1.85739 , -1.37968 ], [-1.1159 , -0.447728 , -0.505903 , ..., 0.962855 , -0.601752 , 0.89427 ], [ 1.60719 , -0.596497 , 0.151931 , ..., -1.28024 , 0.930506 , -0.765005 ], ..., [-0.65252 , -0.933794 , 1.11489 , ..., -0.606474 , 0.323287 , -2.09671 ], [-0.678068 , -0.391203 , 0.887894 , ..., -0.721647 , 0.131326 , -2.29018 ], [ 0.0366895, -0.557451 , 0.756044 , ..., 0.99686 , 0.903742 , -0.308114 ]], [[ 1.52082 , 2.08589 , -1.2005 , ..., -0.602199 , 1.88407 , 0.109757 ], [ 0.0451789, -1.61133 , 1.96004 , ..., -0.548927 , 0.375405 , -0.0377435], [-0.216968 , 1.40354 , -2.17544 , ..., 0.335058 , -0.201998 , -0.0420111], ..., [-1.24541 , 1.44617 , 1.26991 , ..., -0.517744 , 1.06641 , -0.328943 ], [-0.26795 , -0.471647 , 0.916106 , ..., -0.0443553, 1.10523 , 0.802313 ], [ 0.860489 , -0.755706 , -0.221758 , ..., -0.881374 , 1.02386 , 2.26025 ]], [[-0.728935 , -1.30284 , -0.725011 , ..., -1.13638 , -0.623346 , 1.20411 ], [ 0.877633 , 1.57903 , 0.657069 , ..., 1.18061 , 0.873288 , -0.777553 ], [ 1.92013 , 1.41113 , 0.565262 , ..., 0.892794 , 1.17681 , -1.14554 ], ..., [-0.787386 , -1.34728 , 0.938111 , ..., 0.212187 , 1.5131 , -0.159953 ], [ 1.29339 , 0.0357047, -0.315845 , ..., 0.0184302, 0.789759 , 0.502829 ], [ 1.57545 , 0.430001 , 0.0687333, ..., 0.335712 , 1.7016 , -1.64133 ]], [[ 0.409093 , 0.464062 , 0.978 , ..., -0.780695 , -0.585484 , 1.81793 ], [ 0.076946 , -0.649097 , -0.768641 , ..., -0.375243 , 0.651451 , -2.41116 ], [-0.474311 , -0.847334 , 0.663324 , ..., 0.276397 , -0.65441 , 2.32434 ], ..., [-1.25161 , 0.453957 , 2.11518 , ..., -0.90933 , 2.48317 , -0.782639 ], [-0.137756 , -0.0470846, -1.45337 , ..., -2.4094 , -1.58137 , 0.137089 ], [ 1.41579 , -0.0828588, 1.27436 , ..., 0.247186 , 1.75653 , 0.501351 ]]]) - theta(chain, draw, school)float649.721 4.33 2.172 ... 20.26 12.97
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- created_at :
- 2020-06-10T18:21:56.176067
- arviz_version :
- 0.8.3
- inference_library :
- cmdstanpy
- inference_library_version :
- 0.8.0
xarray.Dataset -
- chain: 4
- draw: 1000
- school: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- y_hat(chain, draw, school)float6427.32 16.59 19.23 ... 15.28 -14.33
array([[[ 27.316 , 16.5918 , 19.2331 , ..., -2.68653 , 12.2412 , 27.0189 ], [ 13.7773 , -4.34203 , 3.61368 , ..., 2.72659 , 13.737 , 2.31227 ], [ -3.79392 , -0.568726, -16.99 , ..., 8.77864 , 6.83554 , -24.1435 ], ..., [ 16.0011 , 16.3268 , 0.235298, ..., -14.9994 , 6.60276 , -0.33642 ], [ -3.59346 , -7.50548 , -0.90007 , ..., -0.173541, 3.61428 , 25.8661 ], [ 5.06708 , -4.07957 , -23.1559 , ..., 7.18739 , 9.59156 , 5.01793 ]], [[ -0.843751, -4.98264 , -18.7942 , ..., -6.34356 , -11.4954 , -30.0613 ], [-32.9141 , -6.91807 , -6.90439 , ..., 10.1167 , 3.70618 , 8.15487 ], [ 2.88749 , 0.686142, 24.0905 , ..., 9.77811 , 31.1765 , -18.8176 ], ..., [-10.4054 , 38.8779 , -1.72784 , ..., 2.10858 , 1.71828 , -41.049 ], [-34.6393 , -8.05134 , 0.299065, ..., -5.08346 , 14.0737 , 18.2229 ], [ 20.5415 , -7.11264 , 16.6271 , ..., -6.10246 , 16.3215 , 28.9235 ]], [[ -0.601871, -11.7324 , 20.1891 , ..., 14.0161 , -1.10264 , -0.811892], [ 16.1775 , 19.1952 , 7.63344 , ..., 15.3313 , 20.5808 , -0.475661], [ -6.71155 , -3.46014 , 15.4774 , ..., 22.6551 , -6.43601 , 23.9684 ], ..., [ 19.7332 , -20.677 , 24.276 , ..., 12.3559 , 11.5496 , 17.943 ], [ 13.6132 , 5.89891 , -6.70882 , ..., 5.5949 , 16.5097 , -13.9093 ], [ 26.0067 , -2.92887 , 28.0343 , ..., -11.2195 , 3.37155 , -8.39441 ]], [[ -1.77315 , -0.850641, 31.9772 , ..., 12.9403 , 19.1804 , -11.9612 ], [ 12.9344 , -7.44461 , 0.504742, ..., -11.9935 , -5.35724 , 20.562 ], [-11.582 , -9.02636 , 18.8871 , ..., 2.61293 , -10.874 , 33.0402 ], ..., [ 15.5324 , 14.9454 , 7.0026 , ..., -0.143009, 3.01618 , -5.04935 ], [-14.324 , -4.90844 , -12.5231 , ..., -15.5133 , 7.05567 , -27.792 ], [ 15.8131 , 14.6397 , 33.993 , ..., 1.04319 , 15.2797 , -14.3346 ]]])
- created_at :
- 2020-06-10T18:21:56.187926
- arviz_version :
- 0.8.3
- inference_library :
- cmdstanpy
- inference_library_version :
- 0.8.0
xarray.Dataset -
- chain: 4
- draw: 1000
- school: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- log_lik(chain, draw, school)float64-4.37 -3.289 ... -3.247 -3.811
