Attach trial wise parameters to idata post-hoc¶

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 [1]:

import pandas as pd
import hssm

import pandas as pd import hssm

Simulate Data¶

In [2]:

# 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 [3]:

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: [t, z, a, v_Intercept, v_condition]

Output()

Sampling 4 chains for 500 tune and 500 draw iterations (2_000 + 2_000 draws total) took 17 seconds.
The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details
100%|██████████| 2000/2000 [00:01<00:00, 1468.13it/s]

Checking the idata object¶

In [4]:

idata

idata

Out[4]:

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:
      a                (chain, draw) float64 16kB 1.451 1.525 1.459 ... 1.496 1.5
      v_condition      (chain, draw, v_condition_dim) float64 16kB 0.5384 ... 0...
      t                (chain, draw) float64 16kB 0.13 0.07329 ... 0.0961 0.08384
      v_Intercept      (chain, draw) float64 16kB 0.5206 0.6879 ... 0.6451 0.6132
      z                (chain, draw) float64 16kB 0.4694 0.4642 ... 0.4799 0.4654
  Attributes:
      created_at:                  2025-09-27T18:39:31.023458+00:00
      arviz_version:               0.22.0
      inference_library:           pymc
      inference_library_version:   5.25.1
      sampling_time:               16.67565417289734
      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], shape=(500,))

    • v_condition_dim
      (v_condition_dim)
      <U2
      'C2'

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

  • Data variables: (5)
    • a
      (chain, draw)
      float64
      1.451 1.525 1.459 ... 1.496 1.5

      array([[1.45106251, 1.52540826, 1.4585095 , ..., 1.52873593, 1.45183711,
              1.47778987],
             [1.46361445, 1.44220471, 1.51224383, ..., 1.47909987, 1.50950166,
              1.50950166],
             [1.45868234, 1.54219879, 1.44265243, ..., 1.51037699, 1.53777174,
              1.46544368],
             [1.51788694, 1.49004495, 1.47905407, ..., 1.51462907, 1.49611195,
              1.50037066]], shape=(4, 500))

    • v_condition
      (chain, draw, v_condition_dim)
      float64
      0.5384 0.4482 ... 0.5208 0.5374

      array([[[0.53844103],
              [0.44816191],
              [0.53327817],
              ...,
              [0.43633621],
              [0.60838475],
              [0.52596921]],
      
             [[0.5006698 ],
              [0.50254597],
              [0.43987986],
              ...,
              [0.54335352],
              [0.48653608],
              [0.48653608]],
      
             [[0.52135926],
              [0.56453401],
              [0.42446749],
              ...,
              [0.50524344],
              [0.55846193],
              [0.5269144 ]],
      
             [[0.52615289],
              [0.48857295],
              [0.51738512],
              ...,
              [0.5976951 ],
              [0.52080949],
              [0.53736947]]], shape=(4, 500, 1))

    • t
      (chain, draw)
      float64
      0.13 0.07329 ... 0.0961 0.08384

      array([[0.13002467, 0.07328917, 0.11544478, ..., 0.10161289, 0.11814377,
              0.11359321],
             [0.12548785, 0.12196935, 0.12650266, ..., 0.11752049, 0.09821315,
              0.09821315],
             [0.10997856, 0.09242201, 0.12533099, ..., 0.08185775, 0.09374628,
              0.10354658],
             [0.08482131, 0.09963758, 0.09045551, ..., 0.10063254, 0.09609583,
              0.08383561]], shape=(4, 500))

    • v_Intercept
      (chain, draw)
      float64
      0.5206 0.6879 ... 0.6451 0.6132

      array([[0.52057116, 0.68786649, 0.58917466, ..., 0.6717081 , 0.58515998,
              0.66611895],
             [0.60325827, 0.58101715, 0.62427288, ..., 0.57570264, 0.56480157,
              0.56480157],
             [0.61653292, 0.58269045, 0.6912627 , ..., 0.64704138, 0.55962568,
              0.62759394],
             [0.66574029, 0.63600607, 0.63584347, ..., 0.56674825, 0.64509774,
              0.61320631]], shape=(4, 500))

    • z
      (chain, draw)
      float64
      0.4694 0.4642 ... 0.4799 0.4654

      array([[0.46939311, 0.46419084, 0.47891836, ..., 0.46820404, 0.45072108,
              0.46547088],
             [0.48861865, 0.46088043, 0.49085177, ..., 0.48556738, 0.48940291,
              0.48940291],
             [0.46582484, 0.49091371, 0.45417345, ..., 0.45180981, 0.48274017,
              0.46659174],
             [0.44614093, 0.48027135, 0.4595854 , ..., 0.45017127, 0.479884  ,
              0.46544844]], shape=(4, 500))

  • 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 :

    2025-09-27T18:39:31.023458+00:00

    arviz_version :

