arviz.InferenceData.map

InferenceData.map(fun, groups=None, filter_groups=None, inplace=False, args=None, **kwargs)

Apply a function to multiple groups.

Applies fun groupwise to the selected InferenceData groups and overwrites the group with the result of the function.

Parameters

funcallable

Function to be applied to each group. Assumes the function is called as fun(dataset, *args, **kwargs).

groupsstr or list of str, optional

Groups where the selection is to be applied. Can either be group names or metagroup names.

filter_groups{None, “like”, “regex”}, optional

If None (default), interpret var_names as the real variables names. If “like”, interpret var_names as substrings of the real variables names. If “regex”, interpret var_names as regular expressions on the real variables names. A la pandas.filter.

inplacebool, optional

If True, modify the InferenceData object inplace, otherwise, return the modified copy.

argsarray_like, optional

Positional arguments passed to fun.

**kwargsmapping, optional

Keyword arguments passed to fun.

Returns

InferenceData

A new InferenceData object by default. When inplace==True perform selection in place and return None

Examples

Shift observed_data, prior_predictive and posterior_predictive.

import arviz as az
import numpy as np
idata = az.load_arviz_data("non_centered_eight")
idata_shifted_obs = idata.map(lambda x: x + 3, groups="observed_vars")
idata_shifted_obs

arviz.InferenceData

• posterior

  <xarray.Dataset>
  Dimensions:  (chain: 4, draw: 500, school: 8)
  Coordinates:
    * chain    (chain) int64 0 1 2 3
    * draw     (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499
    * school   (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon'
  Data variables:
      mu       (chain, draw) float64 6.339 6.783 5.168 1.51 ... 3.593 1.325 4.081
      theta_t  (chain, draw, school) float64 -0.9553 -1.162 ... 0.5131 1.119
      tau      (chain, draw) float64 2.574 0.9522 1.832 1.93 ... 3.436 2.333 1.316
      theta    (chain, draw, school) float64 3.88 3.348 6.233 ... 4.756 5.553
  Attributes:
      created_at:                 2022-10-13T14:37:26.351883
      arviz_version:              0.13.0.dev0
      inference_library:          pymc
      inference_library_version:  4.2.2
      sampling_time:              4.738754749298096
      tuning_steps:               1000

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • school: 8
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • school
      (school)
      object
      'Choate' ... 'Mt. Hermon'

      array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
             'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype=object)

  • Data variables: (4)
    • mu
      (chain, draw)
      float64
      ...

      array([[ 6.338685,  6.782693,  5.168359, ..., 12.757075,  5.37869 ,  4.66041 ],
             [ 8.899104,  7.087908, 10.875605, ...,  3.63468 ,  5.345811,  3.12776 ],
             [ 6.329751,  1.03682 ,  3.002742, ...,  8.618238,  3.3819  ,  3.25564 ],
             [ 2.28009 ,  2.451263,  0.615213, ...,  3.592518,  1.324725,  4.080584]])

    • theta_t
      (chain, draw, school)
      float64
      ...

      array([[[-9.552766e-01, -1.161776e+00, ...,  1.226818e-02, -1.058004e+00],
              [-1.415589e+00,  1.124392e+00, ...,  1.211550e-01,  1.287030e+00],
              ...,
              [-4.796663e-01,  7.272129e-01, ..., -6.502985e-01, -1.404462e-01],
              [ 7.657660e-01, -5.631492e-01, ...,  8.740417e-01,  2.631002e+00]],
      
             [[ 1.289875e+00,  1.531183e+00, ..., -5.014688e-01, -1.346764e-03],
              [ 1.493400e+00,  9.438758e-01, ..., -5.228563e-01,  2.784666e-01],
              ...,
              [ 4.632405e-02,  2.925410e-01, ..., -9.871518e-01,  1.353057e+00],
              [ 1.527662e+00,  1.888176e+00, ...,  1.423699e+00, -1.174973e+00]],
      
             [[-4.519245e-01, -1.319565e+00, ...,  1.503257e+00,  1.018622e+00],
              [ 1.181253e+00,  1.829861e+00, ..., -1.799918e-01, -5.713427e-01],
              ...,
              [ 1.610801e+00, -5.440766e-01, ..., -8.404918e-01, -7.115881e-01],
              [ 2.288234e+00, -1.881251e-01, ...,  5.582617e-02, -9.616994e-01]],
      
             [[ 6.211228e-01, -1.582774e-01, ..., -2.804555e-02, -5.580998e-01],
              [ 9.417496e-01,  6.979212e-02, ...,  9.046864e-01, -1.098880e-01],
              ...,
              [ 1.862984e+00, -1.589752e-01, ..., -5.087589e-01, -4.101680e-01],
              [ 5.108890e-01,  6.944514e-01, ...,  5.131132e-01,  1.118939e+00]]])

    • tau
      (chain, draw)
      float64
      ...

      array([[ 2.574017,  0.952235,  1.831751, ...,  1.962487,  2.711848,  0.192105],
             [ 2.505309,  1.677181,  2.733161, ...,  1.183499,  0.773882,  2.276184],
             [ 2.462132,  2.095866,  8.076973, ..., 18.261843,  2.997132,  5.045402],
             [ 5.350197,  7.990503,  2.28072 , ...,  3.436323,  2.332583,  1.316017]])

    • theta
      (chain, draw, school)
      float64
      ...

      array([[[ 3.879786,  3.348254, ...,  6.370263,  3.615363],
              [ 5.43472 ,  7.853378, ...,  6.898061,  8.008247],
              ...,
              [ 4.077907,  7.35078 , ...,  3.615179,  4.997821],
              [ 4.807518,  4.552226, ...,  4.828318,  5.16584 ]],
      
             [[12.130639, 12.735192, ...,  7.64277 ,  8.89573 ],
              [ 9.592611,  8.670959, ...,  6.210984,  7.554947],
              ...,
              [ 5.381661,  5.572203, ...,  4.581872,  6.392918],
              [ 6.605   ,  7.425596, ...,  6.368362,  0.453306]],
      
             [[ 5.217053,  3.080808, ..., 10.030966,  8.837732],
              [ 3.51257 ,  4.871964, ...,  0.659582, -0.160638],
              ...,
              [ 8.209685,  1.751231, ...,  0.862835,  1.249176],
              [14.8007  ,  2.306473, ...,  3.537306, -1.59652 ]],
      
             [[ 5.60322 ,  1.433275, ...,  2.130041, -0.705854],
              [ 9.976316,  3.008937, ...,  9.680162,  1.573202],
              ...,
              [ 5.670289,  0.953903, ...,  0.138003,  0.367975],
              [ 4.752923,  4.994494, ...,  4.75585 ,  5.553127]]])

  • Attributes: (6)

    created_at :

    2022-10-13T14:37:26.351883

    arviz_version :

    0.13.0.dev0

    inference_library :

    pymc

    inference_library_version :

    4.2.2

    sampling_time :

    4.738754749298096

    tuning_steps :

    1000

  
  
• posterior_predictive

  <xarray.Dataset>
  Dimensions:    (chain: 4, draw: 500, obs_dim_0: 8)
  Coordinates:
    * chain      (chain) int64 0 1 2 3
    * draw       (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499
    * obs_dim_0  (obs_dim_0) int64 0 1 2 3 4 5 6 7
  Data variables:
      obs        (chain, draw, obs_dim_0) float64 -8.912 0.4851 ... 13.55 27.95
  Attributes:
      created_at:                 2022-10-13T14:37:34.333731
      arviz_version:              0.13.0.dev0
      inference_library:          pymc
      inference_library_version:  4.2.2

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • obs_dim_0: 8
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • obs_dim_0
      (obs_dim_0)
      int64
      0 1 2 3 4 5 6 7

      array([0, 1, 2, 3, 4, 5, 6, 7])

  • Data variables: (1)
    • obs
      (chain, draw, obs_dim_0)
      float64
      -8.912 0.4851 -4.71 ... 13.55 27.95

      array([[[ -8.91164858,   0.48513691,  -4.70995568, ...,  25.54688492,
                13.94575018,   9.80299148],
              [ 37.4801699 , -10.77370835,  -0.5719224 , ...,   0.43335956,
                27.32805956,  14.09089747],
              [ 17.70959145, -11.12171465, -21.98355095, ...,  19.10421895,
                 8.85410192,  -8.10962076],
              ...,
              [ 27.27407986,   7.61924923,  26.24515535, ...,  -0.3350811 ,
                11.69606961,  39.63282956],
              [  4.79252722,   0.43572688,  -9.33809594, ...,   9.92145935,
                -5.72201279,   4.97166968],
              [  8.34887428,   8.83802449,   4.87002072, ...,   9.48416992,
                -5.19603508,  -1.88720116]],
      
             [[ 14.660454  ,  14.56500642,  30.54658322, ...,   0.820571  ,
                17.58317036,  11.41523916],
              [ 12.23886235,  17.66178128,  10.9959666 , ...,  19.48767939,
                31.47333474,  14.07945178],
              [ 33.47381555,  23.8333277 ,  -0.67617714, ...,   7.95021076,
                 8.66776442,  36.76402444],
      ...
              [ 45.14657727,  19.31827266, -13.77595216, ...,  21.35397137,
                12.08007358,  19.71077765],
              [ 14.1760222 ,  -4.54869822,   8.69720246, ...,   7.5198413 ,
                -9.63781631, -15.25261963],
              [  9.0665652 , -24.09127382,  -5.36918153, ...,  27.94605585,
                -5.79860404, -35.2355531 ]],
      
             [[ 27.4155747 ,  27.81444338,  22.10513881, ...,  12.74755666,
                14.5126698 ,  14.57236846],
              [ -3.76124287, -20.82045621,  31.33247223, ...,  13.29821842,
                 1.41832433,  16.34246786],
              [ -7.00712196,  -7.93492977,   9.95458309, ..., -11.32537975,
                21.94623035,  10.70530684],
              ...,
              [ 13.80440934,  15.44637947, -10.90413704, ...,  10.01640909,
                16.47727939,  31.34665798],
              [-11.99095788,   5.75164919,  28.06463307, ...,   3.68615864,
               -12.96358662, -10.4495535 ],
              [ 12.81063159,  14.01071347,  17.28607254, ...,   7.91079619,
                13.55415258,  27.94927617]]])

  • Attributes: (4)

    created_at :

    2022-10-13T14:37:34.333731

    arviz_version :

    0.13.0.dev0

    inference_library :

    pymc

    inference_library_version :

    4.2.2

  
  
• log_likelihood

  <xarray.Dataset>
  Dimensions:    (chain: 4, draw: 500, obs_dim_0: 8)
  Coordinates:
    * chain      (chain) int64 0 1 2 3
    * draw       (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499
    * obs_dim_0  (obs_dim_0) int64 0 1 2 3 4 5 6 7
  Data variables:
      obs        (chain, draw, obs_dim_0) float64 -4.92 -3.33 ... -4.099 -3.873
  Attributes:
      created_at:                 2022-10-13T14:37:26.571887
      arviz_version:              0.13.0.dev0
      inference_library:          pymc
      inference_library_version:  4.2.2