array([[[-4.3695 , -3.28886, -3.74378, ..., -3.33444, -3.58013, -4.11228], [-4.61162, -3.22211, -3.91087, ..., -3.59162, -3.77323, -3.82245], [-4.8368 , -3.37655, -3.76639, ..., -3.31908, -4.20421, -3.95569], ..., [-4.98279, -3.33594, -3.78243, ..., -3.33894, -4.26005, -3.93788], [-5.06201, -3.36561, -3.75784, ..., -3.32717, -4.39022, -3.95324], [-5.03534, -3.39763, -3.7804 , ..., -3.35537, -4.21069, -3.952 ]], [[-4.61557, -3.22682, -3.69171, ..., -3.33435, -3.69475, -3.97581], [-4.92917, -3.40712, -3.84876, ..., -3.33535, -4.17803, -3.91566], [-4.7708 , -3.22197, -3.73476, ..., -3.43421, -4.02287, -3.87183], ..., [-6.02796, -3.65293, -4.38461, ..., -3.31689, -3.29516, -3.9435 ], [-5.28667, -3.54159, -3.80369, ..., -3.31753, -4.04044, -3.90313], [-4.02262, -3.54064, -3.81187, ..., -3.33554, -3.23887, -4.17253]], [[-4.85497, -3.28456, -3.80119, ..., -3.36636, -4.13267, -3.89293], [-3.91323, -4.94915, -4.22492, ..., -4.96036, -3.23148, -4.35478], [-4.22267, -3.24747, -3.9294 , ..., -3.575 , -3.56954, -3.92078], ..., [-5.32923, -3.60416, -3.77723, ..., -3.32314, -4.10275, -3.97869], [-3.91699, -3.23201, -3.78051, ..., -3.43797, -3.36938, -3.8139 ], [-4.95741, -3.63518, -3.69191, ..., -3.34218, -4.19573, -4.52025]], [[-4.57723, -3.22381, -3.9008 , ..., -3.4787 , -3.79729, -3.84203], [-4.60246, -3.22764, -3.88173, ..., -3.46323, -3.80787, -3.85568], [-5.30159, -3.56015, -3.76003, ..., -3.32197, -4.81053, -3.85792], ..., [-5.08647, -3.33452, -3.78991, ..., -3.32673, -4.16193, -3.9453 ], [-5.06091, -3.3648 , -3.73815, ..., -3.31739, -4.53108, -3.94144], [-3.83703, -3.23392, -4.50885, ..., -3.77167, -3.24699, -3.81075]]])
- created_at :
- 2020-06-10T18:21:56.190772
- arviz_version :
- 0.8.3
- inference_library :
- cmdstanpy
- inference_library_version :
- 0.8.0
xarray.Dataset -
- chain: 4
- draw: 1000
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- lp(chain, draw)float64-7.117 -8.525 ... -11.38 -11.14
array([[ -7.11711, -8.52527, -8.34257, ..., -8.99953, -10.3924 , -5.12677], [ -7.40979, -8.6973 , -8.36134, ..., -9.30419, -4.65713, -9.11054], [ -9.35431, -9.76551, -7.86183, ..., -7.19184, -5.21445, -7.71352], [-10.2665 , -13.9631 , -9.83918, ..., -13.5776 , -11.3765 , -11.145 ]]) - accept_stat(chain, draw)float640.9616 0.9694 ... 0.9886 0.429
array([[0.96156 , 0.969437, 0.984633, ..., 0.966525, 0.988819, 0.919061], [0.892384, 0.952504, 0.999717, ..., 0.981023, 0.945826, 0.627332], [1. , 0.997771, 0.14691 , ..., 1. , 1. , 0.459213], [0.714025, 0.911832, 1. , ..., 0.823447, 0.988555, 0.428968]]) - stepsize(chain, draw)float640.4064 0.4064 ... 0.4323 0.4323
array([[0.406405, 0.406405, 0.406405, ..., 0.406405, 0.406405, 0.406405], [0.466926, 0.466926, 0.466926, ..., 0.466926, 0.466926, 0.466926], [0.50536 , 0.50536 , 0.50536 , ..., 0.50536 , 0.50536 , 0.50536 ], [0.432263, 0.432263, 0.432263, ..., 0.432263, 0.432263, 0.432263]]) - treedepth(chain, draw)int643 4 3 3 4 3 4 3 ... 3 3 3 3 3 3 3 3
array([[3, 4, 3, ..., 3, 3, 3], [3, 3, 3, ..., 3, 3, 3], [3, 3, 3, ..., 3, 3, 3], [3, 3, 3, ..., 3, 3, 3]]) - n_leapfrog(chain, draw)int647 15 7 7 15 7 15 ... 7 7 15 7 15 7
array([[ 7, 15, 7, ..., 7, 7, 7], [ 7, 7, 7, ..., 7, 7, 7], [ 7, 7, 7, ..., 7, 7, 7], [15, 15, 7, ..., 7, 15, 7]]) - diverging(chain, draw)boolFalse False False ... False False
array([[False, False, False, ..., False, False, False], [False, False, False, ..., False, False, False], [False, False, False, ..., False, False, False], [False, False, False, ..., False, False, False]]) - energy(chain, draw)float6413.56 12.9 13.65 ... 20.86 22.16
array([[13.556 , 12.8971 , 13.6523 , ..., 11.4512 , 14.1995 , 12.5183 ], [12.3025 , 16.388 , 10.6192 , ..., 19.1564 , 12.9302 , 13.1066 ], [14.6137 , 11.6894 , 14.2455 , ..., 9.98162, 9.17208, 15.7546 ], [19.118 , 19.03 , 16.7125 , ..., 18.6839 , 20.8571 , 22.1571 ]])
- created_at :
- 2020-06-10T18:21:56.182646
- arviz_version :
- 0.8.3
- inference_library :
- cmdstanpy
- inference_library_version :
- 0.8.0
xarray.Dataset -
- school: 8
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- y(school)float6428.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
array([28., 8., -3., 7., -1., 1., 18., 12.])
