arviz.InferenceData.add_groups

InferenceData.add_groups(group_dict=None, coords=None, dims=None, **kwargs)

Add new groups to InferenceData object.

Parameters

group_dictdict of {strdict or xarray.Dataset}, optional

Groups to be added

coordsdict of {strarray_like}, optional

Coordinates for the dataset

dimsdict of {strlist of str}, optional

Dimensions of each variable. The keys are variable names, values are lists of coordinates.

kwargsdict, optional

The keyword arguments form of group_dict. One of group_dict or kwargs must be provided.

See also

extend

Extend InferenceData with groups from another InferenceData.

concat

Concatenate InferenceData objects.

Examples

Add a log_likelihood group to the “rugby” example InferenceData after loading. It originally doesn’t have the log_likelihood group:

import arviz as az
idata = az.load_arviz_data("rugby")
idata2 = idata.copy()
post = idata.posterior
obs = idata.observed_data
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'
  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: (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])

    • 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: (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'
  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: (1)
    • 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: (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

  
  

Knowing the model, we can compute it manually. In this case however, we will generate random samples with the right shape.

import numpy as np
rng = np.random.default_rng(73)
ary = rng.normal(size=(post.dims["chain"], post.dims["draw"], obs.dims["match"]))
idata.add_groups(
    log_likelihood={"home_points": ary},
    dims={"home_points": ["match"]},
)
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
      0.1642 0.1162 ... 0.148 0.2265

      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
      2.893 2.941 2.939 ... 2.903 2.892

      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
      0.1673 0.04184 ... -0.4652 0.02878

      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
      -0.03638 -0.04109 ... -0.0649

      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
      0.4854 0.1438 ... 0.2883 0.4591

      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
      0.2747 1.033 ... 0.5574 0.2849

      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
      0.1063 -0.01913 ... -0.2911 0.2029

      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
      -0.06765 -0.07235 ... -0.1986

      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'
  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: (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])

    • 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: (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

  
  
• log_likelihood

  <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) int64 0 1 2 3 4 5 6 7 8 ... 51 52 53 54 55 56 57 58 59
  Data variables:
      home_points  (chain, draw, match) float64 -1.093 0.7781 ... 0.2405 1.643
  Attributes:
      created_at:     2022-10-24T16:32:42.132111
      arviz_version:  0.13.0

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • match: 60
  • 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])

    • match
      (match)
      int64
      0 1 2 3 4 5 6 ... 54 55 56 57 58 59

      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])

  • Data variables: (1)
    • home_points
      (chain, draw, match)
      float64
      -1.093 0.7781 ... 0.2405 1.643

      array([[[-1.09330591e+00,  7.78087832e-01, -3.81610306e-01, ...,
                4.84564099e-01, -1.61693937e+00, -4.19842670e-01],
              [-2.00619024e-01, -1.70319742e-01, -2.46113915e-01, ...,
               -1.33266766e+00,  1.80447925e+00, -1.45660509e-01],
              [-2.50712206e+00,  1.79834383e+00,  6.30248678e-01, ...,
               -1.02798516e+00,  1.14356634e+00, -3.50814501e-01],
              ...,
              [ 9.92650794e-01, -1.16693044e+00,  5.99931728e-01, ...,
               -3.48188969e-01,  7.35989921e-01, -8.99216695e-01],
              [-4.51116486e-01,  6.76814555e-01,  5.70786683e-01, ...,
                2.18238000e+00,  1.53865762e+00, -8.74706028e-01],
              [ 1.97950620e-01,  6.17303135e-01,  1.74270395e-03, ...,
               -4.49897157e-01,  6.93927981e-01, -4.03693064e-01]],
      