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • obs_dim_0: 8
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • obs_dim_0
      (obs_dim_0)
      int64
      0 1 2 3 4 5 6 7

      array([0, 1, 2, 3, 4, 5, 6, 7])

  • Data variables: (1)
    • obs
      (chain, draw, obs_dim_0)
      float64
      ...

      array([[[-4.919844, -3.329717, ..., -3.897778, -3.917801],
              [-4.758526, -3.221631, ..., -3.837789, -3.8339  ],
              ...,
              [-4.898692, -3.223631, ..., -4.256139, -3.884975],
              [-4.822303, -3.280959, ..., -4.08899 , -3.881387]],
      
             [[-4.186626, -3.333634, ..., -3.757885, -3.824181],
              [-4.379949, -3.223775, ..., -3.916428, -3.839802],
              ...,
              [-4.763854, -3.250995, ..., -4.121754, -3.857828],
              [-4.644202, -3.223173, ..., -3.897999, -4.015061]],
      
             [[-4.780461, -3.342516, ..., -3.539051, -3.824742],
              [-4.959509, -3.270447, ..., -4.724974, -4.037522],
              ...,
              [-4.497337, -3.416759, ..., -4.689936, -3.987675],
              [-4.014148, -3.383605, ..., -4.267371, -4.094596]],
      
             [[-4.74169 , -3.437133, ..., -4.480802, -4.058444],
              [-4.348885, -3.346077, ..., -3.567622, -3.977085],
              ...,
              [-4.735024, -3.469761, ..., -4.816778, -4.018113],
              [-4.827937, -3.266689, ..., -4.098561, -3.873449]]])

  • Attributes: (4)

    created_at :

    2022-10-13T14:37:26.571887

    arviz_version :

    0.13.0.dev0

    inference_library :

    pymc

    inference_library_version :

    4.2.2

  
  
• sample_stats

  <xarray.Dataset>
  Dimensions:              (chain: 4, draw: 500)
  Coordinates:
    * chain                (chain) int64 0 1 2 3
    * draw                 (draw) int64 0 1 2 3 4 5 6 ... 494 495 496 497 498 499
  Data variables: (12/16)
      lp                   (chain, draw) float64 -47.23 -47.66 ... -45.31 -44.3
      largest_eigval       (chain, draw) float64 nan nan nan nan ... nan nan nan
      perf_counter_start   (chain, draw) float64 6.638e+03 6.638e+03 ... 6.64e+03
      perf_counter_diff    (chain, draw) float64 0.002218 0.002257 ... 0.001373
      step_size            (chain, draw) float64 0.4865 0.4865 ... 0.5299 0.5299
      diverging            (chain, draw) bool False False False ... False False
      ...                   ...
      max_energy_error     (chain, draw) float64 0.1991 0.1653 ... 0.1055 -0.04423
      n_steps              (chain, draw) float64 7.0 7.0 7.0 7.0 ... 7.0 7.0 7.0
      step_size_bar        (chain, draw) float64 0.3976 0.3976 ... 0.4382 0.4382
      energy_error         (chain, draw) float64 0.1991 0.02881 ... -0.02114
      smallest_eigval      (chain, draw) float64 nan nan nan nan ... nan nan nan
      index_in_trajectory  (chain, draw) int64 -7 6 4 -2 -2 4 ... 8 -3 -6 -6 3 4
  Attributes:
      created_at:                 2022-10-13T14:37:26.362154
      arviz_version:              0.13.0.dev0
      inference_library:          pymc
      inference_library_version:  4.2.2
      sampling_time:              4.738754749298096
      tuning_steps:               1000

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

  • Data variables: (16)
    • lp
      (chain, draw)
      float64
      ...

      array([[-47.228704, -47.655423, -43.481296, ..., -48.517638, -44.520163,
              -50.455371],
             [-47.384674, -46.73103 , -49.775671, ..., -47.620235, -44.500447,
              -46.510392],
             [-46.689738, -46.548404, -43.410964, ..., -46.762468, -45.692428,
              -45.812864],
             [-44.698833, -45.889824, -45.645362, ..., -43.755327, -45.313383,
              -44.296362]])

    • largest_eigval
      (chain, draw)
      float64
      ...

      array([[nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan]])

    • perf_counter_start
      (chain, draw)
      float64
      ...

      array([[6638.257224, 6638.259802, 6638.262392, ..., 6639.699995, 6639.701166,
              6639.702686],
             [6639.159517, 6639.162066, 6639.164608, ..., 6640.202134, 6640.203753,
              6640.205395],
             [6638.548384, 6638.550606, 6638.552621, ..., 6639.48563 , 6639.487184,
              6639.488758],
             [6638.39451 , 6638.397361, 6638.399744, ..., 6639.561032, 6639.562592,
              6639.564118]])

    • perf_counter_diff
      (chain, draw)
      float64
      ...

      array([[0.002218, 0.002257, 0.002258, ..., 0.000988, 0.001336, 0.001309],
             [0.002232, 0.002242, 0.002195, ..., 0.001426, 0.001434, 0.00142 ],
             [0.001968, 0.00182 , 0.001631, ..., 0.001335, 0.001342, 0.001369],
             [0.002477, 0.002093, 0.000716, ..., 0.001343, 0.00133 , 0.001373]])

    • step_size
      (chain, draw)
      float64
      ...

      array([[0.486522, 0.486522, 0.486522, ..., 0.486522, 0.486522, 0.486522],
             [0.42203 , 0.42203 , 0.42203 , ..., 0.42203 , 0.42203 , 0.42203 ],
             [0.59357 , 0.59357 , 0.59357 , ..., 0.59357 , 0.59357 , 0.59357 ],
             [0.529915, 0.529915, 0.529915, ..., 0.529915, 0.529915, 0.529915]])

    • diverging
      (chain, draw)
      bool
      ...

      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)
      float64
      ...

      array([[48.90273 , 56.261267, 49.077414, ..., 60.987666, 52.419911, 54.436816],
             [50.863576, 52.4975  , 51.607066, ..., 50.208891, 50.575508, 52.947286],
             [51.661367, 53.18938 , 48.823999, ..., 58.577277, 52.102731, 50.409899],
             [46.723935, 48.143778, 56.081453, ..., 46.075147, 47.996296, 47.747698]])

    • process_time_diff
      (chain, draw)
      float64
      ...

      array([[0.002219, 0.002257, 0.002259, ..., 0.000988, 0.001336, 0.001309],
             [0.002233, 0.002242, 0.002195, ..., 0.001426, 0.001434, 0.00142 ],
             [0.001968, 0.00182 , 0.001631, ..., 0.001335, 0.001343, 0.00137 ],
             [0.002477, 0.002094, 0.000716, ..., 0.001343, 0.00133 , 0.001373]])

    • tree_depth
      (chain, draw)
      int64
      ...

      array([[3, 3, 3, ..., 3, 3, 3],
             [3, 3, 3, ..., 3, 3, 3],
             [3, 3, 3, ..., 3, 3, 3],
             [3, 3, 2, ..., 3, 3, 3]])

    • acceptance_rate
      (chain, draw)
      float64
      ...

      array([[0.883398, 0.911205, 1.      , ..., 0.772518, 0.998285, 0.691737],
             [0.989339, 0.966488, 0.948747, ..., 0.943751, 0.994247, 0.923492],
             [0.962988, 0.956062, 0.983368, ..., 0.914731, 0.847603, 0.995408],
             [0.96703 , 0.97685 , 0.268305, ..., 0.91756 , 0.950502, 0.996952]])

    • max_energy_error
      (chain, draw)
      float64
      ...

      array([[ 1.991396e-01,  1.653443e-01, -2.359897e-01, ...,  1.131924e+02,
              -2.399243e-01,  4.742182e-01],
             [-1.256384e-01,  1.255939e-01,  1.557983e-01, ...,  1.144065e-01,
              -1.572277e-01,  5.984181e-01],
             [ 1.662153e-01,  2.201006e-01, -3.435262e-01, ..., -2.657751e+00,
               5.601741e-01, -1.262098e-01],
             [ 9.217752e-02,  1.077633e-01,  1.353566e+01, ...,  1.597869e-01,
               1.054732e-01, -4.422758e-02]])

    • n_steps
      (chain, draw)
      float64
      ...

      array([[7., 7., 7., ..., 5., 7., 7.],
             [7., 7., 7., ..., 7., 7., 7.],
             [7., 7., 7., ..., 7., 7., 7.],
             [7., 7., 3., ..., 7., 7., 7.]])

    • step_size_bar
      (chain, draw)
      float64
      ...

      array([[0.397567, 0.397567, 0.397567, ..., 0.397567, 0.397567, 0.397567],
             [0.422762, 0.422762, 0.422762, ..., 0.422762, 0.422762, 0.422762],
             [0.517573, 0.517573, 0.517573, ..., 0.517573, 0.517573, 0.517573],
             [0.438217, 0.438217, 0.438217, ..., 0.438217, 0.438217, 0.438217]])

    • energy_error
      (chain, draw)
      float64
      ...

      array([[ 0.19914 ,  0.028808, -0.145284, ...,  0.095319, -0.239924,  0.426006],
             [ 0.03815 , -0.021245,  0.155798, ...,  0.114406, -0.157228, -0.173795],
             [ 0.029674,  0.005882, -0.343526, ..., -2.657751, -0.297449,  0.003349],
             [ 0.052993,  0.058774,  0.854343, ...,  0.110231,  0.057525, -0.021145]])

    • smallest_eigval
      (chain, draw)
      float64
      ...

      array([[nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan],
             [nan, nan, nan, ..., nan, nan, nan]])

    • index_in_trajectory
      (chain, draw)
      int64
      ...

      array([[-7,  6,  4, ...,  2, -4, -3],
             [-4, -1,  2, ..., -4, -2, -5],
             [ 6,  5,  4, ...,  6,  2,  1],
             [-4, -2, -1, ..., -6,  3,  4]])

  • Attributes: (6)

    created_at :

    2022-10-13T14:37:26.362154

    arviz_version :

    0.13.0.dev0

    inference_library :

    pymc

    inference_library_version :

    4.2.2

    sampling_time :

    4.738754749298096

    tuning_steps :

    1000

  
  
• prior

  <xarray.Dataset>
  Dimensions:  (chain: 1, draw: 500, school: 8)
  Coordinates:
    * chain    (chain) int64 0
    * draw     (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499
    * school   (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon'
  Data variables:
      mu       (chain, draw) float64 -1.297 4.331 -4.348 ... 4.195 6.55 7.456
      theta_t  (chain, draw, school) float64 0.9176 -0.281 1.071 ... 0.1039 0.8562
      theta    (chain, draw, school) float64 40.47 -14.09 47.45 ... 7.63 8.887
      tau      (chain, draw) float64 45.52 1.976 11.63 8.993 ... 17.76 104.8 1.671
  Attributes:
      created_at:                 2022-10-13T14:37:18.108887
      arviz_version:              0.13.0.dev0
      inference_library:          pymc
      inference_library_version:  4.2.2

