Alternative sampling backends

In Bambi, the sampler used is automatically selected given the type of variables used in the model. Bambi supports both MCMC and variational inference for fitting models. By default, Bambi uses PyMC’s implementation of the adaptive Hamiltonian Monte Carlo (HMC) algorithm for sampling. Also known as the No-U-Turn Sampler (NUTS). This sampler is a good choice for many models. However, PyMC is not the only library implementing NUTS.

To this extent, Bambi also supports the NumPyro, Blackjax, and Nutpie NUTS samplers. This notebook will cover how to use these alternative samplers in Bambi.

Note: To use these samplers, you need to install numpyro, blackjax and or nutpie with a package manager of your choice.

import bambi as bmb
import numpy as np
import pandas as pd

Specifying an inference_method

To demonstrate the different inference methods, we will first simulate data and build a model.

num_samples = 100
num_features = 1
noise_std = 1.0
random_seed = 42

rng = np.random.default_rng(random_seed)

coefficients = rng.normal(size=num_features)
X = rng.normal(size=(num_samples, num_features))
error = rng.normal(scale=noise_std, size=num_samples)
y = X @ coefficients + error

data = pd.DataFrame({"y": y, "x": X.flatten()})

model = bmb.Model("y ~ x", data)

By default, Bambi uses the PyMC NUTS implementation. To use a different backend, pass the name of the desired MCMC implementation to the inference_method parameter of the fit method.

Blackjax

%%time
blackjax_nuts_idata = model.fit(inference_method="blackjax", progressbar=False)

WARNING:2025-09-28 13:00:20,305:jax._src.xla_bridge:864: An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.

CPU times: user 7.64 s, sys: 3.05 s, total: 10.7 s
Wall time: 7.19 s

blackjax_nuts_idata

arviz.InferenceData

• posterior

  <xarray.Dataset> Size: 104kB
  Dimensions:    (chain: 4, draw: 1000)
  Coordinates:
    * chain      (chain) int64 32B 0 1 2 3
    * draw       (draw) int64 8kB 0 1 2 3 4 5 6 7 ... 993 994 995 996 997 998 999
  Data variables:
      Intercept  (chain, draw) float64 32kB 0.004918 0.02806 ... 0.1205 -0.01849
      x          (chain, draw) float64 32kB 0.3537 0.1788 0.473 ... 0.3752 0.4473
      sigma      (chain, draw) float64 32kB 1.058 1.083 0.9034 ... 1.033 0.9862
  Attributes:
      created_at:                  2025-09-28T16:00:24.433389+00:00
      arviz_version:               0.22.0
      inference_library:           blackjax
      inference_library_version:   1.2.4
      sampling_time:               2.107706
      tuning_steps:                1000
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

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

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

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

  • Data variables: (3)
    • Intercept
      (chain, draw)
      float64
      0.004918 0.02806 ... -0.01849

      array([[ 4.91794194e-03,  2.80562885e-02, -2.80642938e-02, ...,
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             [-1.33210414e-01,  1.36706270e-01, -2.94183599e-02, ...,
               8.03053396e-02, -1.44146739e-01, -1.26193945e-01],
             [ 1.24225721e-04, -9.14519478e-02,  1.28875457e-01, ...,
               7.27116980e-02,  3.73215159e-02,  1.47309486e-01],
             [-9.16987651e-02, -2.27750297e-01, -2.62549483e-01, ...,
               7.57867549e-02,  1.20508172e-01, -1.84873562e-02]],
            shape=(4, 1000))

    • x
      (chain, draw)
      float64
      0.3537 0.1788 ... 0.3752 0.4473

      array([[0.35368982, 0.17876679, 0.47302348, ..., 0.47364814, 0.21463484,
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             [0.32935474, 0.49494605, 0.54949731, ..., 0.68842936, 0.45230934,
              0.37074948],
             [0.51425115, 0.53857576, 0.34285248, ..., 0.48399325, 0.47288574,
              0.52404707],
             [0.7587739 , 0.3778179 , 0.43217596, ..., 0.41837768, 0.37521251,
              0.44725723]], shape=(4, 1000))