    0.22.0

    inference_library :

    pymc

    inference_library_version :

    5.25.1

    sampling_time :

    16.67565417289734

    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 -3.858 -1.374 ... -0.9489
  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], shape=(500,))

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

      array([  0,   1,   2, ..., 997, 998, 999], shape=(1000,))

  • Data variables: (1)
    • rt,response
      (chain, draw, __obs__)
      float64
      -3.858 -1.374 ... -0.4278 -0.9489

      array([[[-3.85848945, -1.37393815, -2.57483123, ..., -0.45588408,
               -0.47506209, -0.94711629],
              [-3.90929099, -1.2063424 , -2.5479039 , ..., -0.44970905,
               -0.46508231, -0.94284191],
              [-3.9386467 , -1.18801417, -2.60364964, ..., -0.37925217,
               -0.38816327, -0.96706647],
              ...,
              [-3.86028023, -1.296508  , -2.51833799, ..., -0.47890596,
               -0.50222945, -0.92133335],
              [-3.91809806, -1.39129426, -2.57636139, ..., -0.37968016,
               -0.39929244, -0.91816928],
              [-3.98012917, -1.23006596, -2.58911706, ..., -0.36675365,
               -0.38235068, -0.93015378]],
      
             [[-3.94997198, -1.14420594, -2.6078308 , ..., -0.37809112,
               -0.38665203, -0.9702782 ],
              [-3.95064076, -1.30635588, -2.60195119, ..., -0.44447482,
               -0.46285426, -0.94508972],
              [-3.84812582, -1.2272447 , -2.53900288, ..., -0.44993658,
               -0.46782362, -0.94648071],
      ...
              [-3.86061607, -1.33697386, -2.52548294, ..., -0.45577065,
               -0.47627026, -0.92238583],
              [-3.70277969, -1.33342965, -2.48515747, ..., -0.43562071,
               -0.45036724, -0.94591531],
              [-3.96435766, -1.20764743, -2.59969025, ..., -0.38372953,
               -0.39519894, -0.95296914]],
      
             [[-3.85974309, -1.38421905, -2.51214968, ..., -0.44281834,
               -0.46671254, -0.90237079],
              [-3.92807279, -1.15154592, -2.58393491, ..., -0.39766475,
               -0.40694348, -0.96529985],
              [-3.93658614, -1.24139837, -2.57904697, ..., -0.409857  ,
               -0.42348133, -0.94614434],
              ...,
              [-3.72702227, -1.53900928, -2.47583538, ..., -0.4625643 ,
               -0.49005786, -0.8964341 ],
              [-3.92713124, -1.14735518, -2.5804977 , ..., -0.36779772,
               -0.37560744, -0.96349689],
              [-3.85505369, -1.2644351 , -2.54458644, ..., -0.41497751,
               -0.42777218, -0.9488609 ]]], shape=(4, 500, 1000))

  • 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: 264kB
  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: (12/18)
      largest_eigval         (chain, draw) float64 16kB nan nan nan ... nan nan
      step_size              (chain, draw) float64 16kB 0.5168 0.5168 ... 0.7723
      process_time_diff      (chain, draw) float64 16kB 0.01719 ... 0.009474
      n_steps                (chain, draw) float64 16kB 15.0 7.0 7.0 ... 7.0 7.0
      divergences            (chain, draw) int64 16kB 0 0 0 0 0 0 ... 0 0 0 0 0 0
      reached_max_treedepth  (chain, draw) bool 2kB False False ... False False
      ...                     ...
      energy_error           (chain, draw) float64 16kB 0.3607 -0.593 ... -0.7798
      perf_counter_diff      (chain, draw) float64 16kB 0.02747 0.01597 ... 0.0147
      step_size_bar          (chain, draw) float64 16kB 0.4898 0.4898 ... 0.4493
      perf_counter_start     (chain, draw) float64 16kB 1.499e+06 ... 1.499e+06
      tree_depth             (chain, draw) int64 16kB 4 3 3 4 3 3 ... 2 3 3 3 3 3
      smallest_eigval        (chain, draw) float64 16kB nan nan nan ... nan nan
  Attributes:
      created_at:                  2025-09-27T18:39:31.034727+00:00
      arviz_version:               0.22.0
      inference_library:           pymc
      inference_library_version:   5.25.1
      sampling_time:               16.67565417289734
      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], shape=(500,))

  • Data variables: (18)
    • 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]], shape=(4, 500))

    • step_size
      (chain, draw)
      float64
      0.5168 0.5168 ... 0.7723 0.7723

      array([[0.51675147, 0.51675147, 0.51675147, ..., 0.51675147, 0.51675147,
              0.51675147],
             [0.55420921, 0.55420921, 0.55420921, ..., 0.55420921, 0.55420921,
              0.55420921],
             [0.53203696, 0.53203696, 0.53203696, ..., 0.53203696, 0.53203696,
              0.53203696],
             [0.77234289, 0.77234289, 0.77234289, ..., 0.77234289, 0.77234289,
              0.77234289]], shape=(4, 500))