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 500
    • school: 8
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • school
      (school)
      object
      'Choate' ... 'Mt. Hermon'

      array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
             'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype=object)

  • Data variables: (4)
    • mu
      (chain, draw)
      float64
      ...

      array([[-1.296925,  4.331389, -4.348197, ...,  4.194706,  6.550406,  7.456061]])

    • theta_t
      (chain, draw, school)
      float64
      ...

      array([[[ 0.917619, -0.281024, ..., -0.732326,  0.52341 ],
              [-1.221302,  0.066861, ..., -0.174084, -0.580162],
              ...,
              [-0.386224, -0.504302, ..., -1.72421 , -0.105772],
              [-0.104081,  0.498367, ...,  0.103861,  0.856243]]])

    • theta
      (chain, draw, school)
      float64
      ...

      array([[[  40.472515,  -14.088946, ...,  -34.631936,   22.528354],
              [   1.917613,    4.463533, ...,    3.987329,    3.184759],
              ...,
              [ -33.910975,  -46.281038, ..., -174.080406,   -4.530474],
              [   7.282148,    8.288803, ...,    7.629607,    8.886792]]])

    • tau
      (chain, draw)
      float64
      ...

      array([[ 45.519351,   1.976396,  11.63387 , ...,  17.757435, 104.761474,
                1.670941]])

  • Attributes: (4)

    created_at :

    2022-10-13T14:37:18.108887

    arviz_version :

    0.13.0.dev0

    inference_library :

    pymc

    inference_library_version :

    4.2.2

  
  
• prior_predictive

  <xarray.Dataset>
  Dimensions:    (chain: 1, draw: 500, obs_dim_0: 8)
  Coordinates:
    * chain      (chain) int64 0
    * draw       (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499
    * obs_dim_0  (obs_dim_0) int64 0 1 2 3 4 5 6 7
  Data variables:
      obs        (chain, draw, obs_dim_0) float64 25.87 -10.84 ... -4.658 17.32
  Attributes:
      created_at:                 2022-10-13T14:37:18.111951
      arviz_version:              0.13.0.dev0
      inference_library:          pymc
      inference_library_version:  4.2.2

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 500
    • obs_dim_0: 8
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • obs_dim_0
      (obs_dim_0)
      int64
      0 1 2 3 4 5 6 7

      array([0, 1, 2, 3, 4, 5, 6, 7])

  • Data variables: (1)
    • obs
      (chain, draw, obs_dim_0)
      float64
      25.87 -10.84 64.31 ... -4.658 17.32

      array([[[  25.86573102,  -10.83562762,   64.30603396, ...,
                 34.12327354,  -31.15539197,   17.40041595],
              [  21.2308377 ,  -15.94389655,   26.47959507, ...,
                 27.48371569,   12.54871934,   12.21388191],
              [ -14.10920978,   30.7429682 ,  -13.36386214, ...,
                 17.25866094,  -20.52897454,  -14.60687912],
              ...,
              [ -26.10606168,   13.11608297,   15.12723183, ...,
                 17.87300987,    7.58948329,   12.374558  ],
              [ -38.39050122,  -45.43587181,  -47.4225284 , ...,
                  6.77697971, -168.96059997,    1.26974321],
              [  28.73909128,   20.70475211,    3.50257694, ...,
                 20.58279319,   -4.65758653,   17.32397509]]])

  • Attributes: (4)

    created_at :

    2022-10-13T14:37:18.111951

    arviz_version :

    0.13.0.dev0

    inference_library :

    pymc

    inference_library_version :

    4.2.2

  
  
• observed_data

  <xarray.Dataset>
  Dimensions:    (obs_dim_0: 8)
  Coordinates:
    * obs_dim_0  (obs_dim_0) int64 0 1 2 3 4 5 6 7
  Data variables:
      obs        (obs_dim_0) float64 31.0 11.0 0.0 10.0 2.0 4.0 21.0 15.0
  Attributes:
      created_at:                 2022-10-13T14:37:18.113060
      arviz_version:              0.13.0.dev0
      inference_library:          pymc
      inference_library_version:  4.2.2

  xarray.Dataset

  • Dimensions:
    • obs_dim_0: 8
  • Coordinates: (1)
    • obs_dim_0
      (obs_dim_0)
      int64
      0 1 2 3 4 5 6 7

      array([0, 1, 2, 3, 4, 5, 6, 7])

  • Data variables: (1)
    • obs
      (obs_dim_0)
      float64
      31.0 11.0 0.0 ... 4.0 21.0 15.0

      array([31., 11.,  0., 10.,  2.,  4., 21., 15.])

  • Attributes: (4)

    created_at :

    2022-10-13T14:37:18.113060

    arviz_version :

    0.13.0.dev0

    inference_library :

    pymc

    inference_library_version :

    4.2.2

  
  
• constant_data

  <xarray.Dataset>
  Dimensions:  (school: 8)
  Coordinates:
    * school   (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon'
  Data variables:
      scores   (school) float64 28.0 8.0 -3.0 7.0 -1.0 1.0 18.0 12.0
  Attributes:
      created_at:                 2022-10-13T14:37:18.114126
      arviz_version:              0.13.0.dev0
      inference_library:          pymc
      inference_library_version:  4.2.2

  xarray.Dataset

  • Dimensions:
    • school: 8
  • Coordinates: (1)
    • school
      (school)
      object
      'Choate' ... 'Mt. Hermon'

      array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
             'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype=object)

  • Data variables: (1)
    • scores
      (school)
      float64
      ...

      array([28.,  8., -3.,  7., -1.,  1., 18., 12.])

  • Attributes: (4)

    created_at :

    2022-10-13T14:37:18.114126

    arviz_version :

    0.13.0.dev0

    inference_library :

    pymc

    inference_library_version :

    4.2.2

  
  

Rename and update the coordinate values in both posterior and prior groups.

idata = az.load_arviz_data("radon")
idata = idata.map(
    lambda ds: ds.rename({"g_coef": "uranium_coefs"}).assign(
        uranium_coefs=["intercept", "u_slope"]
    ),
    groups=["posterior", "prior"]
)
idata

arviz.InferenceData

• posterior

  <xarray.Dataset>
  Dimensions:        (chain: 4, draw: 500, uranium_coefs: 2, County: 85)
  Coordinates:
    * chain          (chain) int64 0 1 2 3
    * draw           (draw) int64 0 1 2 3 4 5 6 7 ... 493 494 495 496 497 498 499
    * uranium_coefs  (uranium_coefs) <U9 'intercept' 'u_slope'
    * County         (County) object 'AITKIN' 'ANOKA' ... 'YELLOW MEDICINE'
  Data variables:
      g              (chain, draw, uranium_coefs) float64 1.499 0.5436 ... 0.6087
      za_county      (chain, draw, County) float64 ...
      b              (chain, draw) float64 -0.5965 -0.5848 ... -0.7949 -0.5402
      sigma_a        (chain, draw) float64 0.2061 0.1526 0.2201 ... 0.1764 0.1121
      a              (chain, draw, County) float64 ...
      a_county       (chain, draw, County) float64 ...
      sigma          (chain, draw) float64 0.7271 0.7161 0.7189 ... 0.7267 0.7324
  Attributes:
      created_at:                 2020-07-24T18:15:12.191355
      arviz_version:              0.9.0
      inference_library:          pymc3
      inference_library_version:  3.9.2
      sampling_time:              18.096983432769775
      tuning_steps:               1000

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • uranium_coefs: 2
    • County: 85
  • Coordinates: (4)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • uranium_coefs
      (uranium_coefs)
      <U9
      'intercept' 'u_slope'

      array(['intercept', 'u_slope'], dtype='<U9')

    • County
      (County)
      object
      'AITKIN' ... 'YELLOW MEDICINE'

      array(['AITKIN', 'ANOKA', 'BECKER', 'BELTRAMI', 'BENTON', 'BIG STONE',
             'BLUE EARTH', 'BROWN', 'CARLTON', 'CARVER', 'CASS', 'CHIPPEWA',
             'CHISAGO', 'CLAY', 'CLEARWATER', 'COOK', 'COTTONWOOD', 'CROW WING',
             'DAKOTA', 'DODGE', 'DOUGLAS', 'FARIBAULT', 'FILLMORE', 'FREEBORN',
             'GOODHUE', 'HENNEPIN', 'HOUSTON', 'HUBBARD', 'ISANTI', 'ITASCA',
             'JACKSON', 'KANABEC', 'KANDIYOHI', 'KITTSON', 'KOOCHICHING',
             'LAC QUI PARLE', 'LAKE', 'LAKE OF THE WOODS', 'LE SUEUR', 'LINCOLN',
             'LYON', 'MAHNOMEN', 'MARSHALL', 'MARTIN', 'MCLEOD', 'MEEKER',
             'MILLE LACS', 'MORRISON', 'MOWER', 'MURRAY', 'NICOLLET', 'NOBLES',
             'NORMAN', 'OLMSTED', 'OTTER TAIL', 'PENNINGTON', 'PINE', 'PIPESTONE',
             'POLK', 'POPE', 'RAMSEY', 'REDWOOD', 'RENVILLE', 'RICE', 'ROCK',
             'ROSEAU', 'SCOTT', 'SHERBURNE', 'SIBLEY', 'ST LOUIS', 'STEARNS',
             'STEELE', 'STEVENS', 'SWIFT', 'TODD', 'TRAVERSE', 'WABASHA', 'WADENA',
             'WASECA', 'WASHINGTON', 'WATONWAN', 'WILKIN', 'WINONA', 'WRIGHT',
             'YELLOW MEDICINE'], dtype=object)

  • Data variables: (7)
    • g
      (chain, draw, uranium_coefs)
      float64
      ...

      array([[[1.499182, 0.543647],
              [1.468924, 0.647096],
              ...,
              [1.47847 , 0.484735],
              [1.489155, 0.57542 ]],
      
             [[1.484451, 0.99103 ],
              [1.547628, 0.738719],
              ...,
              [1.450935, 0.672616],
              [1.505473, 0.67952 ]],
      
             [[1.447203, 0.780061],
              [1.495437, 0.75989 ],
              ...,
              [1.473912, 0.604781],
              [1.548502, 0.755004]],
      
             [[1.474525, 0.763851],
              [1.511727, 0.872679],
              ...,
              [1.501151, 0.880044],
              [1.506491, 0.608711]]])

    • za_county
      (chain, draw, County)
      float64
      ...

      [170000 values with dtype=float64]

    • b
      (chain, draw)
      float64
      ...

      array([[-0.596478, -0.584755, -0.593613, ..., -0.57224 , -0.640129, -0.721395],
             [-0.665642, -0.696652, -0.512868, ..., -0.626958, -0.616887, -0.664136],
             [-0.634431, -0.6546  , -0.545406, ..., -0.542192, -0.632991, -0.704424],
             [-0.684179, -0.658339, -0.570134, ..., -0.488763, -0.794888, -0.540182]])

    • sigma_a
      (chain, draw)
      float64
      ...

      array([[0.206076, 0.152604, 0.220095, ..., 0.110586, 0.173843, 0.142675],
             [0.155506, 0.131196, 0.111168, ..., 0.259368, 0.176735, 0.085373],
             [0.033202, 0.052631, 0.112308, ..., 0.192696, 0.202346, 0.168516],
             [0.108717, 0.112557, 0.145554, ..., 0.155549, 0.176441, 0.112109]])

    • a
      (chain, draw, County)
      float64
      ...