    • sigma
      (chain, draw)
      float64
      1.058 1.083 0.9034 ... 1.033 0.9862

      array([[1.05804313, 1.08304544, 0.90339877, ..., 1.0274421 , 1.03313774,
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             [0.92813087, 0.90883127, 0.95750106, ..., 1.0629137 , 1.03812316,
              0.98170139],
             [0.91313538, 1.00626354, 0.9637941 , ..., 1.01935493, 1.0238816 ,
              0.98776233],
             [0.97923268, 1.04991668, 1.11058387, ..., 0.96670097, 1.03326617,
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  • 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,
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            dtype='int64', name='draw', length=1000))

  • Attributes: (8)

    created_at :

    2025-09-28T16:00:24.433389+00:00

    arviz_version :

    0.22.0

    inference_library :

    blackjax

    inference_library_version :

    1.2.4

    sampling_time :

    2.107706

    tuning_steps :

    1000

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  
• sample_stats

  <xarray.Dataset> Size: 172kB
  Dimensions:          (chain: 4, draw: 1000)
  Coordinates:
    * chain            (chain) int64 32B 0 1 2 3
    * draw             (draw) int64 8kB 0 1 2 3 4 5 6 ... 994 995 996 997 998 999
  Data variables:
      acceptance_rate  (chain, draw) float64 32kB 1.0 0.8539 ... 0.9393 0.9043
      diverging        (chain, draw) bool 4kB False False False ... False False
      energy           (chain, draw) float64 32kB 146.1 147.1 ... 145.1 146.3
      lp               (chain, draw) float64 32kB -144.5 -146.4 ... -144.8 -143.8
      n_steps          (chain, draw) int64 32kB 3 3 3 3 3 7 7 3 ... 7 5 7 7 7 7 3
      tree_depth       (chain, draw) int64 32kB 2 2 2 2 2 3 3 2 ... 3 3 3 3 3 3 2
  Attributes:
      created_at:                  2025-09-28T16:00:24.442990+00:00
      arviz_version:               0.22.0
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

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

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

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

  • Data variables: (6)
    • acceptance_rate
      (chain, draw)
      float64
      1.0 0.8539 0.967 ... 0.9393 0.9043

      array([[1.        , 0.85391933, 0.96701492, ..., 0.96826543, 0.74383773,
              0.95553333],
             [0.93022988, 0.66489315, 0.99680011, ..., 0.8601257 , 0.99508788,
              0.97791681],
             [0.94615669, 0.81733891, 0.97237491, ..., 0.96268828, 1.        ,
              0.94096427],
             [0.98157658, 1.        , 0.96176109, ..., 0.99553367, 0.93931938,
              0.90431683]], shape=(4, 1000))

    • 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, 1000))

    • energy
      (chain, draw)
      float64
      146.1 147.1 147.2 ... 145.1 146.3

      array([[146.12470642, 147.06645862, 147.21675502, ..., 147.16451433,
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             [145.42088493, 150.49066418, 145.88223935, ..., 146.96240758,
              147.40999873, 145.76841248],
             [144.46654762, 147.23355764, 145.64176059, ..., 144.38938058,
              144.337365  , 145.19189544],
             [150.16893656, 150.38540553, 148.6431233 , ..., 144.5371071 ,
              145.08256196, 146.25616965]], shape=(4, 1000))

    • lp
      (chain, draw)
      float64
      -144.5 -146.4 ... -144.8 -143.8

      array([[-144.53602343, -146.4143908 , -144.39756137, ..., -144.22577839,
              -145.41039201, -146.13985305],
             [-145.2100306 , -145.34515218, -144.31608554, ..., -146.50572172,
              -145.1874233 , -144.62587007],
             [-144.38176877, -144.72101355, -144.82315778, ..., -144.24404038,
              -144.08879697, -145.01527747],
             [-147.88353956, -146.71403634, -148.25521096, ..., -143.98081098,
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    • n_steps
      (chain, draw)
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      3 3 3 3 3 7 7 3 ... 7 7 5 7 7 7 7 3

      array([[3, 3, 3, ..., 7, 3, 7],
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    • tree_depth
      (chain, draw)
      int64
      2 2 2 2 2 3 3 2 ... 3 3 3 3 3 3 3 2

      array([[2, 2, 2, ..., 3, 2, 3],
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             [2, 3, 3, ..., 2, 2, 2],
             [3, 3, 2, ..., 3, 3, 2]], shape=(4, 1000))

