Attach trial wise parameters to idata¶

HSSM automatically cleans up the idata object we return from samplers, to avoid unnecessarily huge objects from being passed around (the decision was taken after having observed many inadvertent out of memory errors).

Instead, if so desired, we can attach the trial wise parameters to the idata object ourselves, using the add_likelihood_parameters_to_idata function.

This quick tutorial shows you how to do this.

Load Modules¶

In [ ]:

import pandas as pd

import hssm

import pandas as pd import hssm

Simulate Data¶

In [ ]:

# Condition 1
condition_1 = hssm.simulate_data(
    model="ddm", theta=dict(v=0.5, a=1.5, z=0.5, t=0.1), size=500
)

# Condition 2
condition_2 = hssm.simulate_data(
    model="ddm", theta=dict(v=1.0, a=1.5, z=0.5, t=0.1), size=500
)

condition_1["condition"] = "C1"
condition_2["condition"] = "C2"

data = pd.concat([condition_1, condition_2]).reset_index(drop=True)

# Condition 1 condition_1 = hssm.simulate_data( model="ddm", theta=dict(v=0.5, a=1.5, z=0.5, t=0.1), size=500 ) # Condition 2 condition_2 = hssm.simulate_data( model="ddm", theta=dict(v=1.0, a=1.5, z=0.5, t=0.1), size=500 ) condition_1["condition"] = "C1" condition_2["condition"] = "C2" data = pd.concat([condition_1, condition_2]).reset_index(drop=True)

Define Model and Sample¶

In [ ]:

model = hssm.HSSM(
    model="ddm",
    data=data,
    include=[
        {
            "name": "v",
            "formula": "v ~ 1 + condition",
        }
    ],
)

idata = model.sample(sampler="mcmc", tune=500, draws=500)

model = hssm.HSSM( model="ddm", data=data, include=[ { "name": "v", "formula": "v ~ 1 + condition", } ], ) idata = model.sample(sampler="mcmc", tune=500, draws=500)

Model initialized successfully.
Using default initvals. 

Initializing NUTS using adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [a, t, z, v_Intercept, v_condition]

Output()

Sampling 4 chains for 500 tune and 500 draw iterations (2_000 + 2_000 draws total) took 15 seconds.
100%|██████████| 2000/2000 [00:00<00:00, 2757.59it/s]

Checking the idata object¶

In [ ]:

idata

idata

Out[ ]:

arviz.InferenceData

• posterior

  <xarray.Dataset> Size: 84kB
  Dimensions:          (chain: 4, draw: 500, v_condition_dim: 1)
  Coordinates:
    * chain            (chain) int64 32B 0 1 2 3
    * draw             (draw) int64 4kB 0 1 2 3 4 5 6 ... 494 495 496 497 498 499
    * v_condition_dim  (v_condition_dim) <U2 8B 'C2'
  Data variables:
      v_Intercept      (chain, draw) float64 16kB 0.6073 0.5713 ... 0.5286 0.5562
      z                (chain, draw) float64 16kB 0.5004 0.5106 ... 0.5281 0.4792
      v_condition      (chain, draw, v_condition_dim) float64 16kB 0.3881 ... 0...
      t                (chain, draw) float64 16kB 0.1444 0.1364 ... 0.1289 0.1399
      a                (chain, draw) float64 16kB 1.478 1.499 ... 1.493 1.441
  Attributes:
      created_at:                  2025-02-18T22:11:14.073518+00:00
      arviz_version:               0.19.0
      inference_library:           pymc
      inference_library_version:   5.19.1
      sampling_time:               15.156437873840332
      tuning_steps:                500
      modeling_interface:          bambi
      modeling_interface_version:  0.15.0

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • v_condition_dim: 1
  • 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])

    • v_condition_dim
      (v_condition_dim)
      <U2
      'C2'

      array(['C2'], dtype='<U2')

  • Data variables: (5)
    • v_Intercept
      (chain, draw)
      float64
      0.6073 0.5713 ... 0.5286 0.5562

      array([[0.60732087, 0.57128955, 0.59433837, ..., 0.55928162, 0.50380094,
              0.59812348],
             [0.62577087, 0.59312659, 0.64907674, ..., 0.63602003, 0.55306212,
              0.5262176 ],
             [0.61791294, 0.60825625, 0.62879305, ..., 0.58054304, 0.62012196,
              0.5841064 ],
             [0.55000304, 0.52509877, 0.61947846, ..., 0.58562618, 0.52855784,
              0.5561903 ]])

    • z
      (chain, draw)
      float64
      0.5004 0.5106 ... 0.5281 0.4792

      array([[0.50037035, 0.51064321, 0.49761259, ..., 0.50697951, 0.52700292,
              0.51271323],
             [0.48321997, 0.48722938, 0.50065557, ..., 0.48312787, 0.49678612,
              0.49898795],
             [0.48097507, 0.49120806, 0.48915125, ..., 0.49140223, 0.49168446,
              0.50383578],
             [0.51154826, 0.50502576, 0.49406566, ..., 0.52414976, 0.52814883,
              0.4792322 ]])

    • v_condition
      (chain, draw, v_condition_dim)
      float64
      0.3881 0.4265 ... 0.3998 0.4993

      array([[[0.38813133],
              [0.42645494],
              [0.47837703],
              ...,
              [0.42193226],
              [0.44139445],
              [0.44930881]],
      
             [[0.35814597],
              [0.58333041],
              [0.58194728],
              ...,
              [0.4451829 ],
              [0.46132013],
              [0.44720157]],
      
             [[0.49001661],
              [0.53854141],
              [0.4045351 ],
              ...,
              [0.44210668],
              [0.45728063],
              [0.50587066]],
      
             [[0.58008485],
              [0.57988411],
              [0.48842121],
              ...,
              [0.39303412],
              [0.39976821],
              [0.4993025 ]]])