- created_at :
- 2020-06-10T18:21:56.189062
- arviz_version :
- 0.8.3
- inference_library :
- cmdstanpy
- inference_library_version :
- 0.8.0
xarray.Dataset
From CmdStan#
See from_cmdstan() for details.
CmdStan helpers#
# save for CmdStan example (needs CmdStanPy run)
stan_fit.save_csvfiles(dir="sample_data")
schools_code = """
data {
int<lower=0> J;
real y[J];
real<lower=0> sigma[J];
}
parameters {
real mu;
real<lower=0> tau;
real theta_tilde[J];
}
transformed parameters {
real theta[J];
for (j in 1:J)
theta[j] = mu + tau * theta_tilde[j];
}
model {
mu ~ normal(0, 5);
tau ~ cauchy(0, 5);
theta_tilde ~ normal(0, 1);
y ~ normal(theta, sigma);
}
generated quantities {
vector[J] log_lik;
vector[J] y_hat;
for (j in 1:J) {
log_lik[j] = normal_lpdf(y[j] | theta[j], sigma[j]);
y_hat[j] = normal_rng(theta[j], sigma[j]);
}
}
"""
with open("./eight_school.stan", "w") as f:
print(schools_code, file=f)
import pystan
pystan.stan_rdump(eight_school_data, "./eight_school.data.R")
# Bash shell
#
# $ cd cmdstan
# $ make build
# $ make path/to/eight_school
# $ cd path/to
# $ for i in {1..4}
# do
# ./eight_school sample random seed=12345 \
# id=$i data file=eight_school.data.R \
# output file=sample_data/eight_school_samples-$i.csv &
# done
# $
# Let's use .stan and .csv files created/saved by the CmdStanPy procedure
# glob string
posterior_glob = "sample_data/eight_school-*-[0-9].csv"
# list of paths
# posterior_list = [
# "sample_data/eight_school-*-1.csv",
# "sample_data/eight_school-*-2.csv",
# "sample_data/eight_school-*-3.csv",
# "sample_data/eight_school-*-4.csv",
# ]
obs_data_path = "./eight_school.data.R"
cmdstan_data = az.from_cmdstan(
posterior=posterior_glob,
posterior_predictive="y_hat",
observed_data=obs_data_path,
observed_data_var="y",
log_likelihood="log_lik",
coords={"school": np.arange(eight_school_data["J"])},
dims={
"theta": ["school"],
"y": ["school"],
"log_lik": ["school"],
"y_hat": ["school"],
"theta_tilde": ["school"],
},
)
cmdstan_data
arviz.data.io_cmdstan - INFO - glob found 12 files for 'posterior':
1: sample_data/eight_school-202006100113-1.csv
2: sample_data/eight_school-202006100113-2.csv
3: sample_data/eight_school-202006100113-3.csv
4: sample_data/eight_school-202006100113-4.csv
5: sample_data/eight_school-202006102306-1.csv
6: sample_data/eight_school-202006102306-2.csv
7: sample_data/eight_school-202006102306-3.csv
8: sample_data/eight_school-202006102306-4.csv
9: sample_data/eight_school-202006102351-1.csv
10: sample_data/eight_school-202006102351-2.csv
11: sample_data/eight_school-202006102351-3.csv
12: sample_data/eight_school-202006102351-4.csv
INFO:arviz.data.io_cmdstan:glob found 12 files for 'posterior':
1: sample_data/eight_school-202006100113-1.csv
2: sample_data/eight_school-202006100113-2.csv
3: sample_data/eight_school-202006100113-3.csv
4: sample_data/eight_school-202006100113-4.csv
5: sample_data/eight_school-202006102306-1.csv
6: sample_data/eight_school-202006102306-2.csv
7: sample_data/eight_school-202006102306-3.csv
8: sample_data/eight_school-202006102306-4.csv
9: sample_data/eight_school-202006102351-1.csv
10: sample_data/eight_school-202006102351-2.csv
11: sample_data/eight_school-202006102351-3.csv
12: sample_data/eight_school-202006102351-4.csv
arviz.InferenceData
-
- chain: 12
- draw: 1000
- school: 8
- chain(chain)int640 1 2 3 4 5 6 7 8 9 10 11
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- mu(chain, draw)float643.692 16.11 2.111 ... 2.672 10.06
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array([[ 6.1083 , 3.58214 , 4.86183 , ..., 4.47256 , 1.48153 , 12.0573 ], [ 6.89254 , 2.58141 , 0.803485 , ..., 2.4602 , 0.599099 , 0.97436 ], [ 7.54792 , 3.12201 , 0.912562 , ..., 1.33408 , 5.39912 , 1.91634 ], ..., [ 3.75274 , 1.13823 , 1.8422 , ..., 8.23264 , 3.29958 , 9.06202 ], [ 0.0756374, 14.1684 , 2.65082 , ..., 1.91313 , 7.97043 , 4.03989 ], [ 0.0525536, 0.213029 , 2.08631 , ..., 0.51228 , 0.541425 , 5.80725 ]]) - theta_tilde(chain, draw, school)float640.1507 -0.07589 ... 1.757 0.5014