             [[-5.13438873e-01,  2.06269310e-01, -1.39724013e+00, ...,
               -1.22238899e-01,  5.39511058e-02, -1.41409473e+00],
              [ 2.13292127e-01, -1.25754969e-01, -6.19146328e-01, ...,
               -4.54451615e-01, -9.55102426e-02,  2.46344882e+00],
              [ 1.09944686e+00, -8.36675090e-01, -6.64849313e-01, ...,
                2.06469045e-01, -6.89234364e-01,  1.12970438e+00],
      ...
              [ 1.27649065e+00,  3.26657373e-02, -9.41208951e-02, ...,
               -8.41882764e-01,  4.18612818e-01, -7.45126198e-01],
              [ 1.77302616e+00,  2.40029312e-01, -1.03966264e+00, ...,
                6.70392549e-04,  3.41461316e-01, -3.99132876e-01],
              [-4.90112178e-01,  3.20889351e-02,  5.34696144e-01, ...,
                4.35765135e-01,  7.36805282e-01, -4.66833157e-01]],
      
             [[-7.58144372e-02, -3.20704288e+00,  1.84262524e-01, ...,
                1.37396940e+00, -5.05861694e-01,  1.70371025e+00],
              [-2.22836138e-01, -1.65666088e+00,  8.63975137e-01, ...,
               -4.32667587e-01, -1.62718307e+00, -1.05026418e-01],
              [-6.38274887e-01, -7.06321492e-01, -6.25346451e-01, ...,
               -6.70819376e-02, -3.32003187e-01, -7.02170198e-01],
              ...,
              [-6.50718344e-02,  1.26554918e+00, -6.04798463e-01, ...,
                4.01464480e-01, -8.61955082e-02,  1.23169374e+00],
              [ 9.62742755e-01,  1.69023589e-01, -1.08048616e+00, ...,
                5.23012393e-01, -1.10747981e+00,  8.18173269e-02],
              [-5.08068068e-01,  5.31731357e-01,  9.45057998e-01, ...,
               -1.63968009e-01,  2.40471737e-01,  1.64341233e+00]]])

  • Attributes: (2)

    created_at :

    2022-10-24T16:32:42.132111

    arviz_version :

    0.13.0

  
  
• 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
      -0.07666 -0.4523 ... 0.115 -0.07691

      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
      540.2 545.3 542.3 ... 544.0 545.6

      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
      15.0 63.0 31.0 ... 63.0 31.0 31.0

      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
      True False False ... False False

      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
      1.0 0.8851 0.8875 ... 0.7791 0.7539

      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
      -536.4 -536.0 ... -536.1 -536.4

      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
      4 6 5 4 4 4 5 5 ... 6 4 6 5 3 6 5 5

      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
      -0.5361 -0.5871 ... 0.7109 1.014

      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
      0.2469 0.2469 ... 0.2459 0.2459

      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
      0.2313 0.2313 ... 0.2488 0.2488

      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
      False 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]])

  • 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
      1.322 -2.014 ... -0.8585 -0.1922

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

    • intercept
      (chain, draw)
      float64
      4.464 3.352 1.567 ... 4.128 1.049

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

    • atts_star
      (chain, draw, team)
      float64
      -2.64 4.172 ... -0.2874 -0.8538

      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
      -0.7817 -0.1478 ... 0.1655 0.01067

      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
      11308 0 11 1 0 21442 ... 11 1 2 2 0

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

    • sd_att
      (chain, draw)
      float64
      3.752 0.1334 ... 0.4238 0.8251

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

    • sd_def_log__
      (chain, draw)
      float64
      -0.2662 0.2411 ... 1.402 -1.981

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

    • home
      (chain, draw)
      float64
      -1.511 -0.001582 ... 0.2651

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

    • atts
      (chain, draw, team)
      float64
      -4.667 2.145 ... -0.2702 -0.8365

      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
      0.7663 1.273 1.835 ... 4.063 0.138

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

    • home_points
      (chain, draw, match)
      int64
      0 47 11899 3262 1 ... 3 2 1 12 13

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

    • defs
      (chain, draw, team)
      float64
      -0.2517 0.3823 ... 0.089 -0.06586