      [170000 values with dtype=float64]

    • a_county
      (chain, draw, County)
      float64
      ...

      [170000 values with dtype=float64]

    • sigma
      (chain, draw)
      float64
      ...

      array([[0.727126, 0.716076, 0.718885, ..., 0.736988, 0.719409, 0.706907],
             [0.720298, 0.719041, 0.752979, ..., 0.722316, 0.714444, 0.740726],
             [0.712482, 0.727193, 0.752558, ..., 0.725702, 0.728779, 0.751825],
             [0.750239, 0.718825, 0.713519, ..., 0.718504, 0.72665 , 0.732404]])

  • Attributes: (6)

    created_at :

    2020-07-24T18:15:12.191355

    arviz_version :

    0.9.0

    inference_library :

    pymc3

    inference_library_version :

    3.9.2

    sampling_time :

    18.096983432769775

    tuning_steps :

    1000

  
  
• posterior_predictive

  <xarray.Dataset>
  Dimensions:  (chain: 4, draw: 500, obs_id: 919)
  Coordinates:
    * chain    (chain) int64 0 1 2 3
    * draw     (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499
    * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 911 912 913 914 915 916 917 918
  Data variables:
      y        (chain, draw, obs_id) float64 ...
  Attributes:
      created_at:                 2020-07-24T18:15:12.449843
      arviz_version:              0.9.0
      inference_library:          pymc3
      inference_library_version:  3.9.2

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • obs_id: 919
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • obs_id
      (obs_id)
      int64
      0 1 2 3 4 5 ... 914 915 916 917 918

      array([  0,   1,   2, ..., 916, 917, 918])

  • Data variables: (1)
    • y
      (chain, draw, obs_id)
      float64
      ...

      [1838000 values with dtype=float64]

  • Attributes: (4)

    created_at :

    2020-07-24T18:15:12.449843

    arviz_version :

    0.9.0

    inference_library :

    pymc3

    inference_library_version :

    3.9.2

  
  
• log_likelihood

  <xarray.Dataset>
  Dimensions:  (chain: 4, draw: 500, obs_id: 919)
  Coordinates:
    * chain    (chain) int64 0 1 2 3
    * draw     (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499
    * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 911 912 913 914 915 916 917 918
  Data variables:
      y        (chain, draw, obs_id) float64 ...
  Attributes:
      created_at:                 2020-07-24T18:15:12.448264
      arviz_version:              0.9.0
      inference_library:          pymc3
      inference_library_version:  3.9.2

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • obs_id: 919
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • obs_id
      (obs_id)
      int64
      0 1 2 3 4 5 ... 914 915 916 917 918

      array([  0,   1,   2, ..., 916, 917, 918])

  • Data variables: (1)
    • y
      (chain, draw, obs_id)
      float64
      ...

      [1838000 values with dtype=float64]

  • Attributes: (4)

    created_at :

    2020-07-24T18:15:12.448264

    arviz_version :

    0.9.0

    inference_library :

    pymc3

    inference_library_version :

    3.9.2

  
  
• sample_stats

  <xarray.Dataset>
  Dimensions:           (chain: 4, draw: 500)
  Coordinates:
    * chain             (chain) int64 0 1 2 3
    * draw              (draw) int64 0 1 2 3 4 5 6 ... 493 494 495 496 497 498 499
  Data variables:
      step_size_bar     (chain, draw) float64 0.1102 0.1102 ... 0.1193 0.1193
      diverging         (chain, draw) bool False False False ... False False False
      energy            (chain, draw) float64 1.186e+03 1.184e+03 ... 1.189e+03
      tree_size         (chain, draw) float64 31.0 31.0 31.0 ... 31.0 31.0 31.0
      mean_tree_accept  (chain, draw) float64 0.9877 0.9969 1.0 ... 0.9996 0.9872
      step_size         (chain, draw) float64 0.1006 0.1006 0.1006 ... 0.117 0.117
      depth             (chain, draw) int64 5 5 5 5 5 5 5 5 5 ... 5 5 5 5 5 5 5 5
      energy_error      (chain, draw) float64 0.0289 -0.02917 ... 0.04322
      lp                (chain, draw) float64 -1.145e+03 -1.133e+03 ... -1.152e+03
      max_energy_error  (chain, draw) float64 -0.05888 -0.07148 ... 0.04451
  Attributes:
      created_at:                 2020-07-24T18:15:12.197697
      arviz_version:              0.9.0
      inference_library:          pymc3
      inference_library_version:  3.9.2
      sampling_time:              18.096983432769775
      tuning_steps:               1000

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

  • Data variables: (10)
    • step_size_bar
      (chain, draw)
      float64
      ...

      array([[0.110248, 0.110248, 0.110248, ..., 0.110248, 0.110248, 0.110248],
             [0.114093, 0.114093, 0.114093, ..., 0.114093, 0.114093, 0.114093],
             [0.11341 , 0.11341 , 0.11341 , ..., 0.11341 , 0.11341 , 0.11341 ],
             [0.119259, 0.119259, 0.119259, ..., 0.119259, 0.119259, 0.119259]])

    • diverging
      (chain, draw)
      bool
      ...

      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)
      float64
      ...

      array([[1185.919383, 1184.077515, 1170.830539, ..., 1184.451872, 1199.60514 ,
              1189.923137],
             [1183.059106, 1196.320159, 1201.807046, ..., 1201.835304, 1174.293495,
              1196.067455],
             [1192.032734, 1195.659017, 1186.771536, ..., 1194.239956, 1182.508993,
              1180.396493],
             [1197.198321, 1192.578517, 1195.977774, ..., 1184.748321, 1188.757837,
              1188.921716]])

    • tree_size
      (chain, draw)
      float64
      ...

      array([[31., 31., 31., ..., 31., 31., 31.],
             [31., 31., 31., ..., 31., 31., 31.],
             [31., 31., 31., ..., 31., 31., 31.],
             [31., 31., 31., ..., 31., 31., 31.]])

    • mean_tree_accept
      (chain, draw)
      float64
      ...

      array([[0.987692, 0.99693 , 0.999999, ..., 0.97467 , 0.975585, 0.982974],
             [0.986198, 0.968969, 0.998852, ..., 0.994664, 0.999891, 0.961472],
             [0.976379, 0.986114, 0.995871, ..., 0.997253, 1.      , 0.97814 ],
             [0.998682, 0.999925, 0.999809, ..., 1.      , 0.999624, 0.98724 ]])

    • step_size
      (chain, draw)
      float64
      ...

      array([[0.100579, 0.100579, 0.100579, ..., 0.100579, 0.100579, 0.100579],
             [0.120178, 0.120178, 0.120178, ..., 0.120178, 0.120178, 0.120178],
             [0.124708, 0.124708, 0.124708, ..., 0.124708, 0.124708, 0.124708],
             [0.116962, 0.116962, 0.116962, ..., 0.116962, 0.116962, 0.116962]])

    • depth
      (chain, draw)
      int64
      ...

      array([[5, 5, 5, ..., 5, 5, 5],
             [5, 5, 5, ..., 5, 5, 5],
             [5, 5, 5, ..., 5, 5, 5],
             [5, 5, 5, ..., 5, 5, 5]])

    • energy_error
      (chain, draw)
      float64
      ...

      array([[ 0.028895, -0.02917 , -0.003673, ...,  0.025767,  0.003506,  0.034778],
             [ 0.038317,  0.073749, -0.042081, ..., -0.064664, -0.079109,  0.066645],
             [ 0.01635 ,  0.000573,  0.007805, ..., -0.038538, -0.05603 ,  0.027093],
             [ 0.003654, -0.002015, -0.038562, ..., -0.009363, -0.001725,  0.04322 ]])

    • lp
      (chain, draw)
      float64
      ...

      array([[-1145.248849, -1132.559558, -1134.092128, ..., -1143.267422,
              -1145.077319, -1145.200013],
             [-1145.855897, -1155.94913 , -1154.221723, ..., -1144.685294,
              -1137.303178, -1159.708401],
             [-1149.009952, -1149.862323, -1149.002544, ..., -1143.796115,
              -1135.566078, -1140.154244],
             [-1154.846199, -1152.166895, -1151.032285, ..., -1143.92768 ,
              -1146.221363, -1151.879718]])

    • max_energy_error
      (chain, draw)
      float64
      ...

      array([[-0.058878, -0.071482, -0.022817, ...,  0.050898,  0.056497,  0.067214],
             [-0.084359,  0.104906, -0.097824, ..., -0.096562, -0.15482 ,  0.094925],
             [ 0.049929,  0.049188,  0.012895, ..., -0.052203, -0.05603 ,  0.043076],
             [-0.068504, -0.081574, -0.055777, ..., -0.040145, -0.061979,  0.044507]])

  • Attributes: (6)

    created_at :

    2020-07-24T18:15:12.197697

    arviz_version :

    0.9.0

    inference_library :

    pymc3

    inference_library_version :

    3.9.2

    sampling_time :

    18.096983432769775

    tuning_steps :

    1000

  
  
• prior

  <xarray.Dataset>
  Dimensions:        (chain: 1, draw: 500, County: 85, uranium_coefs: 2)
  Coordinates:
    * chain          (chain) int64 0
    * draw           (draw) int64 0 1 2 3 4 5 6 7 ... 493 494 495 496 497 498 499
    * County         (County) object 'AITKIN' 'ANOKA' ... 'YELLOW MEDICINE'
    * uranium_coefs  (uranium_coefs) <U9 'intercept' 'u_slope'
  Data variables:
      a_county       (chain, draw, County) float64 8.536 5.285 ... 1.061 6.237
      sigma_log__    (chain, draw) float64 -0.9709 -1.344 ... -0.8501 -2.235
      sigma_a        (chain, draw) float64 2.991 2.237 0.3554 ... 0.4417 0.1448
      a              (chain, draw, County) float64 6.139 4.951 ... 0.9329 6.152
      b              (chain, draw) float64 0.5647 1.237 -0.6316 ... -0.01409 0.197
      za_county      (chain, draw, County) float64 0.8012 0.1114 ... 0.8862 0.5826
      sigma          (chain, draw) float64 0.3787 0.2608 0.6214 ... 0.4274 0.107
      g              (chain, draw, uranium_coefs) float64 11.31 7.504 ... 11.72
      sigma_a_log__  (chain, draw) float64 1.096 0.805 -1.035 ... -0.8171 -1.932
  Attributes:
      created_at:                 2020-07-24T18:15:12.454586
      arviz_version:              0.9.0
      inference_library:          pymc3
      inference_library_version:  3.9.2