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- created_at :
- 2020-06-10T18:21:57.128552
- arviz_version :
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xarray.Dataset -
- chain: 12
- draw: 1000
- school: 8
- chain(chain)int640 1 2 3 4 5 6 7 8 9 10 11
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
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- created_at :
- 2020-06-10T18:21:57.962326
- arviz_version :
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xarray.Dataset -
- chain: 12
- draw: 1000
- school: 8
- chain(chain)int640 1 2 3 4 5 6 7 8 9 10 11
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- log_lik(chain, draw, school)float64-4.842 -3.335 ... -3.247 -3.811
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- created_at :
- 2020-06-10T18:21:57.929618
- arviz_version :
- 0.8.3
xarray.Dataset -
- chain: 12
- draw: 1000
- chain(chain)int640 1 2 3 4 5 6 7 8 9 10 11
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
array([ 0, 1, 2, ..., 997, 998, 999])
- lp(chain, draw)float64-5.144 -10.34 ... -11.38 -11.14
array([[ -5.14448, -10.3377 , -4.36231, ..., -11.5328 , -4.41412, -4.53645], [ -6.16728, -7.89382, -8.32759, ..., -6.95914, -8.01642, -6.47187], [ -4.61618, -9.6411 , -6.57635, ..., -7.53224, -5.69699, -6.2396 ], ..., [ -7.40979, -8.6973 , -8.36134, ..., -9.30419, -4.65713, -9.11054], [ -9.35431, -9.76551, -7.86183, ..., -7.19184, -5.21445, -7.71352], [-10.2665 , -13.9631 , -9.83918, ..., -13.5776 , -11.3765 , -11.145 ]]) - accept_stat(chain, draw)float641.0 0.4431 0.9951 ... 0.9886 0.429
array([[1. , 0.44315 , 0.995054, ..., 0.847876, 0.887551, 0.924468], [0.714286, 0.977521, 0.724435, ..., 0.934922, 0.946572, 1. ], [1. , 0.426264, 0.992927, ..., 0.860845, 0.996249, 0.129366], ..., [0.892384, 0.952504, 0.999717, ..., 0.981023, 0.945826, 0.627332], [1. , 0.997771, 0.14691 , ..., 1. , 1. , 0.459213], [0.714025, 0.911832, 1. , ..., 0.823447, 0.988555, 0.428968]]) - stepsize(chain, draw)float640.5095 0.5095 ... 0.4323 0.4323
array([[0.509501, 0.509501, 0.509501, ..., 0.509501, 0.509501, 0.509501], [0.531567, 0.531567, 0.531567, ..., 0.531567, 0.531567, 0.531567], [0.449446, 0.449446, 0.449446, ..., 0.449446, 0.449446, 0.449446], ..., [0.466926, 0.466926, 0.466926, ..., 0.466926, 0.466926, 0.466926], [0.50536 , 0.50536 , 0.50536 , ..., 0.50536 , 0.50536 , 0.50536 ], [0.432263, 0.432263, 0.432263, ..., 0.432263, 0.432263, 0.432263]]) - treedepth(chain, draw)int643 3 3 3 3 3 3 3 ... 3 3 3 3 3 3 3 3
array([[3, 3, 3, ..., 3, 3, 3], [3, 3, 3, ..., 3, 3, 3], [3, 3, 3, ..., 3, 3, 3], ..., [3, 3, 3, ..., 3, 3, 3], [3, 3, 3, ..., 3, 3, 3], [3, 3, 3, ..., 3, 3, 3]]) - n_leapfrog(chain, draw)int647 7 7 7 7 7 7 ... 15 7 7 15 7 15 7
array([[ 7, 7, 7, ..., 7, 7, 7], [ 7, 7, 7, ..., 7, 7, 7], [ 7, 7, 7, ..., 7, 7, 7], ..., [ 7, 7, 7, ..., 7, 7, 7], [ 7, 7, 7, ..., 7, 7, 7], [15, 15, 7, ..., 7, 15, 7]]) - diverging(chain, draw)boolFalse False False ... False False
array([[False, False, False, ..., False, False, False], [False, False, False, ..., False, False, False], [False, False, False, ..., False, False, False], ..., [False, False, False, ..., False, False, False], [False, False, False, ..., False, False, False], [False, False, False, ..., False, False, False]]) - energy(chain, draw)float649.305 15.49 12.04 ... 20.86 22.16
array([[ 9.30492, 15.4901 , 12.0411 , ..., 14.2758 , 13.6856 , 8.80269], [15.0915 , 10.4001 , 15.2596 , ..., 13.6399 , 11.9889 , 10.6035 ], [ 8.96043, 15.8938 , 13.3229 , ..., 11.9587 , 11.6787 , 11.3581 ], ..., [12.3025 , 16.388 , 10.6192 , ..., 19.1564 , 12.9302 , 13.1066 ], [14.6137 , 11.6894 , 14.2455 , ..., 9.98162, 9.17208, 15.7546 ], [19.118 , 19.03 , 16.7125 , ..., 18.6839 , 20.8571 , 22.1571 ]])
- created_at :
- 2020-06-10T18:21:57.892823
- arviz_version :
- 0.8.3
xarray.Dataset -
- school: 8
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- y(school)float6428.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
array([28., 8., -3., 7., -1., 1., 18., 12.])