    • t
      (chain, draw)
      float64
      0.1444 0.1364 ... 0.1289 0.1399

      array([[0.14435059, 0.13643948, 0.10892776, ..., 0.1448519 , 0.14614171,
              0.13048789],
             [0.07731317, 0.11800187, 0.11566988, ..., 0.10589011, 0.12784332,
              0.10803669],
             [0.08987629, 0.1024199 , 0.1005105 , ..., 0.12167029, 0.10962067,
              0.11824606],
             [0.14450353, 0.10531868, 0.126992  , ..., 0.14001202, 0.12890767,
              0.13985528]])

    • a
      (chain, draw)
      float64
      1.478 1.499 1.512 ... 1.493 1.441

      array([[1.47834639, 1.49912589, 1.51242277, ..., 1.46698342, 1.45668508,
              1.48611327],
             [1.50030118, 1.51873956, 1.56097033, ..., 1.51349657, 1.48160511,
              1.4515522 ],
             [1.50273262, 1.52117003, 1.50595712, ..., 1.42781562, 1.55304525,
              1.5217595 ],
             [1.55223514, 1.4911077 , 1.44851785, ..., 1.46721755, 1.49332998,
              1.440747  ]])

  • Indexes: (3)
    • chain
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
            dtype='int64', name='draw', length=500))

    • v_condition_dim
      PandasIndex

      PandasIndex(Index(['C2'], dtype='object', name='v_condition_dim'))

  • Attributes: (8)

    created_at :

    2025-02-18T22:11:14.073518+00:00

    arviz_version :

    0.19.0

    inference_library :

    pymc

    inference_library_version :

    5.19.1

    sampling_time :

    15.156437873840332

    tuning_steps :

    500

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.0

  
  
• log_likelihood

  <xarray.Dataset> Size: 16MB
  Dimensions:      (chain: 4, draw: 500, __obs__: 1000)
  Coordinates:
    * chain        (chain) int64 32B 0 1 2 3
    * draw         (draw) int64 4kB 0 1 2 3 4 5 6 ... 493 494 495 496 497 498 499
    * __obs__      (__obs__) int64 8kB 0 1 2 3 4 5 6 ... 994 995 996 997 998 999
  Data variables:
      rt,response  (chain, draw, __obs__) float64 16MB -0.9346 -4.734 ... -0.6063
  Attributes:
      modeling_interface:          bambi
      modeling_interface_version:  0.15.0

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • __obs__: 1000
  • 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__
      (__obs__)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999])

  • Data variables: (1)
    • rt,response
      (chain, draw, __obs__)
      float64
      -0.9346 -4.734 ... -0.6664 -0.6063

      array([[[-0.93461151, -4.73385822, -1.12004688, ..., -4.31354999,
               -0.69407059, -0.63613238],
              [-0.9490393 , -4.6305489 , -1.15181827, ..., -4.29875594,
               -0.70221461, -0.64276806],
              [-0.97666815, -4.68388574, -1.14881155, ..., -4.45691635,
               -0.68282644, -0.6220915 ],
              ...,
              [-0.93763076, -4.61560899, -1.15770879, ..., -4.32240613,
               -0.70685279, -0.64672235],
              [-0.88718969, -4.49514374, -1.20523032, ..., -4.30740034,
               -0.73938004, -0.67485707],
              [-0.87930102, -4.72482562, -1.13937065, ..., -4.4722753 ,
               -0.69227592, -0.62732112]],
      
             [[-0.95270827, -4.7824691 , -1.14473751, ..., -4.24468295,
               -0.74425476, -0.69075922],
              [-1.05688872, -4.65751979, -1.14233542, ..., -4.69886613,
               -0.62438684, -0.56032313],
              [-0.98680766, -4.81364021, -1.1003504 , ..., -4.80081063,
               -0.60882562, -0.54055048],
      ...
              [-0.89696111, -4.70996795, -1.16022854, ..., -4.51769959,
               -0.71025592, -0.64670975],
              [-1.0485967 , -4.72324102, -1.12502141, ..., -4.35765734,
               -0.66660261, -0.61159375],
              [-0.98452199, -4.65038158, -1.15070967, ..., -4.49002114,
               -0.6695923 , -0.60721418]],
      
             [[-1.07646929, -4.52536755, -1.1600133 , ..., -4.53120472,
               -0.6265591 , -0.56346211],
              [-0.98401059, -4.51395543, -1.20763644, ..., -4.61905017,
               -0.68845242, -0.62099807],
              [-0.87924754, -4.79671196, -1.12667918, ..., -4.68783937,
               -0.66891083, -0.60105544],
              ...,
              [-0.81973537, -4.71628604, -1.14963352, ..., -4.36142669,
               -0.72595572, -0.66088941],
              [-0.89455929, -4.54035551, -1.19454745, ..., -4.18962802,
               -0.75492978, -0.69390912],
              [-1.03164192, -4.60466314, -1.16209092, ..., -4.5245968 ,
               -0.66636432, -0.60633029]]])

  • Indexes: (3)
    • chain
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
            dtype='int64', name='draw', length=500))

    • __obs__
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='__obs__', length=1000))

  • Attributes: (2)

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.0

  
  