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 500
    • County: 85
    • uranium_coefs: 2
  • Coordinates: (4)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • County
      (County)
      object
      'AITKIN' ... 'YELLOW MEDICINE'

      array(['AITKIN', 'ANOKA', 'BECKER', 'BELTRAMI', 'BENTON', 'BIG STONE',
             'BLUE EARTH', 'BROWN', 'CARLTON', 'CARVER', 'CASS', 'CHIPPEWA',
             'CHISAGO', 'CLAY', 'CLEARWATER', 'COOK', 'COTTONWOOD', 'CROW WING',
             'DAKOTA', 'DODGE', 'DOUGLAS', 'FARIBAULT', 'FILLMORE', 'FREEBORN',
             'GOODHUE', 'HENNEPIN', 'HOUSTON', 'HUBBARD', 'ISANTI', 'ITASCA',
             'JACKSON', 'KANABEC', 'KANDIYOHI', 'KITTSON', 'KOOCHICHING',
             'LAC QUI PARLE', 'LAKE', 'LAKE OF THE WOODS', 'LE SUEUR', 'LINCOLN',
             'LYON', 'MAHNOMEN', 'MARSHALL', 'MARTIN', 'MCLEOD', 'MEEKER',
             'MILLE LACS', 'MORRISON', 'MOWER', 'MURRAY', 'NICOLLET', 'NOBLES',
             'NORMAN', 'OLMSTED', 'OTTER TAIL', 'PENNINGTON', 'PINE', 'PIPESTONE',
             'POLK', 'POPE', 'RAMSEY', 'REDWOOD', 'RENVILLE', 'RICE', 'ROCK',
             'ROSEAU', 'SCOTT', 'SHERBURNE', 'SIBLEY', 'ST LOUIS', 'STEARNS',
             'STEELE', 'STEVENS', 'SWIFT', 'TODD', 'TRAVERSE', 'WABASHA', 'WADENA',
             'WASECA', 'WASHINGTON', 'WATONWAN', 'WILKIN', 'WINONA', 'WRIGHT',
             'YELLOW MEDICINE'], dtype=object)

    • uranium_coefs
      (uranium_coefs)
      <U9
      'intercept' 'u_slope'

      array(['intercept', 'u_slope'], dtype='<U9')

  • Data variables: (9)
    • a_county
      (chain, draw, County)
      float64
      ...

      array([[[ 8.535556,  5.284608, ..., 10.379827, 18.174108],
              [ 0.141016,  4.922292, ...,  3.12067 , -3.460489],
              ...,
              [-7.980271, -7.559327, ..., -6.51764 , -4.480575],
              [-5.985271, -8.07112 , ...,  1.061242,  6.236603]]])

    • sigma_log__
      (chain, draw)
      float64
      ...

      array([[-0.970883, -1.343955, -0.475785, ...,  0.087108, -0.850116, -2.235268]])

    • sigma_a
      (chain, draw)
      float64
      ...

      array([[2.991045, 2.236645, 0.355397, ..., 0.016371, 0.44173 , 0.144819]])

    • a
      (chain, draw, County)
      float64
      ...

      array([[[ 6.139055,  4.951408, ..., 10.634218, 13.975903],
              [ 3.408151,  4.36252 , ..., -0.204072, -2.889382],
              ...,
              [-7.399369, -7.84476 , ..., -5.713594, -4.460397],
              [-6.088037, -7.943006, ...,  0.932899,  6.152231]]])

    • b
      (chain, draw)
      float64
      ...

      array([[ 0.564689,  1.237345, -0.631597, ...,  0.050973, -0.014089,  0.197036]])

    • za_county
      (chain, draw, County)
      float64
      ...

      array([[[ 0.801225,  0.111399, ..., -0.085051,  1.403591],
              [-1.460731,  0.250273, ...,  1.486486, -0.255341],
              ...,
              [-1.315062,  0.646171, ..., -1.82022 , -0.045681],
              [ 0.709616, -0.884646, ...,  0.886228,  0.582599]]])

    • sigma
      (chain, draw)
      float64
      ...

      array([[0.378748, 0.260812, 0.621397, ..., 1.091014, 0.427366, 0.106963]])

    • g
      (chain, draw, uranium_coefs)
      float64
      ...

      array([[[11.309774,  7.504154],
              [-0.746935, -6.030187],
              ...,
              [-5.460247,  2.814206],
              [ 1.988041, 11.720638]]])

    • sigma_a_log__
      (chain, draw)
      float64
      ...

      array([[ 1.095623,  0.804977, -1.034521, ..., -4.112273, -0.817057, -1.93227 ]])

  • Attributes: (4)

    created_at :

    2020-07-24T18:15:12.454586

    arviz_version :

    0.9.0

    inference_library :

    pymc3

    inference_library_version :

    3.9.2

  
  
• prior_predictive

  <xarray.Dataset>
  Dimensions:  (chain: 1, draw: 500, obs_id: 919)
  Coordinates:
    * chain    (chain) int64 0
    * draw     (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499
    * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 911 912 913 914 915 916 917 918
  Data variables:
      y        (chain, draw, obs_id) float64 ...
  Attributes:
      created_at:                 2020-07-24T18:15:12.457652
      arviz_version:              0.9.0
      inference_library:          pymc3
      inference_library_version:  3.9.2

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 500
    • obs_id: 919
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • obs_id
      (obs_id)
      int64
      0 1 2 3 4 5 ... 914 915 916 917 918

      array([  0,   1,   2, ..., 916, 917, 918])

  • Data variables: (1)
    • y
      (chain, draw, obs_id)
      float64
      ...

      [459500 values with dtype=float64]

  • Attributes: (4)

    created_at :

    2020-07-24T18:15:12.457652

    arviz_version :

    0.9.0

    inference_library :

    pymc3

    inference_library_version :

    3.9.2

  
  
• observed_data

  <xarray.Dataset>
  Dimensions:  (obs_id: 919)
  Coordinates:
    * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 911 912 913 914 915 916 917 918
  Data variables:
      y        (obs_id) float64 0.8329 0.8329 1.099 0.09531 ... 1.629 1.335 1.099
  Attributes:
      created_at:                 2020-07-24T18:15:12.458415
      arviz_version:              0.9.0
      inference_library:          pymc3
      inference_library_version:  3.9.2

  xarray.Dataset

  • Dimensions:
    • obs_id: 919
  • Coordinates: (1)
    • obs_id
      (obs_id)
      int64
      0 1 2 3 4 5 ... 914 915 916 917 918

      array([  0,   1,   2, ..., 916, 917, 918])

  • Data variables: (1)
    • y
      (obs_id)
      float64
      ...

      array([0.832909, 0.832909, 1.098612, ..., 1.629241, 1.335001, 1.098612])

  • Attributes: (4)

    created_at :

    2020-07-24T18:15:12.458415

    arviz_version :

    0.9.0

    inference_library :

    pymc3

    inference_library_version :

    3.9.2

  
  
• constant_data

  <xarray.Dataset>
  Dimensions:     (obs_id: 919, County: 85)
  Coordinates:
    * obs_id      (obs_id) int64 0 1 2 3 4 5 6 7 ... 912 913 914 915 916 917 918
    * County      (County) object 'AITKIN' 'ANOKA' ... 'WRIGHT' 'YELLOW MEDICINE'
  Data variables:
      floor_idx   (obs_id) int32 1 0 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 1 0 0 0 0 0 0 0
      county_idx  (obs_id) int32 0 0 0 0 1 1 1 1 1 ... 83 83 83 83 83 83 83 84 84
      uranium     (County) float64 -0.689 -0.8473 -0.1135 ... -0.09002 0.3553
  Attributes:
      created_at:                 2020-07-24T18:15:12.459832
      arviz_version:              0.9.0
      inference_library:          pymc3
      inference_library_version:  3.9.2

  xarray.Dataset

  • Dimensions:
    • obs_id: 919
    • County: 85
  • Coordinates: (2)
    • obs_id
      (obs_id)
      int64
      0 1 2 3 4 5 ... 914 915 916 917 918

      array([  0,   1,   2, ..., 916, 917, 918])

    • County
      (County)
      object
      'AITKIN' ... 'YELLOW MEDICINE'

      array(['AITKIN', 'ANOKA', 'BECKER', 'BELTRAMI', 'BENTON', 'BIG STONE',
             'BLUE EARTH', 'BROWN', 'CARLTON', 'CARVER', 'CASS', 'CHIPPEWA',
             'CHISAGO', 'CLAY', 'CLEARWATER', 'COOK', 'COTTONWOOD', 'CROW WING',
             'DAKOTA', 'DODGE', 'DOUGLAS', 'FARIBAULT', 'FILLMORE', 'FREEBORN',
             'GOODHUE', 'HENNEPIN', 'HOUSTON', 'HUBBARD', 'ISANTI', 'ITASCA',
             'JACKSON', 'KANABEC', 'KANDIYOHI', 'KITTSON', 'KOOCHICHING',
             'LAC QUI PARLE', 'LAKE', 'LAKE OF THE WOODS', 'LE SUEUR', 'LINCOLN',
             'LYON', 'MAHNOMEN', 'MARSHALL', 'MARTIN', 'MCLEOD', 'MEEKER',
             'MILLE LACS', 'MORRISON', 'MOWER', 'MURRAY', 'NICOLLET', 'NOBLES',
             'NORMAN', 'OLMSTED', 'OTTER TAIL', 'PENNINGTON', 'PINE', 'PIPESTONE',
             'POLK', 'POPE', 'RAMSEY', 'REDWOOD', 'RENVILLE', 'RICE', 'ROCK',
             'ROSEAU', 'SCOTT', 'SHERBURNE', 'SIBLEY', 'ST LOUIS', 'STEARNS',
             'STEELE', 'STEVENS', 'SWIFT', 'TODD', 'TRAVERSE', 'WABASHA', 'WADENA',
             'WASECA', 'WASHINGTON', 'WATONWAN', 'WILKIN', 'WINONA', 'WRIGHT',
             'YELLOW MEDICINE'], dtype=object)

  • Data variables: (3)
    • floor_idx
      (obs_id)
      int32
      ...

      array([1, 0, 0, ..., 0, 0, 0], dtype=int32)

    • county_idx
      (obs_id)
      int32
      ...

      array([ 0,  0,  0, ..., 83, 84, 84], dtype=int32)

    • uranium
      (County)
      float64
      ...

      array([-0.689048, -0.847313, -0.113459, -0.593353, -0.14289 ,  0.387057,
              0.271614,  0.277579, -0.332315,  0.095865, -0.60822 ,  0.273685,
             -0.73532 ,  0.343781, -0.05986 , -0.504996,  0.33956 , -0.633391,
             -0.024145,  0.263855,  0.155712,  0.295025,  0.414914,  0.224207,
              0.196611, -0.096521,  0.503529, -0.400597, -0.751872, -0.663348,
              0.30902 , -0.053386,  0.109733, -0.007803, -0.881829,  0.31103 ,
             -0.691596, -0.681709,  0.194448,  0.444904,  0.394734,  0.1496  ,
              0.013765,  0.165862,  0.140423,  0.023951, -0.21006 , -0.093227,
              0.260932,  0.39885 ,  0.248047,  0.405452,  0.265222,  0.24315 ,
             -0.20473 , -0.074028, -0.163292,  0.478604,  0.266111,  0.281148,
             -0.418054,  0.366322,  0.380578,  0.193146,  0.528025, -0.212045,
              0.063116, -0.683436,  0.237212, -0.474674,  0.116395,  0.269806,
              0.470778,  0.316029, -0.04684 ,  0.497594,  0.150082, -0.67203 ,
              0.212414, -0.147484,  0.183238,  0.236036,  0.463212, -0.090024,
              0.355287])