      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'
  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: (1)
    • 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: (2)
    • home_points
      (match)
      float64
      23.0 26.0 28.0 ... 29.0 20.0 13.0

      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
      15.0 24.0 6.0 3.0 ... 0.0 18.0 9.0

      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

  
  

This is fine if we have raw data, but a bit inconvenient if we start with labeled data already. Why provide dims and coords manually again? Let’s generate a fake log likelihood (doesn’t match the model but it serves just the same for illustration purposes here) working from the posterior and observed_data groups manually:

import xarray as xr
from xarray_einstats.stats import XrDiscreteRV
from scipy.stats import poisson
dist = XrDiscreteRV(poisson)
log_lik = xr.Dataset()
log_lik["home_points"] = dist.logpmf(obs["home_points"], np.exp(post["atts"]))
idata2.add_groups({"log_likelihood": log_lik})
idata2

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'
  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: (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])

    • 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: (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

  
  
• log_likelihood

  <xarray.Dataset>
  Dimensions:      (match: 60, chain: 4, draw: 500, team: 6)
  Coordinates:
    * match        (match) object 'Wales Italy' ... 'Ireland England'
    * 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
    * team         (team) object 'Wales' 'France' 'Ireland' ... 'Italy' 'England'
  Data variables:
      home_points  (match, chain, draw, team) float64 -50.27 -53.03 ... -21.14

  xarray.Dataset

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

    • 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: (1)
    • home_points
      (match, chain, draw, team)
      float64
      -50.27 -53.03 ... -27.08 -21.14

      array([[[[-50.27340679, -53.02763088, -49.60880645, -54.0949587 ,
                -62.83670609, -45.95963245],
               [-49.23489128, -54.43022627, -49.54759518, -54.04058511,
                -60.85259984, -47.65128777],
               [-48.70614082, -53.56169046, -51.3296424 , -55.90686766,
                -59.21475528, -47.02705307],
               ...,
               [-48.38292302, -55.22150328, -51.04573136, -55.98020613,
                -59.30672607, -45.83824038],
               [-50.16387191, -55.24153061, -50.41938842, -53.98620983,
                -58.14264601, -47.76205157],
               [-49.30549847, -54.33225327, -49.49141469, -53.81059892,
                -59.62302777, -49.16254883]],
      
              [[-47.20574061, -53.16969297, -49.904949  , -56.45851665,
                -62.78384919, -46.30966544],
               [-49.72097095, -53.0125925 , -49.97979965, -55.48001996,
                -59.80024005, -47.74533106],
               [-48.65861079, -52.63480405, -51.27588453, -55.48421341,
                -60.87333574, -46.84022256],
      ...
               [-21.07420765, -24.85696218, -22.43288564, -25.56391285,
                -27.16305238, -20.34882743],
               [-21.94692547, -24.43794791, -22.33531041, -24.04555291,
                -27.90171192, -20.75099542],
               [-21.30265712, -24.31455013, -22.22832286, -23.8844833 ,
                -28.41733435, -21.28299039]],
      
              [[-22.0916242 , -23.10668814, -22.21122819, -24.72579545,
                -27.2498818 , -21.99829746],
               [-20.92629642, -24.55922194, -22.07414212, -25.39004721,
                -28.47517395, -20.05681077],
               [-21.77733448, -25.04409811, -22.62294366, -24.90508263,
                -27.31972085, -19.77252911],
               ...,
               [-21.55768786, -24.41427901, -22.0736515 , -24.56115236,
                -28.66848219, -20.18796241],
               [-21.77257294, -24.299161  , -22.29283009, -24.83788118,
                -28.15446192, -20.09145606],
               [-20.96133141, -24.92572979, -22.42301855, -24.88194918,
                -27.08405599, -21.13980755]]]])

  • Attributes: (0)

  
  
• 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'
  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: (1)
    • 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: (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

  
  

Note that in the first example we have used the kwargs argument and in the second we have used the group_dict one.