• sample_stats

  <xarray.Dataset> Size: 248kB
  Dimensions:                (chain: 4, draw: 500)
  Coordinates:
    * chain                  (chain) int64 32B 0 1 2 3
    * draw                   (draw) int64 4kB 0 1 2 3 4 5 ... 495 496 497 498 499
  Data variables: (12/17)
      acceptance_rate        (chain, draw) float64 16kB 0.9046 0.9813 ... 0.9289
      diverging              (chain, draw) bool 2kB False False ... False False
      energy                 (chain, draw) float64 16kB 1.646e+03 ... 1.647e+03
      energy_error           (chain, draw) float64 16kB 0.08286 -0.3905 ... 0.187
      index_in_trajectory    (chain, draw) int64 16kB 1 -1 2 3 3 ... -3 4 -3 -3 6
      largest_eigval         (chain, draw) float64 16kB nan nan nan ... nan nan
      ...                     ...
      process_time_diff      (chain, draw) float64 16kB 0.007986 ... 0.007488
      reached_max_treedepth  (chain, draw) bool 2kB False False ... False False
      smallest_eigval        (chain, draw) float64 16kB nan nan nan ... nan nan
      step_size              (chain, draw) float64 16kB 0.4256 0.4256 ... 0.3861
      step_size_bar          (chain, draw) float64 16kB 0.5357 0.5357 ... 0.4755
      tree_depth             (chain, draw) int64 16kB 3 3 4 4 4 3 ... 4 3 3 3 3 3
  Attributes:
      created_at:                  2025-02-18T22:11:14.084242+00:00
      arviz_version:               0.19.0
      inference_library:           pymc
      inference_library_version:   5.19.1
      sampling_time:               15.156437873840332
      tuning_steps:                500
      modeling_interface:          bambi
      modeling_interface_version:  0.15.0

  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: (17)
    • acceptance_rate
      (chain, draw)
      float64
      0.9046 0.9813 ... 0.9895 0.9289

      array([[0.90462561, 0.98127922, 0.63106396, ..., 1.        , 0.92482204,
              0.86820278],
             [0.96089489, 0.92012207, 0.28377848, ..., 0.88586289, 0.88509219,
              0.57259714],
             [0.67563642, 0.99246627, 1.        , ..., 0.70154783, 0.71626677,
              0.9489716 ],
             [0.91102615, 1.        , 0.98122019, ..., 0.81575728, 0.98949192,
              0.92889847]])

    • 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]])

    • energy
      (chain, draw)
      float64
      1.646e+03 1.646e+03 ... 1.647e+03

      array([[1645.51987421, 1645.64694605, 1645.31588241, ..., 1646.82515829,
              1644.82970328, 1645.21531822],
             [1649.99277297, 1648.30823824, 1653.90167358, ..., 1643.99439497,
              1644.46006139, 1648.20292782],
             [1644.66809905, 1645.36237083, 1644.66732949, ..., 1647.25492947,
              1647.68418292, 1645.47478074],
             [1651.73847236, 1650.14007844, 1647.88552553, ..., 1646.53340392,
              1645.6136487 , 1646.74255744]])

    • energy_error
      (chain, draw)
      float64
      0.08286 -0.3905 ... -0.1982 0.187

      array([[ 0.0828619 , -0.39053758,  0.10561296, ..., -0.77822663,
               0.09172688,  0.19057659],
             [-0.06252599, -0.13167928,  0.75841185, ...,  0.02300547,
               0.13143257,  0.30664527],
             [ 0.35942533,  0.04264695, -0.16483707, ...,  0.47044111,
              -0.13126664, -0.42543701],
             [ 0.54517756, -0.32585809, -0.12884639, ...,  0.29708815,
              -0.19817063,  0.18695707]])

    • index_in_trajectory
      (chain, draw)
      int64
      1 -1 2 3 3 -5 5 ... -1 -3 4 -3 -3 6

      array([[ 1, -1,  2, ..., -2,  5, -3],
             [-3, -7,  2, ...,  5, -6,  6],
             [-9,  5,  4, ..., -4,  4,  3],
             [-4, -2, -4, ..., -3, -3,  6]])

    • largest_eigval
      (chain, draw)
      float64
      nan nan nan nan ... nan nan nan nan

      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]])

    • lp
      (chain, draw)
      float64
      -1.643e+03 ... -1.644e+03

      array([[-1642.88746356, -1641.97964387, -1641.81421996, ...,
              -1641.91265734, -1643.55172093, -1642.35493823],
             [-1645.99592353, -1645.01696524, -1651.43917502, ...,
              -1642.4281025 , -1641.76423054, -1644.91650779],
             [-1643.29242426, -1643.8852089 , -1642.48579147, ...,
              -1643.96150999, -1644.40823197, -1642.41159187],
             [-1649.06668108, -1645.81452959, -1644.38710209, ...,
              -1643.58737964, -1644.35329061, -1644.48151554]])

    • max_energy_error
      (chain, draw)
      float64
      -0.3233 -0.4068 ... -0.3049 -0.3641

      array([[-0.32331819, -0.406804  ,  1.19993489, ..., -0.77822663,
               0.18258852,  0.26509098],
             [-0.30609368,  0.38079224,  1.84078866, ...,  0.19489209,
               0.27356353,  1.55298412],
             [ 0.75763836, -0.15341209, -0.16483707, ...,  1.09308834,
               0.92024982, -0.42543701],
             [-0.68611123, -1.0420458 , -0.78416922, ...,  0.39115803,
              -0.30494108, -0.36410691]])

    • n_steps
      (chain, draw)
      float64
      7.0 7.0 11.0 15.0 ... 7.0 7.0 7.0

      array([[ 7.,  7., 11., ...,  3.,  7.,  7.],
             [ 7., 15.,  3., ...,  7.,  7., 15.],
             [15.,  7.,  7., ...,  7.,  7.,  7.],
             [ 7.,  3.,  7., ...,  7.,  7.,  7.]])