xarray.Dataset
From NumPyro#
import numpyro
import numpyro.distributions as dist
from jax.random import PRNGKey
from numpyro.distributions.transforms import AffineTransform
from numpyro.infer import MCMC, NUTS, Predictive
numpyro.set_host_device_count(4)
eight_school_data = {
"J": 8,
"y": np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
"sigma": np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}
def model(J, sigma, y=None):
mu = numpyro.sample("mu", dist.Normal(0, 5))
tau = numpyro.sample("tau", dist.HalfCauchy(5))
# use non-centered reparameterization
theta = numpyro.sample(
"theta",
dist.TransformedDistribution(dist.Normal(np.zeros(J), 1), AffineTransform(mu, tau)),
)
numpyro.sample("y", dist.Normal(theta, sigma), obs=y)
kernel = NUTS(model)
mcmc = MCMC(kernel, num_warmup=500, num_samples=500, num_chains=4, chain_method="parallel")
mcmc.run(PRNGKey(0), **eight_school_data, extra_fields=["num_steps", "energy"])
posterior_samples = mcmc.get_samples()
posterior_predictive = Predictive(model, posterior_samples)(
PRNGKey(1), eight_school_data["J"], eight_school_data["sigma"]
)
prior = Predictive(model, num_samples=500)(
PRNGKey(2), eight_school_data["J"], eight_school_data["sigma"]
)
numpyro_data = az.from_numpyro(
mcmc,
prior=prior,
posterior_predictive=posterior_predictive,
coords={"school": np.arange(eight_school_data["J"])},
dims={"theta": ["school"]},
)
numpyro_data
arviz.InferenceData
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- draw: 500
- school: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
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array([[ 5.4749303 , 2.1342402 , 1.4905648 , ..., 0.6671672 , 0.01560028, 3.767334 ], [ 7.9672894 , 1.9319502 , 3.1295881 , ..., 3.3490183 , 3.566799 , 0.39580163], [ 2.9399393 , 0.8484044 , 0.9808714 , ..., 12.281746 , 3.0598812 , 1.0038422 ], [ 2.0114977 , 5.334565 , 1.9803979 , ..., 3.915938 , 3.9908662 , 3.415198 ]], dtype=float32) - theta(chain, draw, school)float3216.805418 -0.4041652 ... 17.367815
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- created_at :
- 2020-06-10T18:22:23.947028
- arviz_version :
- 0.8.3
- inference_library :
- numpyro
- inference_library_version :
- 0.2.3
xarray.Dataset -
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- draw: 500
- y_dim_0: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- y_dim_0(y_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- y(chain, draw, y_dim_0)float329.1578455 ... -4.8099527
array([[[ 9.1578455 , -0.34150663, 15.723784 , ..., -5.102259 , 37.480717 , -10.088353 ], [ -5.3134413 , 6.4528875 , -6.54908 , ..., -4.1057158 , 7.06191 , -8.080217 ], [-19.78724 , 3.4639006 , -15.964477 , ..., -20.008034 , 5.8243866 , 18.86902 ], ..., [-15.180967 , 9.807627 , 27.345123 , ..., -4.84036 , -2.1437302 , 8.3889065 ], [ -5.4775333 , 28.313814 , 7.2766685 , ..., 18.30352 , 20.475103 , -20.46647 ], [ 16.853436 , 10.802054 , 2.6066804 , ..., 11.0614395 , 4.074243 , 16.10594 ]], [[-36.741135 , 2.132221 , -5.1946764 , ..., -8.24964 , 12.281942 , 8.430863 ], [ 2.397912 , 6.8793244 , 18.572903 , ..., -9.415728 , 4.632666 , 0.94791025], [-18.00014 , -17.213095 , -20.43299 , ..., 10.359219 , -8.613728 , 5.810265 ], ..., [-15.850481 , 6.169131 , -1.3056698 , ..., 1.2978272 , 13.411715 , 25.699203 ], [ 10.589049 , 0.5068012 , 16.470114 , ..., -8.520618 , -6.952246 , -3.0879273 ], [ 9.343028 , -11.508167 , -19.114656 , ..., -7.092017 , 10.446011 , -1.5221233 ]], [[-20.391861 , 22.032532 , 5.1348763 , ..., 11.56848 , 4.3738613 , 15.165779 ], [ 18.053 , 2.9446526 , 0.34006357, ..., 3.3776867 , -4.0066824 , -23.29231 ], [ 1.7792162 , 3.8873866 , -8.637331 , ..., -0.90703034, -6.444538 , 10.319935 ], ..., [ 23.217615 , 22.690136 , 11.29295 , ..., 27.433151 , -3.46672 , 61.749702 ], [ 34.18458 , 8.358107 , 8.868971 , ..., -22.360392 , 0.09149265, -1.0741652 ], [ 29.380224 , 4.4413815 , 30.035976 , ..., 2.7786946 , 14.153775 , -41.86547 ]], [[ 9.401894 , -6.2122073 , -6.091647 , ..., 0.5238527 , -0.5514915 , 5.7275 ], [ -1.6696043 , 3.1093576 , 44.24772 , ..., 12.96484 , -6.88388 , 18.44876 ], [ 17.14147 , 20.414312 , 11.990332 , ..., -8.856295 , -7.9003263 , 27.677404 ], ..., [ 6.919694 , 5.4893556 , 0.41990328, ..., -13.118914 , 3.1624792 , 29.015451 ], [ 15.574952 , -0.9990338 , 8.2401 , ..., 2.2999332 , 3.6496153 , 8.287998 ], [ 14.578398 , 0.7358602 , 16.566711 , ..., 23.490755 , -1.5719078 , -4.8099527 ]]], dtype=float32)
- created_at :
- 2020-06-10T18:22:24.051104
- arviz_version :
- 0.8.3