    • process_time_diff
      (chain, draw)
      float64
      0.01719 0.01044 ... 0.009474

      array([[0.01719 , 0.010435, 0.008502, ..., 0.007504, 0.007367, 0.003594],
             [0.017574, 0.00698 , 0.008895, ..., 0.004574, 0.007443, 0.004378],
             [0.007771, 0.007692, 0.008376, ..., 0.007151, 0.007274, 0.007837],
             [0.009783, 0.009288, 0.009394, ..., 0.007894, 0.007694, 0.009474]],
            shape=(4, 500))

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

      array([[15.,  7.,  7., ...,  7.,  7.,  3.],
             [15.,  7.,  7., ...,  3.,  7.,  3.],
             [ 7.,  7.,  7., ...,  7.,  7.,  7.],
             [ 7.,  7.,  7., ...,  7.,  7.,  7.]], shape=(4, 500))

    • divergences
      (chain, draw)
      int64
      0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0

      array([[0, 0, 0, ..., 0, 0, 0],
             [0, 0, 0, ..., 0, 0, 0],
             [0, 0, 0, ..., 0, 0, 0],
             [0, 0, 0, ..., 0, 0, 0]], shape=(4, 500))

    • 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]], shape=(4, 500))

    • energy
      (chain, draw)
      float64
      1.623e+03 1.621e+03 ... 1.621e+03

      array([[1622.55753976, 1621.4752906 , 1617.83769046, ..., 1618.89207187,
              1622.2453911 , 1621.02435687],
             [1619.85581743, 1619.24036813, 1620.30010332, ..., 1619.66374189,
              1618.36403591, 1620.58369708],
             [1618.62393975, 1619.41508679, 1619.87868432, ..., 1620.83553985,
              1623.34006535, 1619.36081427],
             [1618.05695539, 1619.22692425, 1617.45198434, ..., 1621.9103877 ,
              1622.49794265, 1620.635279  ]], shape=(4, 500))

    • max_energy_error
      (chain, draw)
      float64
      1.064 -1.087 ... -1.033 -1.04

      array([[ 1.06365648, -1.08669436, -0.2592765 , ..., -0.27414452,
               0.85031687,  0.25236655],
             [-0.20014867, -0.16155421,  0.61043222, ..., -0.26262394,
               0.12648184,  0.47195494],
             [ 0.12098678,  0.16736508, -0.16541261, ..., -1.51278415,
               1.07130559,  0.39162307],
             [ 0.10180616,  0.40247401, -0.48494692, ...,  1.67033313,
              -1.03348825, -1.03957123]], shape=(4, 500))

    • lp
      (chain, draw)
      float64
      -1.621e+03 ... -1.616e+03

      array([[-1620.90291372, -1617.45456518, -1616.63852423, ...,
              -1617.30435871, -1619.81645372, -1617.36216118],
             [-1616.78713398, -1617.9929163 , -1617.98586336, ...,
              -1616.45919   , -1617.36262687, -1617.36262687],
             [-1616.22871125, -1618.76464982, -1618.81421381, ...,
              -1616.31029488, -1618.03942512, -1616.62017112],
             [-1617.15041356, -1616.68226689, -1616.37548286, ...,
              -1621.46744027, -1618.24789559, -1616.3530092 ]], shape=(4, 500))

    • acceptance_rate
      (chain, draw)
      float64
      0.6481 1.0 0.9938 ... 0.9967 0.8867

      array([[0.64809912, 1.        , 0.99382154, ..., 0.99420815, 0.71218516,
              0.92134003],
             [0.98046137, 0.96383016, 0.77709434, ..., 1.        , 0.95804722,
              0.73047262],
             [0.95341966, 0.94517137, 0.99974494, ..., 0.94760509, 0.61317598,
              0.9003985 ],
             [0.95807264, 0.85073795, 0.98497829, ..., 0.42711303, 0.99674609,
              0.8867474 ]], shape=(4, 500))

    • 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]], shape=(4, 500))

    • index_in_trajectory
      (chain, draw)
      int64
      -1 6 5 -5 6 -5 1 ... 3 7 2 -4 2 -1

      array([[-1,  6,  5, ...,  2,  4, -2],
             [ 1, -2,  5, ..., -3, -3,  0],
             [-5,  4,  6, ..., -3, -2,  3],
             [ 4, -6,  5, ..., -4,  2, -1]], shape=(4, 500))