    • perf_counter_diff
      (chain, draw)
      float64
      0.009509 0.009175 ... 0.007497

      array([[0.00950929, 0.00917517, 0.01158771, ..., 0.00347908, 0.00695896,
              0.00697204],
             [0.00740504, 0.01483683, 0.00391454, ..., 0.00736675, 0.00761587,
              0.01472121],
             [0.01521888, 0.01060496, 0.00839917, ..., 0.00728917, 0.00731758,
              0.00728862],
             [0.00813412, 0.00555529, 0.00844287, ..., 0.00733138, 0.00857692,
              0.00749696]])

    • perf_counter_start
      (chain, draw)
      float64
      2.431e+06 2.431e+06 ... 2.431e+06

      array([[2431026.99619729, 2431027.0058935 , 2431027.01515679, ...,
              2431030.89105325, 2431030.89456579, 2431030.90155883],
             [2431026.94878788, 2431026.95626788, 2431026.97116912, ...,
              2431030.93996046, 2431030.94741288, 2431030.95512075],
             [2431026.33617792, 2431026.35166488, 2431026.36236317, ...,
              2431030.66275083, 2431030.67009292, 2431030.67748538],
             [2431025.97671083, 2431025.98499921, 2431025.99066612, ...,
              2431030.31140508, 2431030.31879804, 2431030.32745546]])

    • process_time_diff
      (chain, draw)
      float64
      0.007986 0.008114 ... 0.007488

      array([[0.007986, 0.008114, 0.011469, ..., 0.003479, 0.006959, 0.006972],
             [0.007405, 0.014784, 0.003834, ..., 0.007338, 0.007546, 0.014699],
             [0.014956, 0.008515, 0.007899, ..., 0.007272, 0.007309, 0.007286],
             [0.007987, 0.00469 , 0.008112, ..., 0.007323, 0.008097, 0.007488]])

    • reached_max_treedepth
      (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]])

    • smallest_eigval
      (chain, draw)
      float64
      nan nan nan nan ... nan nan nan nan

      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]])

    • step_size
      (chain, draw)
      float64
      0.4256 0.4256 ... 0.3861 0.3861

      array([[0.42557006, 0.42557006, 0.42557006, ..., 0.42557006, 0.42557006,
              0.42557006],
             [0.6043351 , 0.6043351 , 0.6043351 , ..., 0.6043351 , 0.6043351 ,
              0.6043351 ],
             [0.74596757, 0.74596757, 0.74596757, ..., 0.74596757, 0.74596757,
              0.74596757],
             [0.38606666, 0.38606666, 0.38606666, ..., 0.38606666, 0.38606666,
              0.38606666]])

    • step_size_bar
      (chain, draw)
      float64
      0.5357 0.5357 ... 0.4755 0.4755

      array([[0.53572783, 0.53572783, 0.53572783, ..., 0.53572783, 0.53572783,
              0.53572783],
             [0.46537907, 0.46537907, 0.46537907, ..., 0.46537907, 0.46537907,
              0.46537907],
             [0.43209038, 0.43209038, 0.43209038, ..., 0.43209038, 0.43209038,
              0.43209038],
             [0.4755282 , 0.4755282 , 0.4755282 , ..., 0.4755282 , 0.4755282 ,
              0.4755282 ]])

    • tree_depth
      (chain, draw)
      int64
      3 3 4 4 4 3 3 3 ... 3 2 4 3 3 3 3 3

      array([[3, 3, 4, ..., 2, 3, 3],
             [3, 4, 2, ..., 3, 3, 4],
             [4, 3, 3, ..., 3, 3, 3],
             [3, 2, 3, ..., 3, 3, 3]])

  • Indexes: (2)
    • chain
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
            dtype='int64', name='draw', length=500))

  • Attributes: (8)

    created_at :

    2025-02-18T22:11:14.084242+00:00

    arviz_version :

    0.19.0

    inference_library :

    pymc

    inference_library_version :

    5.19.1

    sampling_time :

    15.156437873840332

    tuning_steps :

    500

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.0

  
  
• observed_data

  <xarray.Dataset> Size: 24kB
  Dimensions:                  (__obs__: 1000, rt,response_extra_dim_0: 2)
  Coordinates:
    * __obs__                  (__obs__) int64 8kB 0 1 2 3 4 ... 996 997 998 999
    * rt,response_extra_dim_0  (rt,response_extra_dim_0) int64 16B 0 1
  Data variables:
      rt,response              (__obs__, rt,response_extra_dim_0) float64 16kB ...
  Attributes:
      created_at:                  2025-02-18T22:11:14.103497+00:00
      arviz_version:               0.19.0
      inference_library:           pymc
      inference_library_version:   5.19.1
      modeling_interface:          bambi
      modeling_interface_version:  0.15.0

  xarray.Dataset

  • Dimensions:
    • __obs__: 1000
    • rt,response_extra_dim_0: 2
  • Coordinates: (2)
    • __obs__
      (__obs__)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999])

    • rt,response_extra_dim_0
      (rt,response_extra_dim_0)
      int64
      0 1

      array([0, 1])

  • Data variables: (1)
    • rt,response
      (__obs__, rt,response_extra_dim_0)
      float64
      0.6262 1.0 4.277 ... 1.0 1.081 1.0

      array([[ 0.6262266 ,  1.        ],
             [ 4.27727699, -1.        ],
             [ 1.39999413,  1.        ],
             ...,
             [ 4.7823925 ,  1.        ],
             [ 1.1470964 ,  1.        ],
             [ 1.08128822,  1.        ]])

  • Indexes: (2)
    • __obs__
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='__obs__', length=1000))

    • rt,response_extra_dim_0
      PandasIndex

      PandasIndex(Index([0, 1], dtype='int64', name='rt,response_extra_dim_0'))

  • Attributes: (6)

    created_at :

    2025-02-18T22:11:14.103497+00:00

    arviz_version :

    0.19.0

    inference_library :

    pymc

    inference_library_version :

    5.19.1

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.0

  
  

Note that none of the parameters attached in the posterior have the observation coordinate (__obs__). However, looking at the model graph, we clearly see that for variables that are represented as regression targets, we in fact compute intermediate deterministics which do have dimensionality __obs__.

In [ ]:

model.graph()

model.graph()

Out[ ]:

Computing Trial Wise Parameters¶

We can use the compute_likelihood_parameters_to_idata function to recompute and include in our idata the trial wise deterministics, which are part of our model graph.