- inference_library :
- numpyro
- inference_library_version :
- 0.2.3
xarray.Dataset -
- chain: 4
- draw: 500
- y_dim_0: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- y_dim_0(y_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- y(chain, draw, y_dim_0)float32-3.9054747 ... -3.8537753
array([[[-3.9054747, -3.5746734, -4.035902 , ..., -3.3210766, -3.3395207, -4.1072197], [-4.947741 , -3.338458 , -3.7338667, ..., -3.3257196, -3.9088354, -3.9957902], [-5.2131925, -3.2507231, -3.7116504, ..., -3.3312411, -3.986606 , -3.9916313], ..., [-4.6342645, -3.2492669, -3.9270694, ..., -3.442984 , -4.001714 , -3.8605828], [-4.7191763, -3.245434 , -3.8421748, ..., -3.413361 , -3.9625223, -3.8684025], [-4.4831963, -3.2859464, -3.9756005, ..., -3.3713636, -4.612568 , -3.8412926]], [[-5.9492664, -3.8084335, -4.0817366, ..., -3.3383892, -4.037158 , -4.051816 ], [-4.8890285, -3.3304648, -3.7801523, ..., -3.3203022, -4.229318 , -3.9864793], [-5.174517 , -4.3684187, -3.7065926, ..., -3.359255 , -6.1360354, -3.968368 ], ..., [-4.5735445, -3.3055634, -4.1853056, ..., -3.3445625, -3.5230136, -3.9288855], [-4.7513547, -3.519569 , -3.8657544, ..., -3.352072 , -3.6622877, -3.9238944], [-4.9259505, -3.2858365, -3.7777483, ..., -3.3694305, -4.247264 , -3.9104798]], [[-4.906596 , -3.284901 , -3.7431939, ..., -3.3367038, -3.5718522, -4.021849 ], [-4.7673435, -3.2952716, -3.792354 , ..., -3.3593068, -4.2786293, -3.8775108], [-4.8043127, -3.267864 , -3.8223267, ..., -3.3797553, -4.0338464, -3.8800478], ..., [-3.6741579, -3.2672462, -3.748196 , ..., -4.747017 , -3.8203554, -4.2222123], [-4.136871 , -3.2232811, -3.867456 , ..., -3.3794975, -3.9430165, -3.8095303], [-4.6403756, -3.2978368, -3.8082085, ..., -3.3598197, -4.053319 , -3.8586538]], [[-4.7323647, -3.5893457, -3.7572649, ..., -3.3174245, -3.9466212, -3.9173644], [-5.207679 , -3.5794165, -3.8724306, ..., -3.81882 , -4.454218 , -3.8412328], [-4.727004 , -3.227339 , -3.8272705, ..., -3.4697766, -3.9262924, -3.86802 ], ..., [-4.4444165, -3.2617114, -3.809705 , ..., -3.4990802, -3.7516966, -3.8093758], [-4.8811502, -3.5942247, -3.728438 , ..., -3.3177028, -4.0894656, -4.179348 ], [-4.5754213, -3.229128 , -3.8275847, ..., -3.4972098, -3.9231424, -3.8537753]]], dtype=float32)
- created_at :
- 2020-06-10T18:22:24.049535
- arviz_version :
- 0.8.3
- inference_library :
- numpyro
- inference_library_version :
- 0.2.3
xarray.Dataset -
- chain: 4
- draw: 500
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- diverging(chain, draw)boolFalse False False ... False False
array([[False, False, False, ..., False, False, False], [False, False, False, ..., False, False, False], [False, False, False, ..., False, False, False], [False, False, False, ..., False, False, False]]) - energy(chain, draw)float3254.622334 53.479084 ... 49.01058
array([[54.622334, 53.479084, 53.991596, ..., 53.81039 , 59.236557, 56.882545], [49.65902 , 48.335026, 56.860115, ..., 49.79985 , 48.931656, 50.302807], [51.492855, 51.79956 , 55.82659 , ..., 51.77163 , 50.36808 , 51.65256 ], [49.366512, 50.623386, 55.419903, ..., 51.691166, 47.321953, 49.01058 ]], dtype=float32) - tree_size(chain, draw)int327 15 7 7 7 15 7 7 ... 7 7 7 7 7 7 7
array([[ 7, 15, 7, ..., 7, 15, 7], [ 7, 15, 15, ..., 7, 7, 7], [ 7, 7, 7, ..., 3, 7, 7], [ 7, 7, 7, ..., 7, 7, 7]], dtype=int32) - depth(chain, draw)int643 4 3 3 3 4 3 3 ... 3 3 3 3 3 3 3 3
array([[3, 4, 3, ..., 3, 4, 3], [3, 4, 4, ..., 3, 3, 3], [3, 3, 3, ..., 2, 3, 3], [3, 3, 3, ..., 3, 3, 3]])
- created_at :
- 2020-06-10T18:22:23.951922
- arviz_version :
- 0.8.3
- inference_library :
- numpyro
- inference_library_version :
- 0.2.3
xarray.Dataset -
- chain: 1
- draw: 500
- school: 8
- chain(chain)int640
array([0])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- school(school)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- mu(chain, draw)float321.8776392 3.322776 ... -0.5562178
array([[ 1.87763917e+00, 3.32277608e+00, -9.43409824e+00, -6.36535287e-01, 4.97456253e-01, -7.59930372e+00, -1.73702741e+00, -6.81911755e+00, -5.64398336e+00, -2.23989189e-01, 5.17267179e+00, 8.54710960e+00, 3.31850290e+00, 1.21073082e-01, 7.83620691e+00, 4.69881475e-01, -1.08328164e+00, 8.50991058e+00, -8.41802776e-01, -4.04251289e+00, 3.32294011e+00, 5.99611139e+00, -6.17558670e+00, 6.03334332e+00, -5.70485020e+00, -2.03827691e+00, -1.12319574e+01, 4.22157764e+00, 2.38109422e+00, -4.61673450e+00, 5.93315411e+00, 4.55151653e+00, -7.10970700e-01, -6.31284094e+00, -4.34699202e+00, 6.09261799e+00, -6.14266682e+00, 9.26569998e-01, 1.61548471e+00, -4.15261239e-01, -7.68356943e+00, -2.56281686e+00, -4.79618311e+00, 7.81891727e+00, -3.24380898e+00, 1.65736473e+00, -5.14156342e+00, 1.10072966e+01, -1.44031830e+01, 5.42257833e+00, 5.59339571e+00, 1.49750960e+00, -3.32892269e-01, -4.46871185e+00, 2.56567287e+00, 2.47131181e+00, -1.37173009e+00, -1.49122763e+00, -1.84207225e+00, 9.69244099e+00, 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1.42294288e+00, 3.44097424e+00, 1.10320222e+00, 2.76839256e+01]], dtype=float32) - theta(chain, draw, school)float320.61433244 1.9731792 ... -21.27477