  • Attributes: (4)

    created_at :

    2020-07-24T18:15:12.459832

    arviz_version :

    0.9.0

    inference_library :

    pymc3

    inference_library_version :

    3.9.2

  
  

Add extra coordinates to all groups containing observed variables

idata = az.load_arviz_data("rugby")
home_team, away_team = np.array([
    m.split() for m in idata.observed_data.match.values
]).T
idata = idata.map(
    lambda ds, **kwargs: ds.assign_coords(**kwargs),
    groups="observed_vars",
    home_team=("match", home_team),
    away_team=("match", away_team),
)
idata

arviz.InferenceData

• posterior

  <xarray.Dataset>
  Dimensions:    (chain: 4, draw: 500, team: 6)
  Coordinates:
    * chain      (chain) int64 0 1 2 3
    * draw       (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499
    * team       (team) object 'Wales' 'France' 'Ireland' ... 'Italy' 'England'
  Data variables:
      home       (chain, draw) float64 0.1642 0.1162 0.09299 ... 0.148 0.2265
      intercept  (chain, draw) float64 2.893 2.941 2.939 ... 2.951 2.903 2.892
      atts_star  (chain, draw, team) float64 0.1673 0.04184 ... -0.4652 0.02878
      defs_star  (chain, draw, team) float64 -0.03638 -0.04109 ... 0.7136 -0.0649
      sd_att     (chain, draw) float64 0.4854 0.1438 0.2139 ... 0.2883 0.4591
      sd_def     (chain, draw) float64 0.2747 1.033 0.6363 ... 0.5574 0.2849
      atts       (chain, draw, team) float64 0.1063 -0.01913 ... -0.2911 0.2029
      defs       (chain, draw, team) float64 -0.06765 -0.07235 ... 0.5799 -0.1986
  Attributes:
      created_at:                 2019-07-12T20:31:53.545143
      inference_library:          pymc3
      inference_library_version:  3.7

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • team: 6
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • team
      (team)
      object
      'Wales' 'France' ... 'England'

      array(['Wales', 'France', 'Ireland', 'Scotland', 'Italy', 'England'],
            dtype=object)

  • Data variables: (8)
    • home
      (chain, draw)
      float64
      ...

      array([[0.164161, 0.116153, 0.092994, ..., 0.214051, 0.072698, 0.082984],
             [0.15806 , 0.160676, 0.15073 , ..., 0.223864, 0.212598, 0.233929],
             [0.141884, 0.141949, 0.15516 , ..., 0.135413, 0.13054 , 0.112781],
             [0.195016, 0.057941, 0.147605, ..., 0.145207, 0.147984, 0.22647 ]])

    • intercept
      (chain, draw)
      float64
      ...

      array([[2.892979, 2.941319, 2.939326, ..., 2.886779, 2.963654, 2.963762],
             [2.876342, 2.951752, 2.915163, ..., 2.839776, 2.879831, 2.877929],
             [2.925151, 2.926391, 2.885594, ..., 2.915365, 2.923843, 2.965493],
             [2.891176, 2.964279, 2.942421, ..., 2.950802, 2.90315 , 2.892364]])

    • atts_star
      (chain, draw, team)
      float64
      ...

      array([[[ 0.167295,  0.041845, ..., -0.399867,  0.365447],
              [ 0.225956, -0.010611, ..., -0.299899,  0.298631],
              ...,
              [ 0.049192, -0.181591, ..., -0.31246 ,  0.159274],
              [ 0.106038, -0.122857, ..., -0.361424,  0.112585]],
      
             [[ 0.485254,  0.212672, ..., -0.220226,  0.526561],
              [ 0.297627,  0.147604, ..., -0.158775,  0.388227],
              ...,
              [ 0.14273 ,  0.05296 , ..., -0.188875,  0.307996],
              [ 0.336067,  0.0194  , ..., -0.314777,  0.34282 ]],
      
             [[ 0.287279,  0.061858, ..., -0.158301,  0.384035],
              [ 0.381883,  0.030331, ..., -0.222792,  0.386507],
              ...,
              [ 0.198707, -0.009448, ..., -0.293566,  0.300091],
              [ 0.257041,  0.004626, ..., -0.331588,  0.258708]],
      
             [[ 0.146666,  0.061486, ..., -0.280336,  0.154532],
              [ 0.208815, -0.09584 , ..., -0.416475,  0.283097],
              ...,
              [-0.15318 , -0.364549, ..., -0.680705, -0.010129],
              [ 0.043951, -0.288028, ..., -0.465197,  0.028782]]])

    • defs_star
      (chain, draw, team)
      float64
      ...

      array([[[-0.03638 , -0.041086, ...,  0.584928, -0.189714],
              [ 0.016886,  0.182324, ...,  0.778653, -0.052074],
              ...,
              [ 0.072459,  0.163862, ...,  0.833056, -0.047742],
              [ 0.138345,  0.113047, ...,  0.822887, -0.034236]],
      
             [[-0.140504, -0.042564, ...,  0.626642, -0.117471],
              [-0.490723, -0.244406, ...,  0.31501 , -0.382403],
              ...,
              [-0.249843, -0.146006, ...,  0.496428, -0.287326],
              [-0.194958, -0.080926, ...,  0.470339, -0.279154]],
      
             [[-0.185428, -0.098863, ...,  0.512546, -0.247842],
              [-0.247562, -0.163494, ...,  0.51405 , -0.31746 ],
              ...,
              [-0.187025, -0.058429, ...,  0.452229, -0.232257],
              [-0.222536, -0.134085, ...,  0.341259, -0.345908]],
      
             [[ 0.001567,  0.15085 , ...,  0.808143, -0.034143],
              [-0.169989, -0.057984, ...,  0.563197, -0.222999],
              ...,
              [-0.047669,  0.157389, ...,  0.676568, -0.063255],
              [ 0.084996,  0.011842, ...,  0.713593, -0.064897]]])

    • sd_att
      (chain, draw)
      float64
      ...

      array([[0.485359, 0.14382 , 0.213867, ..., 0.440261, 0.16548 , 0.181004],
             [0.258151, 0.193417, 0.309057, ..., 0.296865, 0.25503 , 0.266773],
             [0.213465, 0.207954, 0.26893 , ..., 0.460579, 0.13788 , 0.453573],
             [0.131209, 0.528685, 0.245339, ..., 0.44718 , 0.288321, 0.459119]])

    • sd_def
      (chain, draw)
      float64
      ...

      array([[0.274656, 1.032653, 0.636286, ..., 0.409115, 0.522454, 0.394847],
             [0.232875, 0.469776, 0.593915, ..., 0.299503, 0.755438, 0.329001],
             [0.338346, 0.371307, 0.404925, ..., 0.559502, 0.914684, 0.243773],
             [0.336731, 0.369357, 0.283272, ..., 0.329351, 0.55741 , 0.284901]])

    • atts
      (chain, draw, team)
      float64
      ...

      array([[[ 0.106324, -0.019126, ..., -0.460838,  0.304476],
              [ 0.153829, -0.082737, ..., -0.372026,  0.226504],
              ...,
              [ 0.111329, -0.119454, ..., -0.250323,  0.221411],
              [ 0.150596, -0.0783  , ..., -0.316866,  0.157143]],
      
             [[ 0.247005, -0.025577, ..., -0.458475,  0.288312],
              [ 0.13158 , -0.018443, ..., -0.324822,  0.22218 ],
              ...,
              [ 0.065695, -0.024075, ..., -0.26591 ,  0.230961],
              [ 0.261962, -0.054704, ..., -0.388882,  0.268715]],
      
             [[ 0.139701, -0.085719, ..., -0.305878,  0.236458],
              [ 0.219363, -0.132189, ..., -0.385312,  0.223987],
              ...,
              [ 0.134559, -0.073595, ..., -0.357713,  0.235944],
              [ 0.189046, -0.063368, ..., -0.399582,  0.190714]],
      
             [[ 0.122362,  0.037181, ..., -0.304641,  0.130227],
              [ 0.221016, -0.083638, ..., -0.404273,  0.295298],
              ...,
              [ 0.149276, -0.062092, ..., -0.378249,  0.292327],
              [ 0.218036, -0.113943, ..., -0.291112,  0.202867]]])

    • defs
      (chain, draw, team)
      float64
      ...

      array([[[-0.067649, -0.072355, ...,  0.553659, -0.220983],
              [-0.179218, -0.013781, ...,  0.582549, -0.248178],
              ...,
              [-0.126842, -0.035439, ...,  0.633755, -0.247043],
              [-0.067536, -0.092833, ...,  0.617006, -0.240117]],
      
             [[-0.176185, -0.078245, ...,  0.590961, -0.153152],
              [-0.223863,  0.022454, ...,  0.58187 , -0.115543],
              ...,
              [-0.127986, -0.02415 , ...,  0.618285, -0.165469],
              [-0.121789, -0.007756, ...,  0.543508, -0.205984]],
      
             [[-0.105583, -0.019018, ...,  0.59239 , -0.167997],
              [-0.147452, -0.063383, ...,  0.61416 , -0.217349],
              ...,
              [-0.122697,  0.005899, ...,  0.516557, -0.167929],
              [-0.061287,  0.027163, ...,  0.502507, -0.18466 ]],
      
             [[-0.167655, -0.018371, ...,  0.638922, -0.203364],
              [-0.141152, -0.029146, ...,  0.592034, -0.194161],
              ...,
              [-0.187728,  0.01733 , ...,  0.536509, -0.203314],
              [-0.048666, -0.121819, ...,  0.579931, -0.198558]]])

  • Attributes: (3)

    created_at :

    2019-07-12T20:31:53.545143

    inference_library :

    pymc3

    inference_library_version :

    3.7

  
  
• posterior_predictive

  <xarray.Dataset>
  Dimensions:      (chain: 4, draw: 500, match: 60)
  Coordinates:
    * chain        (chain) int64 0 1 2 3
    * draw         (draw) int64 0 1 2 3 4 5 6 7 ... 493 494 495 496 497 498 499
    * match        (match) object 'Wales Italy' ... 'Ireland England'
      home_team    (match) <U8 'Wales' 'France' 'Ireland' ... 'France' 'Ireland'
      away_team    (match) <U8 'Italy' 'England' 'Scotland' ... 'Wales' 'England'
  Data variables:
      home_points  (chain, draw, match) int64 ...
      away_points  (chain, draw, match) int64 ...
  Attributes:
      created_at:                 2019-07-12T20:31:53.563854
      inference_library:          pymc3
      inference_library_version:  3.7