    • energy_error
      (chain, draw)
      float64
      0.3607 -0.593 ... -0.5461 -0.7798

      array([[ 0.36071587, -0.59302466,  0.02225975, ..., -0.05641847,
              -0.12101546, -0.09211537],
             [-0.04110109,  0.13004571,  0.08141575, ..., -0.20037088,
               0.0103881 ,  0.        ],
             [ 0.02060882,  0.16736508,  0.00178702, ..., -1.21627901,
               0.13934482,  0.12449368],
             [ 0.06952252,  0.27998519, -0.20413714, ...,  1.67033313,
              -0.54613277, -0.779776  ]], shape=(4, 500))

    • perf_counter_diff
      (chain, draw)
      float64
      0.02747 0.01597 ... 0.009273 0.0147

      array([[0.02747221, 0.01596596, 0.01357229, ..., 0.00915821, 0.00919796,
              0.00438154],
             [0.02059396, 0.00763917, 0.01051242, ..., 0.00525967, 0.00765942,
              0.00562883],
             [0.01049604, 0.00923392, 0.01029546, ..., 0.00736713, 0.00870612,
              0.00984667],
             [0.01467388, 0.01012329, 0.01065242, ..., 0.00864583, 0.00927275,
              0.01470104]], shape=(4, 500))

    • step_size_bar
      (chain, draw)
      float64
      0.4898 0.4898 ... 0.4493 0.4493

      array([[0.48981696, 0.48981696, 0.48981696, ..., 0.48981696, 0.48981696,
              0.48981696],
             [0.4695521 , 0.4695521 , 0.4695521 , ..., 0.4695521 , 0.4695521 ,
              0.4695521 ],
             [0.51710055, 0.51710055, 0.51710055, ..., 0.51710055, 0.51710055,
              0.51710055],
             [0.44930076, 0.44930076, 0.44930076, ..., 0.44930076, 0.44930076,
              0.44930076]], shape=(4, 500))

    • perf_counter_start
      (chain, draw)
      float64
      1.499e+06 1.499e+06 ... 1.499e+06

      array([[1499376.95434575, 1499376.981935  , 1499376.99869779, ...,
              1499382.57976129, 1499382.58900408, 1499382.59829046],
             [1499376.35775242, 1499376.3784425 , 1499376.38620508, ...,
              1499382.07366817, 1499382.07909338, 1499382.08684254],
             [1499377.18749921, 1499377.19809488, 1499377.20743017, ...,
              1499382.58103742, 1499382.58849342, 1499382.59731133],
             [1499376.436144  , 1499376.45097575, 1499376.46117792, ...,
              1499382.24516879, 1499382.25424417, 1499382.26360346]],
            shape=(4, 500))

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

      array([[4, 3, 3, ..., 3, 3, 2],
             [4, 3, 3, ..., 2, 3, 2],
             [3, 3, 3, ..., 3, 3, 3],
             [3, 3, 3, ..., 3, 3, 3]], shape=(4, 500))

    • 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]], shape=(4, 500))

  • 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 :

    2025-09-27T18:39:31.034727+00:00

    arviz_version :

    0.22.0

    inference_library :

    pymc

    inference_library_version :

    5.25.1

    sampling_time :

    16.67565417289734

    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:                  2025-09-27T18:39:31.038482+00:00
      arviz_version:               0.22.0
      inference_library:           pymc
      inference_library_version:   5.25.1
      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], shape=(1000,))

    • 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
      5.32 1.0 0.5291 ... 1.0 1.435 1.0

      array([[5.31995773, 1.        ],
             [0.5291388 , 1.        ],
             [3.41043663, 1.        ],
             ...,
             [0.71072024, 1.        ],
             [0.67398906, 1.        ],
             [1.4347496 , 1.        ]], shape=(1000, 2))

  • 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 :

    2025-09-27T18:39:31.038482+00:00

    arviz_version :

    0.22.0

    inference_library :

    pymc

    inference_library_version :

    5.25.1

    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 [5]:

model.graph()

model.graph()

Out[5]:

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 [6]:

### 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[6]:

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:
      a                (chain, draw) float64 16kB 1.451 1.525 1.459 ... 1.496 1.5
      v_condition      (chain, draw, v_condition_dim) float64 16kB 0.5384 ... 0...
      t                (chain, draw) float64 16kB 0.13 0.07329 ... 0.0961 0.08384
      v_Intercept      (chain, draw) float64 16kB 0.5206 0.6879 ... 0.6451 0.6132
      z                (chain, draw) float64 16kB 0.4694 0.4642 ... 0.4799 0.4654
      v                (chain, draw, __obs__) float64 16MB 0.5206 0.5206 ... 1.151
  Attributes:
      created_at:                  2025-09-27T18:39:31.023458+00:00
      arviz_version:               0.22.0
      inference_library:           pymc
      inference_library_version:   5.25.1
      sampling_time:               16.67565417289734
      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], shape=(500,))

    • 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], shape=(1000,))