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- created_at :
- 2020-06-10T18:22:24.053369
- arviz_version :
- 0.8.3
- inference_library :
- numpyro
- inference_library_version :
- 0.2.3
xarray.Dataset -
- chain: 1
- draw: 500
- y_dim_0: 8
- chain(chain)int640
array([0])
- draw(draw)int640 1 2 3 4 5 ... 495 496 497 498 499
array([ 0, 1, 2, ..., 497, 498, 499])
- y_dim_0(y_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- y(chain, draw, y_dim_0)float3219.690388 -0.3481581 ... -34.692043
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- created_at :
- 2020-06-10T18:22:24.055633
- arviz_version :
- 0.8.3
- inference_library :
- numpyro
- inference_library_version :
- 0.2.3
xarray.Dataset -
- y_dim_0: 8
- y_dim_0(y_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- y(y_dim_0)float6428.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
array([28., 8., -3., 7., -1., 1., 18., 12.])
- created_at :
- 2020-06-10T18:22:24.056692
- arviz_version :
- 0.8.3
- inference_library :
- numpyro
- inference_library_version :
- 0.2.3
xarray.Dataset
From PyJAGS#
Import Package#
import pyjags
JAGS Model Code#
Prior Model#
eight_school_prior_model_code = """
model {
mu ~ dnorm(0.0, 1.0/25)
tau ~ dt(0.0, 1.0/25, 1.0) T(0, )
for (j in 1:J) {
theta_tilde[j] ~ dnorm(0.0, 1.0)
}
}
"""
Posterior Model#
eight_school_posterior_model_code = """
model {
mu ~ dnorm(0.0, 1.0/25)
tau ~ dt(0.0, 1.0/25, 1.0) T(0, )
for (j in 1:J) {
theta_tilde[j] ~ dnorm(0.0, 1.0)
y[j] ~ dnorm(mu + tau * theta_tilde[j], 1.0/(sigma[j]^2))
log_like[j] = logdensity.norm(y[j], mu + tau * theta_tilde[j], 1.0/(sigma[j]^2))
}
}
"""
parameters = ["mu", "tau", "theta_tilde"]
variables = parameters + ["log_like"]
Construct JAGS Model and Run Adaptation Steps#
Prior Model#
jags_prior_model = pyjags.Model(
code=eight_school_prior_model_code, data={"J": 8}, chains=4, threads=4, chains_per_thread=1
)
Posterior Model#
jags_posterior_model = pyjags.Model(
code=eight_school_posterior_model_code,
data=eight_school_data,
chains=4,
threads=4,
chains_per_thread=1,
)
adapting: iterations 4000 of 4000, elapsed 0:00:00, remaining 0:00:00
Draw 1000 Burn-In Samples and 5000 Actual Samples per Chain#
jags_prior_samples = jags_prior_model.sample(5000 + 1000, vars=parameters)
jags_posterior_samples = jags_posterior_model.sample(5000 + 1000, vars=variables)
sampling: iterations 24000 of 24000, elapsed 0:00:00, remaining 0:00:00
sampling: iterations 24000 of 24000, elapsed 0:00:00, remaining 0:00:00
Convert PyJAGS Samples Dictionary to ArviZ Inference Data Object#
pyjags_data = az.from_pyjags(
posterior=jags_posterior_samples,
prior=jags_prior_samples,
log_likelihood={"y": "log_like"},
save_warmup=True,
warmup_iterations=1000,
)
pyjags_data
arviz.InferenceData
-
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- draw: 5000
- theta_tilde_dim_0: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 ... 4996 4997 4998 4999
array([ 0, 1, 2, ..., 4997, 4998, 4999])
- theta_tilde_dim_0(theta_tilde_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- theta_tilde(chain, draw, theta_tilde_dim_0)float64-0.8817 0.8312 ... -0.3614 0.2794
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array([[ 9.5660161 , 8.86161166, -0.65416323, ..., 8.65878056, 8.51434694, 4.75722624], [13.0860039 , 10.90145526, 0.11474836, ..., 11.68939865, -0.9937689 , 4.37219633], [ 3.32283619, 6.94982458, 6.6868707 , ..., -0.16083202, 1.94741381, 1.6089792 ], [ 5.79470397, 6.00639881, 4.22307168, ..., 4.3675311 , 10.54271823, 7.43480709]]) - tau(chain, draw)float640.4225 0.7076 ... 0.6132 0.3754
array([[0.4225129 , 0.70764354, 4.11318626, ..., 1.06549024, 0.84353229, 1.22666774], [5.6051199 , 1.60676596, 1.23003475, ..., 2.15813014, 3.75102582, 4.20842298], [7.48864072, 8.89845878, 3.85519405, ..., 0.35845809, 0.80083886, 4.63863181], [3.45441525, 0.77457384, 1.72308523, ..., 0.77028832, 0.6131635 , 0.37541366]])
- created_at :