In [ ]:

### Attach Trial Wise Parameters
idata_trialwise = model.add_likelihood_parameters_to_idata(idata)

### Checking the `idata` object
idata_trialwise

### Attach Trial Wise Parameters idata_trialwise = model.add_likelihood_parameters_to_idata(idata) ### Checking the `idata` object idata_trialwise

Out[ ]:

arviz.InferenceData

• posterior

  <xarray.Dataset> Size: 16MB
  Dimensions:          (chain: 4, draw: 500, v_condition_dim: 1, __obs__: 1000)
  Coordinates:
    * chain            (chain) int64 32B 0 1 2 3
    * draw             (draw) int64 4kB 0 1 2 3 4 5 6 ... 494 495 496 497 498 499
    * v_condition_dim  (v_condition_dim) <U2 8B 'C2'
    * __obs__          (__obs__) int64 8kB 0 1 2 3 4 5 ... 994 995 996 997 998 999
  Data variables:
      v_Intercept      (chain, draw) float64 16kB 0.6073 0.5713 ... 0.5286 0.5562
      z                (chain, draw) float64 16kB 0.5004 0.5106 ... 0.5281 0.4792
      v_condition      (chain, draw, v_condition_dim) float64 16kB 0.3881 ... 0...
      t                (chain, draw) float64 16kB 0.1444 0.1364 ... 0.1289 0.1399
      a                (chain, draw) float64 16kB 1.478 1.499 ... 1.493 1.441
      v                (chain, draw, __obs__) float64 16MB 0.6073 0.6073 ... 1.055
  Attributes:
      created_at:                  2025-02-18T22:11:14.073518+00:00
      arviz_version:               0.19.0
      inference_library:           pymc
      inference_library_version:   5.19.1
      sampling_time:               15.156437873840332
      tuning_steps:                500
      modeling_interface:          bambi
      modeling_interface_version:  0.15.0

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • v_condition_dim: 1
    • __obs__: 1000
  • 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])

    • v_condition_dim
      (v_condition_dim)
      <U2
      'C2'

      array(['C2'], dtype='<U2')

    • __obs__
      (__obs__)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999])

  • Data variables: (6)
    • v_Intercept
      (chain, draw)
      float64
      0.6073 0.5713 ... 0.5286 0.5562

      array([[0.60732087, 0.57128955, 0.59433837, ..., 0.55928162, 0.50380094,
              0.59812348],
             [0.62577087, 0.59312659, 0.64907674, ..., 0.63602003, 0.55306212,
              0.5262176 ],
             [0.61791294, 0.60825625, 0.62879305, ..., 0.58054304, 0.62012196,
              0.5841064 ],
             [0.55000304, 0.52509877, 0.61947846, ..., 0.58562618, 0.52855784,
              0.5561903 ]])

    • z
      (chain, draw)
      float64
      0.5004 0.5106 ... 0.5281 0.4792

      array([[0.50037035, 0.51064321, 0.49761259, ..., 0.50697951, 0.52700292,
              0.51271323],
             [0.48321997, 0.48722938, 0.50065557, ..., 0.48312787, 0.49678612,
              0.49898795],
             [0.48097507, 0.49120806, 0.48915125, ..., 0.49140223, 0.49168446,
              0.50383578],
             [0.51154826, 0.50502576, 0.49406566, ..., 0.52414976, 0.52814883,
              0.4792322 ]])

    • v_condition
      (chain, draw, v_condition_dim)
      float64
      0.3881 0.4265 ... 0.3998 0.4993

      array([[[0.38813133],
              [0.42645494],
              [0.47837703],
              ...,
              [0.42193226],
              [0.44139445],
              [0.44930881]],
      
             [[0.35814597],
              [0.58333041],
              [0.58194728],
              ...,
              [0.4451829 ],
              [0.46132013],
              [0.44720157]],
      
             [[0.49001661],
              [0.53854141],
              [0.4045351 ],
              ...,
              [0.44210668],
              [0.45728063],
              [0.50587066]],
      
             [[0.58008485],
              [0.57988411],
              [0.48842121],
              ...,
              [0.39303412],
              [0.39976821],
              [0.4993025 ]]])

    • t
      (chain, draw)
      float64
      0.1444 0.1364 ... 0.1289 0.1399

      array([[0.14435059, 0.13643948, 0.10892776, ..., 0.1448519 , 0.14614171,
              0.13048789],
             [0.07731317, 0.11800187, 0.11566988, ..., 0.10589011, 0.12784332,
              0.10803669],
             [0.08987629, 0.1024199 , 0.1005105 , ..., 0.12167029, 0.10962067,
              0.11824606],
             [0.14450353, 0.10531868, 0.126992  , ..., 0.14001202, 0.12890767,
              0.13985528]])

    • a
      (chain, draw)
      float64
      1.478 1.499 1.512 ... 1.493 1.441

      array([[1.47834639, 1.49912589, 1.51242277, ..., 1.46698342, 1.45668508,
              1.48611327],
             [1.50030118, 1.51873956, 1.56097033, ..., 1.51349657, 1.48160511,
              1.4515522 ],
             [1.50273262, 1.52117003, 1.50595712, ..., 1.42781562, 1.55304525,
              1.5217595 ],
             [1.55223514, 1.4911077 , 1.44851785, ..., 1.46721755, 1.49332998,
              1.440747  ]])

    • v
      (chain, draw, __obs__)
      float64
      0.6073 0.6073 ... 1.055 1.055

      array([[[0.60732087, 0.60732087, 0.60732087, ..., 0.9954522 ,
               0.9954522 , 0.9954522 ],
              [0.57128955, 0.57128955, 0.57128955, ..., 0.99774449,
               0.99774449, 0.99774449],
              [0.59433837, 0.59433837, 0.59433837, ..., 1.07271539,
               1.07271539, 1.07271539],
              ...,
              [0.55928162, 0.55928162, 0.55928162, ..., 0.98121388,
               0.98121388, 0.98121388],
              [0.50380094, 0.50380094, 0.50380094, ..., 0.94519539,
               0.94519539, 0.94519539],
              [0.59812348, 0.59812348, 0.59812348, ..., 1.04743228,
               1.04743228, 1.04743228]],
      