  • Data variables: (6)
    • a
      (chain, draw)
      float64
      1.451 1.525 1.459 ... 1.496 1.5

      array([[1.45106251, 1.52540826, 1.4585095 , ..., 1.52873593, 1.45183711,
              1.47778987],
             [1.46361445, 1.44220471, 1.51224383, ..., 1.47909987, 1.50950166,
              1.50950166],
             [1.45868234, 1.54219879, 1.44265243, ..., 1.51037699, 1.53777174,
              1.46544368],
             [1.51788694, 1.49004495, 1.47905407, ..., 1.51462907, 1.49611195,
              1.50037066]], shape=(4, 500))

    • v_condition
      (chain, draw, v_condition_dim)
      float64
      0.5384 0.4482 ... 0.5208 0.5374

      array([[[0.53844103],
              [0.44816191],
              [0.53327817],
              ...,
              [0.43633621],
              [0.60838475],
              [0.52596921]],
      
             [[0.5006698 ],
              [0.50254597],
              [0.43987986],
              ...,
              [0.54335352],
              [0.48653608],
              [0.48653608]],
      
             [[0.52135926],
              [0.56453401],
              [0.42446749],
              ...,
              [0.50524344],
              [0.55846193],
              [0.5269144 ]],
      
             [[0.52615289],
              [0.48857295],
              [0.51738512],
              ...,
              [0.5976951 ],
              [0.52080949],
              [0.53736947]]], shape=(4, 500, 1))

    • t
      (chain, draw)
      float64
      0.13 0.07329 ... 0.0961 0.08384

      array([[0.13002467, 0.07328917, 0.11544478, ..., 0.10161289, 0.11814377,
              0.11359321],
             [0.12548785, 0.12196935, 0.12650266, ..., 0.11752049, 0.09821315,
              0.09821315],
             [0.10997856, 0.09242201, 0.12533099, ..., 0.08185775, 0.09374628,
              0.10354658],
             [0.08482131, 0.09963758, 0.09045551, ..., 0.10063254, 0.09609583,
              0.08383561]], shape=(4, 500))

    • v_Intercept
      (chain, draw)
      float64
      0.5206 0.6879 ... 0.6451 0.6132

      array([[0.52057116, 0.68786649, 0.58917466, ..., 0.6717081 , 0.58515998,
              0.66611895],
             [0.60325827, 0.58101715, 0.62427288, ..., 0.57570264, 0.56480157,
              0.56480157],
             [0.61653292, 0.58269045, 0.6912627 , ..., 0.64704138, 0.55962568,
              0.62759394],
             [0.66574029, 0.63600607, 0.63584347, ..., 0.56674825, 0.64509774,
              0.61320631]], shape=(4, 500))

    • z
      (chain, draw)
      float64
      0.4694 0.4642 ... 0.4799 0.4654

      array([[0.46939311, 0.46419084, 0.47891836, ..., 0.46820404, 0.45072108,
              0.46547088],
             [0.48861865, 0.46088043, 0.49085177, ..., 0.48556738, 0.48940291,
              0.48940291],
             [0.46582484, 0.49091371, 0.45417345, ..., 0.45180981, 0.48274017,
              0.46659174],
             [0.44614093, 0.48027135, 0.4595854 , ..., 0.45017127, 0.479884  ,
              0.46544844]], shape=(4, 500))

    • v
      (chain, draw, __obs__)
      float64
      0.5206 0.5206 ... 1.151 1.151

      array([[[0.52057116, 0.52057116, 0.52057116, ..., 1.05901219,
               1.05901219, 1.05901219],
              [0.68786649, 0.68786649, 0.68786649, ..., 1.1360284 ,
               1.1360284 , 1.1360284 ],
              [0.58917466, 0.58917466, 0.58917466, ..., 1.12245284,
               1.12245284, 1.12245284],
              ...,
              [0.6717081 , 0.6717081 , 0.6717081 , ..., 1.1080443 ,
               1.1080443 , 1.1080443 ],
              [0.58515998, 0.58515998, 0.58515998, ..., 1.19354473,
               1.19354473, 1.19354473],
              [0.66611895, 0.66611895, 0.66611895, ..., 1.19208816,
               1.19208816, 1.19208816]],
      
             [[0.60325827, 0.60325827, 0.60325827, ..., 1.10392808,
               1.10392808, 1.10392808],
              [0.58101715, 0.58101715, 0.58101715, ..., 1.08356311,
               1.08356311, 1.08356311],
              [0.62427288, 0.62427288, 0.62427288, ..., 1.06415273,
               1.06415273, 1.06415273],
      ...
              [0.64704138, 0.64704138, 0.64704138, ..., 1.15228481,
               1.15228481, 1.15228481],
              [0.55962568, 0.55962568, 0.55962568, ..., 1.11808761,
               1.11808761, 1.11808761],
              [0.62759394, 0.62759394, 0.62759394, ..., 1.15450835,
               1.15450835, 1.15450835]],
      