  • Indexes: (2)
    • chain
      PandasIndex

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

    • draw
      PandasIndex

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            dtype='int64', name='draw', length=1000))

  • Attributes: (4)

    created_at :

    2025-09-28T16:00:24.442990+00:00

    arviz_version :

    0.22.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  
• observed_data

  <xarray.Dataset> Size: 2kB
  Dimensions:  (__obs__: 100)
  Coordinates:
    * __obs__  (__obs__) int64 800B 0 1 2 3 4 5 6 7 8 ... 92 93 94 95 96 97 98 99
  Data variables:
      y        (__obs__) float64 800B 0.9823 -0.1276 1.024 ... -0.4394 0.2223
  Attributes:
      created_at:                  2025-09-28T16:00:24.445274+00:00
      arviz_version:               0.22.0
      inference_library:           blackjax
      inference_library_version:   1.2.4
      sampling_time:               2.107706
      tuning_steps:                1000
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • __obs__: 100
  • Coordinates: (1)
    • __obs__
      (__obs__)
      int64
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      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
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             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
             54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,
             72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
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  • Data variables: (1)
    • y
      (__obs__)
      float64
      0.9823 -0.1276 ... -0.4394 0.2223

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              0.47474209, -0.57402927, -1.10256821,  0.21458759, -0.7913338 ,
              0.34504087, -0.27033576,  1.8694577 , -0.25456891, -1.07982821,
             -0.02821523,  0.59252591,  1.3120998 ,  0.70459244,  0.24956995,
              1.62550659, -1.07740601, -0.51398486, -0.79529742,  0.2627868 ,
             -1.50052774,  0.47906184, -0.47019315, -1.28310684, -0.67156194,
              0.27879211,  0.58211654,  1.74549738,  3.1121092 ,  0.64089167,
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             -0.34655757, -0.0726575 ,  1.27285679,  0.17764106, -0.07053522,
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  • Indexes: (1)
    • __obs__
      PandasIndex

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  • Attributes: (8)

    created_at :

    2025-09-28T16:00:24.445274+00:00

    arviz_version :

    0.22.0

    inference_library :

    blackjax

    inference_library_version :

    1.2.4

    sampling_time :

    2.107706

    tuning_steps :

    1000

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  

NumPyro

%%time
numpyro_nuts_idata = model.fit(inference_method="numpyro", progressbar=False)

CPU times: user 3.43 s, sys: 294 ms, total: 3.72 s
Wall time: 1.55 s

numpyro_nuts_idata

arviz.InferenceData

• posterior

  <xarray.Dataset> Size: 104kB
  Dimensions:    (chain: 4, draw: 1000)
  Coordinates:
    * chain      (chain) int64 32B 0 1 2 3
    * draw       (draw) int64 8kB 0 1 2 3 4 5 6 7 ... 993 994 995 996 997 998 999
  Data variables:
      Intercept  (chain, draw) float64 32kB 0.184 -0.1767 ... -0.1061 0.07233
      x          (chain, draw) float64 32kB 0.3783 0.4742 0.5178 ... 0.5458 0.3218
      sigma      (chain, draw) float64 32kB 0.9515 1.011 1.006 ... 1.018 0.939
  Attributes:
      created_at:                  2025-09-28T16:00:26.212193+00:00
      arviz_version:               0.22.0
      inference_library:           numpyro
      inference_library_version:   0.19.0
      sampling_time:               1.23596
      tuning_steps:                1000
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