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • match: 60
  • Coordinates: (5)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • match
      (match)
      object
      'Wales Italy' ... 'Ireland England'

      array(['Wales Italy', 'France England', 'Ireland Scotland', 'Ireland Wales',
             'Scotland England', 'France Italy', 'Wales France', 'Italy Scotland',
             'England Ireland', 'Ireland Italy', 'Scotland France', 'England Wales',
             'Italy England', 'Wales Scotland', 'France Ireland', 'Wales England',
             'Italy Ireland', 'France Scotland', 'England Italy', 'Ireland France',
             'Scotland Wales', 'Scotland Italy', 'France Wales', 'Ireland England',
             'Wales Ireland', 'England Scotland', 'Italy France', 'Italy Wales',
             'Scotland Ireland', 'England France', 'France Italy',
             'Scotland England', 'Ireland Wales', 'France Ireland', 'Wales Scotland',
             'Italy England', 'Wales France', 'Italy Scotland', 'England Ireland',
             'Ireland Italy', 'England Wales', 'Scotland France', 'Wales Italy',
             'Ireland Scotland', 'France England', 'Scotland Ireland',
             'England France', 'Italy Wales', 'Italy Ireland', 'Wales England',
             'France Scotland', 'Scotland Wales', 'Ireland France', 'England Italy',
             'Wales Ireland', 'Italy France', 'England Scotland', 'Scotland Italy',
             'France Wales', 'Ireland England'], dtype=object)

    • home_team
      (match)
      <U8
      'Wales' 'France' ... 'Ireland'

      array(['Wales', 'France', 'Ireland', 'Ireland', 'Scotland', 'France',
             'Wales', 'Italy', 'England', 'Ireland', 'Scotland', 'England',
             'Italy', 'Wales', 'France', 'Wales', 'Italy', 'France', 'England',
             'Ireland', 'Scotland', 'Scotland', 'France', 'Ireland', 'Wales',
             'England', 'Italy', 'Italy', 'Scotland', 'England', 'France',
             'Scotland', 'Ireland', 'France', 'Wales', 'Italy', 'Wales',
             'Italy', 'England', 'Ireland', 'England', 'Scotland', 'Wales',
             'Ireland', 'France', 'Scotland', 'England', 'Italy', 'Italy',
             'Wales', 'France', 'Scotland', 'Ireland', 'England', 'Wales',
             'Italy', 'England', 'Scotland', 'France', 'Ireland'], dtype='<U8')

    • away_team
      (match)
      <U8
      'Italy' 'England' ... 'England'

      array(['Italy', 'England', 'Scotland', 'Wales', 'England', 'Italy',
             'France', 'Scotland', 'Ireland', 'Italy', 'France', 'Wales',
             'England', 'Scotland', 'Ireland', 'England', 'Ireland', 'Scotland',
             'Italy', 'France', 'Wales', 'Italy', 'Wales', 'England', 'Ireland',
             'Scotland', 'France', 'Wales', 'Ireland', 'France', 'Italy',
             'England', 'Wales', 'Ireland', 'Scotland', 'England', 'France',
             'Scotland', 'Ireland', 'Italy', 'Wales', 'France', 'Italy',
             'Scotland', 'England', 'Ireland', 'France', 'Wales', 'Ireland',
             'England', 'Scotland', 'Wales', 'France', 'Italy', 'Ireland',
             'France', 'Scotland', 'Italy', 'Wales', 'England'], dtype='<U8')

  • Data variables: (2)
    • home_points
      (chain, draw, match)
      int64
      ...

      [120000 values with dtype=int64]

    • away_points
      (chain, draw, match)
      int64
      ...

      [120000 values with dtype=int64]

  • Attributes: (3)

    created_at :

    2019-07-12T20:31:53.563854

    inference_library :

    pymc3

    inference_library_version :

    3.7

  
  
• sample_stats

  <xarray.Dataset>
  Dimensions:           (chain: 4, draw: 500)
  Coordinates:
    * chain             (chain) int64 0 1 2 3
    * draw              (draw) int64 0 1 2 3 4 5 6 ... 493 494 495 496 497 498 499
  Data variables:
      energy_error      (chain, draw) float64 -0.07666 -0.4523 ... 0.115 -0.07691
      energy            (chain, draw) float64 540.2 545.3 542.3 ... 544.0 545.6
      tree_size         (chain, draw) float64 15.0 63.0 31.0 ... 63.0 31.0 31.0
      tune              (chain, draw) bool True False False ... False False False
      mean_tree_accept  (chain, draw) float64 1.0 0.8851 0.8875 ... 0.7791 0.7539
      lp                (chain, draw) float64 -536.4 -536.0 ... -536.1 -536.4
      depth             (chain, draw) int64 4 6 5 4 4 4 5 5 5 ... 6 4 6 5 3 6 5 5
      max_energy_error  (chain, draw) float64 -0.5361 -0.5871 ... 0.7109 1.014
      step_size         (chain, draw) float64 0.2469 0.2469 ... 0.2459 0.2459
      step_size_bar     (chain, draw) float64 0.2313 0.2313 ... 0.2488 0.2488
      diverging         (chain, draw) bool False False False ... False False False
  Attributes:
      created_at:                 2019-07-12T20:31:53.555203
      inference_library:          pymc3
      inference_library_version:  3.7

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

  • Data variables: (11)
    • energy_error
      (chain, draw)
      float64
      ...

      array([[-0.076655, -0.45233 ,  0.225407, ...,  0.333968, -0.068296,  0.493063],
             [ 0.014834,  0.142365,  0.067541, ..., -0.427857, -0.344963,  0.303286],
             [-0.106168,  0.592308,  0.412017, ...,  1.01555 , -0.166712,  0.635391],
             [ 0.145159, -1.081507,  0.040228, ...,  0.105551,  0.115021, -0.076914]])

    • energy
      (chain, draw)
      float64
      ...

      array([[540.221904, 545.262322, 542.285897, ..., 548.532014, 540.720807,
              551.425367],
             [545.24547 , 546.673316, 546.396987, ..., 546.77714 , 545.57127 ,
              546.292385],
             [540.880498, 543.057444, 547.080365, ..., 545.277491, 543.372405,
              545.729314],
             [547.11624 , 543.897897, 542.221528, ..., 543.992174, 544.025085,
              545.587116]])

    • tree_size
      (chain, draw)
      float64
      ...

      array([[15., 63., 31., ..., 63., 15., 15.],
             [23., 63., 63., ..., 31., 31., 15.],
             [63.,  7., 23., ..., 15., 15., 31.],
             [31., 15., 15., ..., 63., 31., 31.]])

    • tune
      (chain, draw)
      bool
      ...

      array([[ True, False, False, ..., False, False, False],
             [ True, False, False, ..., False, False, False],
             [ True, False, False, ..., False, False, False],
             [ True, False, False, ..., False, False, False]])

    • mean_tree_accept
      (chain, draw)
      float64
      ...

      array([[1.      , 0.885101, 0.887543, ..., 0.342066, 0.972386, 0.661149],
             [0.55958 , 0.880434, 0.816291, ..., 0.988092, 0.917685, 0.827569],
             [0.872701, 0.392872, 0.807609, ..., 0.309044, 0.991352, 0.71033 ],
             [0.827102, 0.974503, 0.745041, ..., 0.956577, 0.77911 , 0.753853]])

    • lp
      (chain, draw)
      float64
      ...

      array([[-536.351407, -536.012813, -533.757274, ..., -535.648849, -535.859232,
              -537.5678  ],
             [-538.151681, -537.516214, -536.01874 , ..., -538.701921, -536.751107,
              -536.932902],
             [-531.394378, -537.273471, -540.626811, ..., -535.275807, -536.616406,
              -541.01812 ],
             [-538.057028, -534.970676, -531.13036 , ..., -536.000292, -536.122958,
              -536.369149]])

    • depth
      (chain, draw)
      int64
      ...

      array([[4, 6, 5, ..., 6, 4, 4],
             [5, 6, 6, ..., 5, 5, 4],
             [6, 3, 5, ..., 4, 4, 5],
             [5, 4, 4, ..., 6, 5, 5]])

    • max_energy_error
      (chain, draw)
      float64
      ...

      array([[-0.53611 , -0.587084,  0.398083, ...,  2.531672, -0.466122,  1.197046],
             [ 1.710848,  0.468178,  0.822984, ..., -1.09541 , -0.494912,  0.578139],
             [ 0.57202 ,  1.33828 ,  0.772054, ...,  2.222766, -0.941677,  1.640272],
             [ 0.655216, -1.081507,  0.7934  , ...,  0.338782,  0.710941,  1.013586]])

    • step_size
      (chain, draw)
      float64
      ...

      array([[0.246893, 0.246893, 0.246893, ..., 0.246893, 0.246893, 0.246893],
             [0.181178, 0.181178, 0.181178, ..., 0.181178, 0.181178, 0.181178],
             [0.186982, 0.186982, 0.186982, ..., 0.186982, 0.186982, 0.186982],
             [0.245945, 0.245945, 0.245945, ..., 0.245945, 0.245945, 0.245945]])

    • step_size_bar
      (chain, draw)
      float64
      ...

      array([[0.231272, 0.231272, 0.231272, ..., 0.231272, 0.231272, 0.231272],
             [0.170199, 0.170199, 0.170199, ..., 0.170199, 0.170199, 0.170199],
             [0.203328, 0.203328, 0.203328, ..., 0.203328, 0.203328, 0.203328],
             [0.248831, 0.248831, 0.248831, ..., 0.248831, 0.248831, 0.248831]])

    • diverging
      (chain, draw)
      bool
      ...