             [[0.66574029, 0.66574029, 0.66574029, ..., 1.19189318,
               1.19189318, 1.19189318],
              [0.63600607, 0.63600607, 0.63600607, ..., 1.12457902,
               1.12457902, 1.12457902],
              [0.63584347, 0.63584347, 0.63584347, ..., 1.15322859,
               1.15322859, 1.15322859],
              ...,
              [0.56674825, 0.56674825, 0.56674825, ..., 1.16444335,
               1.16444335, 1.16444335],
              [0.64509774, 0.64509774, 0.64509774, ..., 1.16590723,
               1.16590723, 1.16590723],
              [0.61320631, 0.61320631, 0.61320631, ..., 1.15057578,
               1.15057578, 1.15057578]]], shape=(4, 500, 1000))

  • 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 :

    2025-09-27T18:39:31.023458+00:00

    arviz_version :

    0.22.0

    inference_library :

    pymc

    inference_library_version :

    5.25.1

    sampling_time :

    16.67565417289734

    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 -3.858 -1.374 ... -0.9489
  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], shape=(500,))

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

      array([  0,   1,   2, ..., 997, 998, 999], shape=(1000,))

  • Data variables: (1)
    • rt,response
      (chain, draw, __obs__)
      float64
      -3.858 -1.374 ... -0.4278 -0.9489

      array([[[-3.85848945, -1.37393815, -2.57483123, ..., -0.45588408,
               -0.47506209, -0.94711629],
              [-3.90929099, -1.2063424 , -2.5479039 , ..., -0.44970905,
               -0.46508231, -0.94284191],
              [-3.9386467 , -1.18801417, -2.60364964, ..., -0.37925217,
               -0.38816327, -0.96706647],
              ...,
              [-3.86028023, -1.296508  , -2.51833799, ..., -0.47890596,
               -0.50222945, -0.92133335],
              [-3.91809806, -1.39129426, -2.57636139, ..., -0.37968016,
               -0.39929244, -0.91816928],
              [-3.98012917, -1.23006596, -2.58911706, ..., -0.36675365,
               -0.38235068, -0.93015378]],
      
             [[-3.94997198, -1.14420594, -2.6078308 , ..., -0.37809112,
               -0.38665203, -0.9702782 ],
              [-3.95064076, -1.30635588, -2.60195119, ..., -0.44447482,
               -0.46285426, -0.94508972],
              [-3.84812582, -1.2272447 , -2.53900288, ..., -0.44993658,
               -0.46782362, -0.94648071],
      ...
              [-3.86061607, -1.33697386, -2.52548294, ..., -0.45577065,
               -0.47627026, -0.92238583],
              [-3.70277969, -1.33342965, -2.48515747, ..., -0.43562071,
               -0.45036724, -0.94591531],
              [-3.96435766, -1.20764743, -2.59969025, ..., -0.38372953,
               -0.39519894, -0.95296914]],
      
             [[-3.85974309, -1.38421905, -2.51214968, ..., -0.44281834,
               -0.46671254, -0.90237079],
              [-3.92807279, -1.15154592, -2.58393491, ..., -0.39766475,
               -0.40694348, -0.96529985],
              [-3.93658614, -1.24139837, -2.57904697, ..., -0.409857  ,
               -0.42348133, -0.94614434],
              ...,
              [-3.72702227, -1.53900928, -2.47583538, ..., -0.4625643 ,
               -0.49005786, -0.8964341 ],
              [-3.92713124, -1.14735518, -2.5804977 , ..., -0.36779772,
               -0.37560744, -0.96349689],
              [-3.85505369, -1.2644351 , -2.54458644, ..., -0.41497751,
               -0.42777218, -0.9488609 ]]], shape=(4, 500, 1000))

  • 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: 264kB
  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: (12/18)
      largest_eigval         (chain, draw) float64 16kB nan nan nan ... nan nan
      step_size              (chain, draw) float64 16kB 0.5168 0.5168 ... 0.7723
      process_time_diff      (chain, draw) float64 16kB 0.01719 ... 0.009474
      n_steps                (chain, draw) float64 16kB 15.0 7.0 7.0 ... 7.0 7.0
      divergences            (chain, draw) int64 16kB 0 0 0 0 0 0 ... 0 0 0 0 0 0
      reached_max_treedepth  (chain, draw) bool 2kB False False ... False False
      ...                     ...
      energy_error           (chain, draw) float64 16kB 0.3607 -0.593 ... -0.7798
      perf_counter_diff      (chain, draw) float64 16kB 0.02747 0.01597 ... 0.0147
      step_size_bar          (chain, draw) float64 16kB 0.4898 0.4898 ... 0.4493
      perf_counter_start     (chain, draw) float64 16kB 1.499e+06 ... 1.499e+06
      tree_depth             (chain, draw) int64 16kB 4 3 3 4 3 3 ... 2 3 3 3 3 3
      smallest_eigval        (chain, draw) float64 16kB nan nan nan ... nan nan
  Attributes:
      created_at:                  2025-09-27T18:39:31.034727+00:00
      arviz_version:               0.22.0
      inference_library:           pymc
      inference_library_version:   5.25.1
      sampling_time:               16.67565417289734
      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], shape=(500,))