             [[0.62577087, 0.62577087, 0.62577087, ..., 0.98391684,
               0.98391684, 0.98391684],
              [0.59312659, 0.59312659, 0.59312659, ..., 1.17645701,
               1.17645701, 1.17645701],
              [0.64907674, 0.64907674, 0.64907674, ..., 1.23102402,
               1.23102402, 1.23102402],
      ...
              [0.58054304, 0.58054304, 0.58054304, ..., 1.02264972,
               1.02264972, 1.02264972],
              [0.62012196, 0.62012196, 0.62012196, ..., 1.07740259,
               1.07740259, 1.07740259],
              [0.5841064 , 0.5841064 , 0.5841064 , ..., 1.08997706,
               1.08997706, 1.08997706]],
      
             [[0.55000304, 0.55000304, 0.55000304, ..., 1.13008789,
               1.13008789, 1.13008789],
              [0.52509877, 0.52509877, 0.52509877, ..., 1.10498289,
               1.10498289, 1.10498289],
              [0.61947846, 0.61947846, 0.61947846, ..., 1.10789967,
               1.10789967, 1.10789967],
              ...,
              [0.58562618, 0.58562618, 0.58562618, ..., 0.97866031,
               0.97866031, 0.97866031],
              [0.52855784, 0.52855784, 0.52855784, ..., 0.92832605,
               0.92832605, 0.92832605],
              [0.5561903 , 0.5561903 , 0.5561903 , ..., 1.0554928 ,
               1.0554928 , 1.0554928 ]]])

  • Indexes: (4)
    • chain
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
            dtype='int64', name='draw', length=500))

    • v_condition_dim
      PandasIndex

      PandasIndex(Index(['C2'], dtype='object', name='v_condition_dim'))

    • __obs__
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='__obs__', length=1000))

  • Attributes: (8)

    created_at :

    2025-02-18T22:11:14.073518+00:00

    arviz_version :

    0.19.0

    inference_library :

    pymc

    inference_library_version :

    5.19.1

    sampling_time :

    15.156437873840332

    tuning_steps :

    500

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.0

  
  
• log_likelihood

  <xarray.Dataset> Size: 16MB
  Dimensions:      (chain: 4, draw: 500, __obs__: 1000)
  Coordinates:
    * chain        (chain) int64 32B 0 1 2 3
    * draw         (draw) int64 4kB 0 1 2 3 4 5 6 ... 493 494 495 496 497 498 499
    * __obs__      (__obs__) int64 8kB 0 1 2 3 4 5 6 ... 994 995 996 997 998 999
  Data variables:
      rt,response  (chain, draw, __obs__) float64 16MB -0.9346 -4.734 ... -0.6063
  Attributes:
      modeling_interface:          bambi
      modeling_interface_version:  0.15.0

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 500
    • __obs__: 1000
  • 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__
      (__obs__)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999])

  • Data variables: (1)
    • rt,response
      (chain, draw, __obs__)
      float64
      -0.9346 -4.734 ... -0.6664 -0.6063

      array([[[-0.93461151, -4.73385822, -1.12004688, ..., -4.31354999,
               -0.69407059, -0.63613238],
              [-0.9490393 , -4.6305489 , -1.15181827, ..., -4.29875594,
               -0.70221461, -0.64276806],
              [-0.97666815, -4.68388574, -1.14881155, ..., -4.45691635,
               -0.68282644, -0.6220915 ],
              ...,
              [-0.93763076, -4.61560899, -1.15770879, ..., -4.32240613,
               -0.70685279, -0.64672235],
              [-0.88718969, -4.49514374, -1.20523032, ..., -4.30740034,
               -0.73938004, -0.67485707],
              [-0.87930102, -4.72482562, -1.13937065, ..., -4.4722753 ,
               -0.69227592, -0.62732112]],
      
             [[-0.95270827, -4.7824691 , -1.14473751, ..., -4.24468295,
               -0.74425476, -0.69075922],
              [-1.05688872, -4.65751979, -1.14233542, ..., -4.69886613,
               -0.62438684, -0.56032313],
              [-0.98680766, -4.81364021, -1.1003504 , ..., -4.80081063,
               -0.60882562, -0.54055048],
      ...
              [-0.89696111, -4.70996795, -1.16022854, ..., -4.51769959,
               -0.71025592, -0.64670975],
              [-1.0485967 , -4.72324102, -1.12502141, ..., -4.35765734,
               -0.66660261, -0.61159375],
              [-0.98452199, -4.65038158, -1.15070967, ..., -4.49002114,
               -0.6695923 , -0.60721418]],
      
             [[-1.07646929, -4.52536755, -1.1600133 , ..., -4.53120472,
               -0.6265591 , -0.56346211],
              [-0.98401059, -4.51395543, -1.20763644, ..., -4.61905017,
               -0.68845242, -0.62099807],
              [-0.87924754, -4.79671196, -1.12667918, ..., -4.68783937,
               -0.66891083, -0.60105544],
              ...,
              [-0.81973537, -4.71628604, -1.14963352, ..., -4.36142669,
               -0.72595572, -0.66088941],
              [-0.89455929, -4.54035551, -1.19454745, ..., -4.18962802,
               -0.75492978, -0.69390912],
              [-1.03164192, -4.60466314, -1.16209092, ..., -4.5245968 ,
               -0.66636432, -0.60633029]]])

  • Indexes: (3)
    • chain
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
            dtype='int64', name='draw', length=500))

    • __obs__
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='__obs__', length=1000))

  • Attributes: (2)

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.0

  
  