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

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

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

  • Data variables: (3)
    • Intercept
      (chain, draw)
      float64
      0.184 -0.1767 ... -0.1061 0.07233

      array([[ 0.18401831, -0.17669268,  0.04883402, ..., -0.0077284 ,
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              -0.1114524 ,  0.06342714],
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              -0.10611858,  0.0723307 ]], shape=(4, 1000))

    • x
      (chain, draw)
      float64
      0.3783 0.4742 ... 0.5458 0.3218

      array([[0.37830558, 0.47422638, 0.51776939, ..., 0.52210026, 0.30455979,
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             [0.53227134, 0.20270225, 0.58512545, ..., 0.52236569, 0.38371171,
              0.45487183],
             [0.522337  , 0.46261773, 0.61402066, ..., 0.1236397 , 0.45802115,
              0.56050949],
             [0.28027649, 0.28902443, 0.45660752, ..., 0.58410362, 0.5458288 ,
              0.3218251 ]], shape=(4, 1000))

    • sigma
      (chain, draw)
      float64
      0.9515 1.011 1.006 ... 1.018 0.939

      array([[0.95147699, 1.01094478, 1.00571331, ..., 0.95051426, 1.09091123,
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             [0.91243247, 1.07953629, 0.89254852, ..., 1.00808039, 0.96980928,
              0.94271915],
             [0.94543459, 1.10677686, 1.05865136, ..., 1.01885814, 0.91864727,
              0.98215822],
             [0.92582327, 1.00607134, 1.01032978, ..., 1.01253909, 1.018336  ,
              0.9389868 ]], shape=(4, 1000))

  • 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,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='draw', length=1000))

  • Attributes: (8)

    created_at :

    2025-09-28T16:00:26.212193+00:00

    arviz_version :

    0.22.0

    inference_library :

    numpyro

    inference_library_version :

    0.19.0

    sampling_time :

    1.23596

    tuning_steps :

    1000

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  
• sample_stats

  <xarray.Dataset> Size: 204kB
  Dimensions:          (chain: 4, draw: 1000)
  Coordinates:
    * chain            (chain) int64 32B 0 1 2 3
    * draw             (draw) int64 8kB 0 1 2 3 4 5 6 ... 994 995 996 997 998 999
  Data variables:
      acceptance_rate  (chain, draw) float64 32kB 0.8278 1.0 0.9665 ... 1.0 0.814
      step_size        (chain, draw) float64 32kB 0.7569 0.7569 ... 0.9014 0.9014
      diverging        (chain, draw) bool 4kB False False False ... False False
      energy           (chain, draw) float64 32kB 146.4 145.8 ... 145.7 147.1
      n_steps          (chain, draw) int64 32kB 3 7 3 7 7 3 7 7 ... 3 3 3 3 7 1 11
      tree_depth       (chain, draw) int64 32kB 2 3 2 3 3 2 3 3 ... 2 2 2 2 3 1 4
      lp               (chain, draw) float64 32kB 145.7 145.6 ... 145.0 144.5
  Attributes:
      created_at:                  2025-09-28T16:00:26.216944+00:00
      arviz_version:               0.22.0
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

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

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

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

  • Data variables: (7)
    • acceptance_rate
      (chain, draw)
      float64
      0.8278 1.0 0.9665 ... 1.0 0.814

      array([[0.82784786, 1.        , 0.96646067, ..., 0.91904825, 0.76945507,
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             [0.91662269, 0.76183416, 0.92562922, ..., 0.94655857, 0.99708979,
              0.70682999],
             [1.        , 1.        , 0.99364941, ..., 0.82323695, 0.98153898,
              0.99373216],
             [0.99618934, 0.99799453, 0.87237379, ..., 0.96396777, 1.        ,
              0.81397396]], shape=(4, 1000))