  • Data variables: (18)
    • 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]], shape=(4, 500))

    • step_size
      (chain, draw)
      float64
      0.5168 0.5168 ... 0.7723 0.7723

      array([[0.51675147, 0.51675147, 0.51675147, ..., 0.51675147, 0.51675147,
              0.51675147],
             [0.55420921, 0.55420921, 0.55420921, ..., 0.55420921, 0.55420921,
              0.55420921],
             [0.53203696, 0.53203696, 0.53203696, ..., 0.53203696, 0.53203696,
              0.53203696],
             [0.77234289, 0.77234289, 0.77234289, ..., 0.77234289, 0.77234289,
              0.77234289]], shape=(4, 500))

    • process_time_diff
      (chain, draw)
      float64
      0.01719 0.01044 ... 0.009474

      array([[0.01719 , 0.010435, 0.008502, ..., 0.007504, 0.007367, 0.003594],
             [0.017574, 0.00698 , 0.008895, ..., 0.004574, 0.007443, 0.004378],
             [0.007771, 0.007692, 0.008376, ..., 0.007151, 0.007274, 0.007837],
             [0.009783, 0.009288, 0.009394, ..., 0.007894, 0.007694, 0.009474]],
            shape=(4, 500))

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

      array([[15.,  7.,  7., ...,  7.,  7.,  3.],
             [15.,  7.,  7., ...,  3.,  7.,  3.],
             [ 7.,  7.,  7., ...,  7.,  7.,  7.],
             [ 7.,  7.,  7., ...,  7.,  7.,  7.]], shape=(4, 500))

    • divergences
      (chain, draw)
      int64
      0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0

      array([[0, 0, 0, ..., 0, 0, 0],
             [0, 0, 0, ..., 0, 0, 0],
             [0, 0, 0, ..., 0, 0, 0],
             [0, 0, 0, ..., 0, 0, 0]], shape=(4, 500))

    • 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]], shape=(4, 500))

    • energy
      (chain, draw)
      float64
      1.623e+03 1.621e+03 ... 1.621e+03

      array([[1622.55753976, 1621.4752906 , 1617.83769046, ..., 1618.89207187,
              1622.2453911 , 1621.02435687],
             [1619.85581743, 1619.24036813, 1620.30010332, ..., 1619.66374189,
              1618.36403591, 1620.58369708],
             [1618.62393975, 1619.41508679, 1619.87868432, ..., 1620.83553985,
              1623.34006535, 1619.36081427],
             [1618.05695539, 1619.22692425, 1617.45198434, ..., 1621.9103877 ,
              1622.49794265, 1620.635279  ]], shape=(4, 500))

    • max_energy_error
      (chain, draw)
      float64
      1.064 -1.087 ... -1.033 -1.04

      array([[ 1.06365648, -1.08669436, -0.2592765 , ..., -0.27414452,
               0.85031687,  0.25236655],
             [-0.20014867, -0.16155421,  0.61043222, ..., -0.26262394,
               0.12648184,  0.47195494],
             [ 0.12098678,  0.16736508, -0.16541261, ..., -1.51278415,
               1.07130559,  0.39162307],
             [ 0.10180616,  0.40247401, -0.48494692, ...,  1.67033313,
              -1.03348825, -1.03957123]], shape=(4, 500))

    • lp
      (chain, draw)
      float64
      -1.621e+03 ... -1.616e+03

      array([[-1620.90291372, -1617.45456518, -1616.63852423, ...,
              -1617.30435871, -1619.81645372, -1617.36216118],
             [-1616.78713398, -1617.9929163 , -1617.98586336, ...,
              -1616.45919   , -1617.36262687, -1617.36262687],
             [-1616.22871125, -1618.76464982, -1618.81421381, ...,
              -1616.31029488, -1618.03942512, -1616.62017112],
             [-1617.15041356, -1616.68226689, -1616.37548286, ...,
              -1621.46744027, -1618.24789559, -1616.3530092 ]], shape=(4, 500))