      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]])

  • Attributes: (3)

    created_at :

    2019-07-12T20:31:53.555203

    inference_library :

    pymc3

    inference_library_version :

    3.7

  
  
• prior

  <xarray.Dataset>
  Dimensions:       (chain: 1, draw: 500, team: 6, match: 60)
  Coordinates:
    * chain         (chain) int64 0
    * draw          (draw) int64 0 1 2 3 4 5 6 7 ... 493 494 495 496 497 498 499
    * team          (team) object 'Wales' 'France' 'Ireland' ... 'Italy' 'England'
    * match         (match) object 'Wales Italy' ... 'Ireland England'
  Data variables:
      sd_att_log__  (chain, draw) float64 1.322 -2.014 1.588 ... -0.8585 -0.1922
      intercept     (chain, draw) float64 4.464 3.352 1.567 ... 4.363 4.128 1.049
      atts_star     (chain, draw, team) float64 -2.64 4.172 ... -0.2874 -0.8538
      defs_star     (chain, draw, team) float64 -0.7817 -0.1478 ... 0.1655 0.01067
      away_points   (chain, draw, match) int64 11308 0 11 1 0 21442 ... 11 1 2 2 0
      sd_att        (chain, draw) float64 3.752 0.1334 4.896 ... 0.4238 0.8251
      sd_def_log__  (chain, draw) float64 -0.2662 0.2411 0.6071 ... 1.402 -1.981
      home          (chain, draw) float64 -1.511 -0.001582 ... -0.02416 0.2651
      atts          (chain, draw, team) float64 -4.667 2.145 ... -0.2702 -0.8365
      sd_def        (chain, draw) float64 0.7663 1.273 1.835 ... 3.922 4.063 0.138
      home_points   (chain, draw, match) int64 0 47 11899 3262 1 ... 3 2 1 12 13
      defs          (chain, draw, team) float64 -0.2517 0.3823 ... 0.089 -0.06586
  Attributes:
      created_at:                 2019-07-12T20:31:53.573731
      inference_library:          pymc3
      inference_library_version:  3.7

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 500
    • team: 6
    • match: 60
  • Coordinates: (4)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • team
      (team)
      object
      'Wales' 'France' ... 'England'

      array(['Wales', 'France', 'Ireland', 'Scotland', 'Italy', 'England'],
            dtype=object)

    • match
      (match)
      object
      'Wales Italy' ... 'Ireland England'

      array(['Wales Italy', 'France England', 'Ireland Scotland', 'Ireland Wales',
             'Scotland England', 'France Italy', 'Wales France', 'Italy Scotland',
             'England Ireland', 'Ireland Italy', 'Scotland France', 'England Wales',
             'Italy England', 'Wales Scotland', 'France Ireland', 'Wales England',
             'Italy Ireland', 'France Scotland', 'England Italy', 'Ireland France',
             'Scotland Wales', 'Scotland Italy', 'France Wales', 'Ireland England',
             'Wales Ireland', 'England Scotland', 'Italy France', 'Italy Wales',
             'Scotland Ireland', 'England France', 'France Italy',
             'Scotland England', 'Ireland Wales', 'France Ireland', 'Wales Scotland',
             'Italy England', 'Wales France', 'Italy Scotland', 'England Ireland',
             'Ireland Italy', 'England Wales', 'Scotland France', 'Wales Italy',
             'Ireland Scotland', 'France England', 'Scotland Ireland',
             'England France', 'Italy Wales', 'Italy Ireland', 'Wales England',
             'France Scotland', 'Scotland Wales', 'Ireland France', 'England Italy',
             'Wales Ireland', 'Italy France', 'England Scotland', 'Scotland Italy',
             'France Wales', 'Ireland England'], dtype=object)

  • Data variables: (12)
    • sd_att_log__
      (chain, draw)
      float64
      ...

      array([[ 1.322372, -2.014126,  1.588406, ...,  0.797415, -0.858474, -0.192244]])

    • intercept
      (chain, draw)
      float64
      ...

      array([[4.464075, 3.352013, 1.56735 , ..., 4.36349 , 4.128357, 1.04875 ]])

    • atts_star
      (chain, draw, team)
      float64
      ...

      array([[[-2.639728,  4.17221 , ...,  7.157236, -3.797814],
              [-0.049678,  0.024149, ..., -0.2262  , -0.025755],
              ...,
              [ 0.457378,  0.132317, ..., -0.007425, -0.017128],
              [-0.056827,  0.703097, ..., -0.28743 , -0.853817]]])

    • defs_star
      (chain, draw, team)
      float64
      ...

      array([[[-0.781698, -0.147788, ..., -0.60283 , -1.730481],
              [ 0.915138, -0.860825, ..., -0.777608,  0.242252],
              ...,
              [-5.951886, -0.971664, ..., -3.886546, -1.922478],
              [ 0.291683, -0.139104, ...,  0.16553 ,  0.010672]]])

    • away_points
      (chain, draw, match)
      int64
      ...

      array([[[11308,     0, ...,     3,     0],
              [   61,    11, ...,    18,    34],
              ...,
              [    1,   111, ...,   171,   259],
              [    2,     0, ...,     2,     0]]])

    • sd_att
      (chain, draw)
      float64
      ...

      array([[3.752311, 0.133437, 4.895938, ..., 2.219795, 0.423808, 0.825106]])

    • sd_def_log__
      (chain, draw)
      float64
      ...

      array([[-0.266231,  0.241119,  0.607108, ...,  1.366511,  1.401933, -1.9808  ]])

    • home
      (chain, draw)
      float64
      ...

      array([[-1.511038e+00, -1.582147e-03,  1.749661e+00, ..., -3.357659e-01,
              -2.415969e-02,  2.650645e-01]])

    • atts
      (chain, draw, team)
      float64
      ...

      array([[[-4.667414,  2.144524, ...,  5.12955 , -5.8255  ],
              [ 0.036528,  0.110355, ..., -0.139994,  0.060451],
              ...,
              [ 0.294725, -0.030336, ..., -0.170078, -0.179781],
              [-0.03956 ,  0.720365, ..., -0.270163, -0.83655 ]]])

    • sd_def
      (chain, draw)
      float64
      ...

      array([[0.766262, 1.272673, 1.835117, ..., 3.921644, 4.063046, 0.137959]])

    • home_points
      (chain, draw, match)
      int64
      ...

      array([[[   0,   47, ...,  122, 1280],
              [  16,   27, ...,  103,   45],
              ...,
              [   9,   53, ...,    1,   71],
              [   2,    9, ...,   12,   13]]])

    • defs
      (chain, draw, team)
      float64
      ...

      array([[[-0.251656,  0.382255, ..., -0.072787, -1.200439],
              [ 0.888674, -0.887289, ..., -0.804072,  0.215788],
              ...,
              [-4.183837,  0.796386, ..., -2.118497, -0.154428],
              [ 0.215149, -0.215638, ...,  0.088996, -0.065862]]])

  • Attributes: (3)

    created_at :

    2019-07-12T20:31:53.573731

    inference_library :

    pymc3

    inference_library_version :

    3.7

  
  
• observed_data

  <xarray.Dataset>
  Dimensions:      (match: 60)
  Coordinates:
    * match        (match) object 'Wales Italy' ... 'Ireland England'
      home_team    (match) <U8 'Wales' 'France' 'Ireland' ... 'France' 'Ireland'
      away_team    (match) <U8 'Italy' 'England' 'Scotland' ... 'Wales' 'England'
  Data variables:
      home_points  (match) float64 23.0 26.0 28.0 26.0 0.0 ... 61.0 29.0 20.0 13.0
      away_points  (match) float64 15.0 24.0 6.0 3.0 20.0 ... 21.0 0.0 18.0 9.0
  Attributes:
      created_at:                 2019-07-12T20:31:53.581293
      inference_library:          pymc3
      inference_library_version:  3.7

  xarray.Dataset

  • Dimensions:
    • match: 60
  • Coordinates: (3)
    • match
      (match)
      object
      'Wales Italy' ... 'Ireland England'

      array(['Wales Italy', 'France England', 'Ireland Scotland', 'Ireland Wales',
             'Scotland England', 'France Italy', 'Wales France', 'Italy Scotland',
             'England Ireland', 'Ireland Italy', 'Scotland France', 'England Wales',
             'Italy England', 'Wales Scotland', 'France Ireland', 'Wales England',
             'Italy Ireland', 'France Scotland', 'England Italy', 'Ireland France',
             'Scotland Wales', 'Scotland Italy', 'France Wales', 'Ireland England',
             'Wales Ireland', 'England Scotland', 'Italy France', 'Italy Wales',
             'Scotland Ireland', 'England France', 'France Italy',
             'Scotland England', 'Ireland Wales', 'France Ireland', 'Wales Scotland',
             'Italy England', 'Wales France', 'Italy Scotland', 'England Ireland',
             'Ireland Italy', 'England Wales', 'Scotland France', 'Wales Italy',
             'Ireland Scotland', 'France England', 'Scotland Ireland',
             'England France', 'Italy Wales', 'Italy Ireland', 'Wales England',
             'France Scotland', 'Scotland Wales', 'Ireland France', 'England Italy',
             'Wales Ireland', 'Italy France', 'England Scotland', 'Scotland Italy',
             'France Wales', 'Ireland England'], dtype=object)

    • home_team
      (match)
      <U8
      'Wales' 'France' ... 'Ireland'

      array(['Wales', 'France', 'Ireland', 'Ireland', 'Scotland', 'France',
             'Wales', 'Italy', 'England', 'Ireland', 'Scotland', 'England',
             'Italy', 'Wales', 'France', 'Wales', 'Italy', 'France', 'England',
             'Ireland', 'Scotland', 'Scotland', 'France', 'Ireland', 'Wales',
             'England', 'Italy', 'Italy', 'Scotland', 'England', 'France',
             'Scotland', 'Ireland', 'France', 'Wales', 'Italy', 'Wales',
             'Italy', 'England', 'Ireland', 'England', 'Scotland', 'Wales',
             'Ireland', 'France', 'Scotland', 'England', 'Italy', 'Italy',
             'Wales', 'France', 'Scotland', 'Ireland', 'England', 'Wales',
             'Italy', 'England', 'Scotland', 'France', 'Ireland'], dtype='<U8')

    • away_team
      (match)
      <U8
      'Italy' 'England' ... 'England'

      array(['Italy', 'England', 'Scotland', 'Wales', 'England', 'Italy',
             'France', 'Scotland', 'Ireland', 'Italy', 'France', 'Wales',
             'England', 'Scotland', 'Ireland', 'England', 'Ireland', 'Scotland',
             'Italy', 'France', 'Wales', 'Italy', 'Wales', 'England', 'Ireland',
             'Scotland', 'France', 'Wales', 'Ireland', 'France', 'Italy',
             'England', 'Wales', 'Ireland', 'Scotland', 'England', 'France',
             'Scotland', 'Ireland', 'Italy', 'Wales', 'France', 'Italy',
             'Scotland', 'England', 'Ireland', 'France', 'Wales', 'Ireland',
             'England', 'Scotland', 'Wales', 'France', 'Italy', 'Ireland',
             'France', 'Scotland', 'Italy', 'Wales', 'England'], dtype='<U8')

  • Data variables: (2)
    • home_points
      (match)
      float64
      ...

      array([23., 26., 28., 26.,  0., 30., 27., 20., 13., 46., 17., 29., 11., 51.,
             20., 16.,  3., 15., 47., 18., 23., 19., 13., 19., 23., 25.,  0., 20.,
             10., 55., 23.,  9., 16., 10., 27.,  9., 19., 20., 21., 58., 25., 29.,
             67., 35., 21., 27., 19.,  7., 10., 16., 22., 29., 19., 36., 22., 18.,
             61., 29., 20., 13.])

    • away_points
      (match)
      float64
      ...

      array([15., 24.,  6.,  3., 20., 10.,  6., 21., 10.,  7., 19., 18., 52.,  3.,
             22., 21., 26.,  8., 17., 11., 26., 22., 20.,  9., 16., 13., 29., 61.,
             40., 35., 21., 15., 16.,  9., 23., 40., 10., 36., 10., 15., 21., 18.,
             14., 25., 31., 22., 16., 33., 63., 21., 16., 13.,  9., 15.,  9., 40.,
             21.,  0., 18.,  9.])

  • Attributes: (3)

    created_at :

    2019-07-12T20:31:53.581293

    inference_library :

    pymc3

    inference_library_version :

    3.7