• sample_stats

  <xarray.Dataset> Size: 248kB
  Dimensions:                (chain: 4, draw: 500)
  Coordinates:
    * chain                  (chain) int64 32B 0 1 2 3
    * draw                   (draw) int64 4kB 0 1 2 3 4 5 ... 495 496 497 498 499
  Data variables: (12/17)
      acceptance_rate        (chain, draw) float64 16kB 0.9046 0.9813 ... 0.9289
      diverging              (chain, draw) bool 2kB False False ... False False
      energy                 (chain, draw) float64 16kB 1.646e+03 ... 1.647e+03
      energy_error           (chain, draw) float64 16kB 0.08286 -0.3905 ... 0.187
      index_in_trajectory    (chain, draw) int64 16kB 1 -1 2 3 3 ... -3 4 -3 -3 6
      largest_eigval         (chain, draw) float64 16kB nan nan nan ... nan nan
      ...                     ...
      process_time_diff      (chain, draw) float64 16kB 0.007986 ... 0.007488
      reached_max_treedepth  (chain, draw) bool 2kB False False ... False False
      smallest_eigval        (chain, draw) float64 16kB nan nan nan ... nan nan
      step_size              (chain, draw) float64 16kB 0.4256 0.4256 ... 0.3861
      step_size_bar          (chain, draw) float64 16kB 0.5357 0.5357 ... 0.4755
      tree_depth             (chain, draw) int64 16kB 3 3 4 4 4 3 ... 4 3 3 3 3 3
  Attributes:
      created_at:                  2025-02-18T22:11:14.084242+00:00
      arviz_version:               0.19.0
      inference_library:           pymc
      inference_library_version:   5.19.1
      sampling_time:               15.156437873840332
      tuning_steps:                500
      modeling_interface:          bambi
      modeling_interface_version:  0.15.0

  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: (17)
    • acceptance_rate
      (chain, draw)
      float64
      0.9046 0.9813 ... 0.9895 0.9289

      array([[0.90462561, 0.98127922, 0.63106396, ..., 1.        , 0.92482204,
              0.86820278],
             [0.96089489, 0.92012207, 0.28377848, ..., 0.88586289, 0.88509219,
              0.57259714],
             [0.67563642, 0.99246627, 1.        , ..., 0.70154783, 0.71626677,
              0.9489716 ],
             [0.91102615, 1.        , 0.98122019, ..., 0.81575728, 0.98949192,
              0.92889847]])

    • 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]])

    • energy
      (chain, draw)
      float64
      1.646e+03 1.646e+03 ... 1.647e+03

      array([[1645.51987421, 1645.64694605, 1645.31588241, ..., 1646.82515829,
              1644.82970328, 1645.21531822],
             [1649.99277297, 1648.30823824, 1653.90167358, ..., 1643.99439497,
              1644.46006139, 1648.20292782],
             [1644.66809905, 1645.36237083, 1644.66732949, ..., 1647.25492947,
              1647.68418292, 1645.47478074],
             [1651.73847236, 1650.14007844, 1647.88552553, ..., 1646.53340392,
              1645.6136487 , 1646.74255744]])

    • energy_error
      (chain, draw)
      float64
      0.08286 -0.3905 ... -0.1982 0.187

      array([[ 0.0828619 , -0.39053758,  0.10561296, ..., -0.77822663,
               0.09172688,  0.19057659],
             [-0.06252599, -0.13167928,  0.75841185, ...,  0.02300547,
               0.13143257,  0.30664527],
             [ 0.35942533,  0.04264695, -0.16483707, ...,  0.47044111,
              -0.13126664, -0.42543701],
             [ 0.54517756, -0.32585809, -0.12884639, ...,  0.29708815,
              -0.19817063,  0.18695707]])

    • index_in_trajectory
      (chain, draw)
      int64
      1 -1 2 3 3 -5 5 ... -1 -3 4 -3 -3 6

      array([[ 1, -1,  2, ..., -2,  5, -3],
             [-3, -7,  2, ...,  5, -6,  6],
             [-9,  5,  4, ..., -4,  4,  3],
             [-4, -2, -4, ..., -3, -3,  6]])

    • largest_eigval
      (chain, draw)
      float64
      nan nan nan nan ... nan nan nan nan

      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]])

    • lp
      (chain, draw)
      float64
      -1.643e+03 ... -1.644e+03

      array([[-1642.88746356, -1641.97964387, -1641.81421996, ...,
              -1641.91265734, -1643.55172093, -1642.35493823],
             [-1645.99592353, -1645.01696524, -1651.43917502, ...,
              -1642.4281025 , -1641.76423054, -1644.91650779],
             [-1643.29242426, -1643.8852089 , -1642.48579147, ...,
              -1643.96150999, -1644.40823197, -1642.41159187],
             [-1649.06668108, -1645.81452959, -1644.38710209, ...,
              -1643.58737964, -1644.35329061, -1644.48151554]])

    • max_energy_error
      (chain, draw)
      float64
      -0.3233 -0.4068 ... -0.3049 -0.3641

      array([[-0.32331819, -0.406804  ,  1.19993489, ..., -0.77822663,
               0.18258852,  0.26509098],
             [-0.30609368,  0.38079224,  1.84078866, ...,  0.19489209,
               0.27356353,  1.55298412],
             [ 0.75763836, -0.15341209, -0.16483707, ...,  1.09308834,
               0.92024982, -0.42543701],
             [-0.68611123, -1.0420458 , -0.78416922, ...,  0.39115803,
              -0.30494108, -0.36410691]])

    • n_steps
      (chain, draw)
      float64
      7.0 7.0 11.0 15.0 ... 7.0 7.0 7.0

      array([[ 7.,  7., 11., ...,  3.,  7.,  7.],
             [ 7., 15.,  3., ...,  7.,  7., 15.],
             [15.,  7.,  7., ...,  7.,  7.,  7.],
             [ 7.,  3.,  7., ...,  7.,  7.,  7.]])