    • acceptance_rate
      (chain, draw)
      float64
      0.6481 1.0 0.9938 ... 0.9967 0.8867

      array([[0.64809912, 1.        , 0.99382154, ..., 0.99420815, 0.71218516,
              0.92134003],
             [0.98046137, 0.96383016, 0.77709434, ..., 1.        , 0.95804722,
              0.73047262],
             [0.95341966, 0.94517137, 0.99974494, ..., 0.94760509, 0.61317598,
              0.9003985 ],
             [0.95807264, 0.85073795, 0.98497829, ..., 0.42711303, 0.99674609,
              0.8867474 ]], shape=(4, 500))

    • 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]], shape=(4, 500))

    • index_in_trajectory
      (chain, draw)
      int64
      -1 6 5 -5 6 -5 1 ... 3 7 2 -4 2 -1

      array([[-1,  6,  5, ...,  2,  4, -2],
             [ 1, -2,  5, ..., -3, -3,  0],
             [-5,  4,  6, ..., -3, -2,  3],
             [ 4, -6,  5, ..., -4,  2, -1]], shape=(4, 500))

    • energy_error
      (chain, draw)
      float64
      0.3607 -0.593 ... -0.5461 -0.7798

      array([[ 0.36071587, -0.59302466,  0.02225975, ..., -0.05641847,
              -0.12101546, -0.09211537],
             [-0.04110109,  0.13004571,  0.08141575, ..., -0.20037088,
               0.0103881 ,  0.        ],
             [ 0.02060882,  0.16736508,  0.00178702, ..., -1.21627901,
               0.13934482,  0.12449368],
             [ 0.06952252,  0.27998519, -0.20413714, ...,  1.67033313,
              -0.54613277, -0.779776  ]], shape=(4, 500))

    • perf_counter_diff
      (chain, draw)
      float64
      0.02747 0.01597 ... 0.009273 0.0147

      array([[0.02747221, 0.01596596, 0.01357229, ..., 0.00915821, 0.00919796,
              0.00438154],
             [0.02059396, 0.00763917, 0.01051242, ..., 0.00525967, 0.00765942,
              0.00562883],
             [0.01049604, 0.00923392, 0.01029546, ..., 0.00736713, 0.00870612,
              0.00984667],
             [0.01467388, 0.01012329, 0.01065242, ..., 0.00864583, 0.00927275,
              0.01470104]], shape=(4, 500))

    • step_size_bar
      (chain, draw)
      float64
      0.4898 0.4898 ... 0.4493 0.4493

      array([[0.48981696, 0.48981696, 0.48981696, ..., 0.48981696, 0.48981696,
              0.48981696],
             [0.4695521 , 0.4695521 , 0.4695521 , ..., 0.4695521 , 0.4695521 ,
              0.4695521 ],
             [0.51710055, 0.51710055, 0.51710055, ..., 0.51710055, 0.51710055,
              0.51710055],
             [0.44930076, 0.44930076, 0.44930076, ..., 0.44930076, 0.44930076,
              0.44930076]], shape=(4, 500))

    • perf_counter_start
      (chain, draw)
      float64
      1.499e+06 1.499e+06 ... 1.499e+06

      array([[1499376.95434575, 1499376.981935  , 1499376.99869779, ...,
              1499382.57976129, 1499382.58900408, 1499382.59829046],
             [1499376.35775242, 1499376.3784425 , 1499376.38620508, ...,
              1499382.07366817, 1499382.07909338, 1499382.08684254],
             [1499377.18749921, 1499377.19809488, 1499377.20743017, ...,
              1499382.58103742, 1499382.58849342, 1499382.59731133],
             [1499376.436144  , 1499376.45097575, 1499376.46117792, ...,
              1499382.24516879, 1499382.25424417, 1499382.26360346]],
            shape=(4, 500))

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

      array([[4, 3, 3, ..., 3, 3, 2],
             [4, 3, 3, ..., 2, 3, 2],
             [3, 3, 3, ..., 3, 3, 3],
             [3, 3, 3, ..., 3, 3, 3]], shape=(4, 500))

    • 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]], shape=(4, 500))

  • 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 :

    2025-09-27T18:39:31.034727+00:00

    arviz_version :

    0.22.0

    inference_library :

    pymc

    inference_library_version :

    5.25.1

    sampling_time :

    16.67565417289734

    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:                  2025-09-27T18:39:31.038482+00:00
      arviz_version:               0.22.0
      inference_library:           pymc
      inference_library_version:   5.25.1
      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], shape=(1000,))

    • 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
      5.32 1.0 0.5291 ... 1.0 1.435 1.0

      array([[5.31995773, 1.        ],
             [0.5291388 , 1.        ],
             [3.41043663, 1.        ],
             ...,
             [0.71072024, 1.        ],
             [0.67398906, 1.        ],
             [1.4347496 , 1.        ]], shape=(1000, 2))

  • 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 :

    2025-09-27T18:39:31.038482+00:00

    arviz_version :

    0.22.0

    inference_library :

    pymc

    inference_library_version :

    5.25.1

    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.