- 2020-06-19T06:23:52.830658
- arviz_version :
- 0.8.3
- inference_library :
- pyjags
- inference_library_version :
- 1.3.5
xarray.Dataset -
- chain: 4
- draw: 5000
- y_dim_0: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 ... 4996 4997 4998 4999
array([ 0, 1, 2, ..., 4997, 4998, 4999])
- y_dim_0(y_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- y(chain, draw, y_dim_0)float64-4.413 -3.24 ... -3.794 -3.84
array([[[-4.41295677, -3.2399018 , -4.0232753 , ..., -3.63912029, -3.52078213, -3.82640716], [-4.31509256, -3.22162344, -3.99068419, ..., -3.56748162, -3.55034381, -3.82286355], [-5.04891945, -3.70705532, -3.77625556, ..., -3.34864634, -4.55113302, -4.28479863], ..., [-4.57549557, -3.23482517, -4.01823734, ..., -3.57741287, -3.585355 , -3.82076215], [-4.57247255, -3.23159539, -3.98052409, ..., -3.59250129, -3.72757614, -3.82801715], [-4.87983078, -3.3277593 , -3.79014798, ..., -3.32357386, -3.94179764, -3.86291249]], [[-3.88340544, -3.22314713, -4.2701937 , ..., -4.37453804, -3.38603872, -3.83667629], [-4.221597 , -3.23390992, -3.97852171, ..., -3.74635412, -3.44994946, -3.8337397 ], [-5.34200815, -3.50911079, -3.70869184, ..., -3.31735259, -4.64941234, -4.07160487], ..., [-4.08276392, -3.37737117, -4.06582723, ..., -3.95438653, -3.66981257, -3.8119491 ], [-5.32402199, -3.48507739, -3.73106848, ..., -3.45648859, -5.09537619, -4.1362768 ], [-4.62087894, -3.22357815, -4.21957583, ..., -3.40873634, -3.83677346, -4.04205096]], [[-3.78352715, -3.40900932, -3.70158341, ..., -3.64521677, -3.37344317, -3.87679339], [-3.72078639, -3.22560172, -3.72425037, ..., -3.32683227, -3.22502685, -3.81327925], [-4.48565386, -3.2626736 , -3.79190448, ..., -3.38193609, -3.45890796, -3.82233402], ..., [-5.31929045, -3.53858749, -3.7128791 , ..., -3.32697111, -4.80227792, -4.04456905], [-5.16587742, -3.34020609, -3.77092501, ..., -3.31702605, -4.48076103, -3.95673557], [-4.50969454, -3.44164719, -3.71327649, ..., -3.32285998, -4.13955032, -4.26052812]], [[-5.01082765, -3.22183215, -3.79043025, ..., -3.34410517, -3.83240815, -3.86623926], [-4.69585506, -3.23209846, -3.81836553, ..., -3.41064335, -3.77885422, -3.88800986], [-4.79397359, -3.34960285, -3.72735417, ..., -3.389163 , -4.03063314, -3.86514653], ..., [-4.87660795, -3.28317162, -3.79517349, ..., -3.39384957, -4.3145215 , -3.88518398], [-4.28402686, -3.30611707, -4.04866815, ..., -3.73655814, -3.53212736, -3.8115928 ], [-4.56507981, -3.22335652, -3.91577671, ..., -3.46070254, -3.794065 , -3.84001127]]])
- created_at :
- 2020-06-19T06:23:52.839616
- arviz_version :
- 0.8.3
- inference_library :
- pyjags
- inference_library_version :
- 1.3.5
xarray.Dataset -
- chain: 4
- draw: 5000
- theta_tilde_dim_0: 8
- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 ... 4996 4997 4998 4999
array([ 0, 1, 2, ..., 4997, 4998, 4999])
- theta_tilde_dim_0(theta_tilde_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- theta_tilde(chain, draw, theta_tilde_dim_0)float64-1.889 1.346 ... -0.8655 0.5383
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- 2020-06-19T06:23:52.835882
- arviz_version :
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- inference_library :
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xarray.Dataset -
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- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
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- theta_tilde_dim_0(theta_tilde_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
- theta_tilde(chain, draw, theta_tilde_dim_0)float640.6259 -0.05823 ... 0.933 -1.011
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xarray.Dataset -
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- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
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array([0, 1, 2, 3, 4, 5, 6, 7])
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- 2020-06-19T06:23:52.840708
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xarray.Dataset -
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- chain(chain)int640 1 2 3
array([0, 1, 2, 3])
- draw(draw)int640 1 2 3 4 5 ... 995 996 997 998 999
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- theta_tilde_dim_0(theta_tilde_dim_0)int640 1 2 3 4 5 6 7
array([0, 1, 2, 3, 4, 5, 6, 7])
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- 2020-06-19T06:23:52.837977
- arviz_version :
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- inference_library :
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xarray.Dataset