    • perf_counter_diff
      (chain, draw)
      float64
      0.009509 0.009175 ... 0.007497

      array([[0.00950929, 0.00917517, 0.01158771, ..., 0.00347908, 0.00695896,
              0.00697204],
             [0.00740504, 0.01483683, 0.00391454, ..., 0.00736675, 0.00761587,
              0.01472121],
             [0.01521888, 0.01060496, 0.00839917, ..., 0.00728917, 0.00731758,
              0.00728862],
             [0.00813412, 0.00555529, 0.00844287, ..., 0.00733138, 0.00857692,
              0.00749696]])

    • perf_counter_start
      (chain, draw)
      float64
      2.431e+06 2.431e+06 ... 2.431e+06

      array([[2431026.99619729, 2431027.0058935 , 2431027.01515679, ...,
              2431030.89105325, 2431030.89456579, 2431030.90155883],
             [2431026.94878788, 2431026.95626788, 2431026.97116912, ...,
              2431030.93996046, 2431030.94741288, 2431030.95512075],
             [2431026.33617792, 2431026.35166488, 2431026.36236317, ...,
              2431030.66275083, 2431030.67009292, 2431030.67748538],
             [2431025.97671083, 2431025.98499921, 2431025.99066612, ...,
              2431030.31140508, 2431030.31879804, 2431030.32745546]])

    • process_time_diff
      (chain, draw)
      float64
      0.007986 0.008114 ... 0.007488

      array([[0.007986, 0.008114, 0.011469, ..., 0.003479, 0.006959, 0.006972],
             [0.007405, 0.014784, 0.003834, ..., 0.007338, 0.007546, 0.014699],
             [0.014956, 0.008515, 0.007899, ..., 0.007272, 0.007309, 0.007286],
             [0.007987, 0.00469 , 0.008112, ..., 0.007323, 0.008097, 0.007488]])

    • reached_max_treedepth
      (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]])

    • smallest_eigval
      (chain, draw)
      float64
      nan nan nan nan ... nan nan nan nan

      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]])

    • step_size
      (chain, draw)
      float64
      0.4256 0.4256 ... 0.3861 0.3861

      array([[0.42557006, 0.42557006, 0.42557006, ..., 0.42557006, 0.42557006,
              0.42557006],
             [0.6043351 , 0.6043351 , 0.6043351 , ..., 0.6043351 , 0.6043351 ,
              0.6043351 ],
             [0.74596757, 0.74596757, 0.74596757, ..., 0.74596757, 0.74596757,
              0.74596757],
             [0.38606666, 0.38606666, 0.38606666, ..., 0.38606666, 0.38606666,
              0.38606666]])

    • step_size_bar
      (chain, draw)
      float64
      0.5357 0.5357 ... 0.4755 0.4755

      array([[0.53572783, 0.53572783, 0.53572783, ..., 0.53572783, 0.53572783,
              0.53572783],
             [0.46537907, 0.46537907, 0.46537907, ..., 0.46537907, 0.46537907,
              0.46537907],
             [0.43209038, 0.43209038, 0.43209038, ..., 0.43209038, 0.43209038,
              0.43209038],
             [0.4755282 , 0.4755282 , 0.4755282 , ..., 0.4755282 , 0.4755282 ,
              0.4755282 ]])

    • tree_depth
      (chain, draw)
      int64
      3 3 4 4 4 3 3 3 ... 3 2 4 3 3 3 3 3

      array([[3, 3, 4, ..., 2, 3, 3],
             [3, 4, 2, ..., 3, 3, 4],
             [4, 3, 3, ..., 3, 3, 3],
             [3, 2, 3, ..., 3, 3, 3]])

  • Indexes: (2)
    • chain
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
            dtype='int64', name='draw', length=500))

  • Attributes: (8)

    created_at :

    2025-02-18T22:11:14.084242+00:00

    arviz_version :

    0.19.0

    inference_library :

    pymc

    inference_library_version :

    5.19.1

    sampling_time :

    15.156437873840332

    tuning_steps :

    500

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.0

  
  
• observed_data

  <xarray.Dataset> Size: 24kB
  Dimensions:                  (__obs__: 1000, rt,response_extra_dim_0: 2)
  Coordinates:
    * __obs__                  (__obs__) int64 8kB 0 1 2 3 4 ... 996 997 998 999
    * rt,response_extra_dim_0  (rt,response_extra_dim_0) int64 16B 0 1
  Data variables:
      rt,response              (__obs__, rt,response_extra_dim_0) float64 16kB ...
  Attributes:
      created_at:                  2025-02-18T22:11:14.103497+00:00
      arviz_version:               0.19.0
      inference_library:           pymc
      inference_library_version:   5.19.1
      modeling_interface:          bambi
      modeling_interface_version:  0.15.0

  xarray.Dataset

  • Dimensions:
    • __obs__: 1000
    • rt,response_extra_dim_0: 2
  • Coordinates: (2)
    • __obs__
      (__obs__)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999])

    • rt,response_extra_dim_0
      (rt,response_extra_dim_0)
      int64
      0 1

      array([0, 1])

  • Data variables: (1)
    • rt,response
      (__obs__, rt,response_extra_dim_0)
      float64
      0.6262 1.0 4.277 ... 1.0 1.081 1.0

      array([[ 0.6262266 ,  1.        ],
             [ 4.27727699, -1.        ],
             [ 1.39999413,  1.        ],
             ...,
             [ 4.7823925 ,  1.        ],
             [ 1.1470964 ,  1.        ],
             [ 1.08128822,  1.        ]])

  • Indexes: (2)
    • __obs__
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='__obs__', length=1000))

    • rt,response_extra_dim_0
      PandasIndex

      PandasIndex(Index([0, 1], dtype='int64', name='rt,response_extra_dim_0'))

  • Attributes: (6)

    created_at :

    2025-02-18T22:11:14.103497+00:00

    arviz_version :

    0.19.0

    inference_library :

    pymc

    inference_library_version :

    5.19.1

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.0

  
  

Note how the idata include the v parameter which has the __obs__ coordinate. Computing these trial-wise parameters, can serve us well for plotting and other post-hoc analyses, here we would otherwise struggle to be effective without incurring some pre-computation pain (which in addition would be error prone). See e.g. the tutorial on hierarchical Variational Inference for an example.