    • step_size
      (chain, draw)
      float64
      0.7569 0.7569 ... 0.9014 0.9014

      array([[0.75685877, 0.75685877, 0.75685877, ..., 0.75685877, 0.75685877,
              0.75685877],
             [0.84465801, 0.84465801, 0.84465801, ..., 0.84465801, 0.84465801,
              0.84465801],
             [0.82787036, 0.82787036, 0.82787036, ..., 0.82787036, 0.82787036,
              0.82787036],
             [0.90136426, 0.90136426, 0.90136426, ..., 0.90136426, 0.90136426,
              0.90136426]], shape=(4, 1000))

    • 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, 1000))

    • energy
      (chain, draw)
      float64
      146.4 145.8 146.5 ... 145.7 147.1

      array([[146.41068035, 145.84871735, 146.52391825, ..., 144.741246  ,
              146.88937758, 147.90411185],
             [145.83080402, 146.9011951 , 147.24404111, ..., 145.98256967,
              144.51816849, 146.56804799],
             [149.18360657, 148.92453828, 146.52676063, ..., 147.90780188,
              147.55361051, 145.51731478],
             [145.99648868, 145.50276379, 146.51147203, ..., 148.05493125,
              145.74316931, 147.126705  ]], shape=(4, 1000))

    • n_steps
      (chain, draw)
      int64
      3 7 3 7 7 3 7 7 ... 3 3 3 3 7 1 11

      array([[ 3,  7,  3, ...,  3,  3,  7],
             [ 3,  3,  3, ...,  3,  7,  7],
             [ 1,  3,  7, ...,  3,  7,  7],
             [19,  7,  7, ...,  7,  1, 11]], shape=(4, 1000))

    • tree_depth
      (chain, draw)
      int64
      2 3 2 3 3 2 3 3 ... 2 2 2 2 2 3 1 4

      array([[2, 3, 2, ..., 2, 2, 3],
             [2, 2, 2, ..., 2, 3, 3],
             [1, 2, 3, ..., 2, 3, 3],
             [5, 3, 3, ..., 3, 1, 4]], shape=(4, 1000))

    • lp
      (chain, draw)
      float64
      145.7 145.6 144.2 ... 145.0 144.5

      array([[145.66073533, 145.57178034, 144.16103857, ..., 144.07454074,
              146.41359925, 146.3383686 ],
             [144.5403781 , 146.05276145, 145.6251923 , ..., 144.37861908,
              143.9188432 , 143.82304889],
             [147.55689186, 145.60374953, 145.4744971 , ..., 146.74886366,
              144.85959835, 144.4310138 ],
             [144.94096787, 144.3570476 , 144.54451025, ..., 145.82739078,
              145.00518981, 144.47678769]], shape=(4, 1000))

  • 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,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='draw', length=1000))

  • Attributes: (4)

    created_at :

    2025-09-28T16:00:26.216944+00:00

    arviz_version :

    0.22.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  
• observed_data

  <xarray.Dataset> Size: 2kB
  Dimensions:  (__obs__: 100)
  Coordinates:
    * __obs__  (__obs__) int64 800B 0 1 2 3 4 5 6 7 8 ... 92 93 94 95 96 97 98 99
  Data variables:
      y        (__obs__) float64 800B 0.9823 -0.1276 1.024 ... -0.4394 0.2223
  Attributes:
      created_at:                  2025-09-28T16:00:26.218137+00:00
      arviz_version:               0.22.0
      inference_library:           numpyro
      inference_library_version:   0.19.0
      sampling_time:               1.23596
      tuning_steps:                1000
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • __obs__: 100
  • Coordinates: (1)
    • __obs__
      (__obs__)
      int64
      0 1 2 3 4 5 6 ... 94 95 96 97 98 99

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
             54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,
             72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
             90, 91, 92, 93, 94, 95, 96, 97, 98, 99])

  • Data variables: (1)
    • y
      (__obs__)
      float64
      0.9823 -0.1276 ... -0.4394 0.2223

      array([ 0.98232738, -0.12758867,  1.0241217 , -1.52813143, -0.60223389,
             -0.9110669 , -0.4353976 ,  0.83518854, -1.98725748,  0.70239123,
              0.47474209, -0.57402927, -1.10256821,  0.21458759, -0.7913338 ,
              0.34504087, -0.27033576,  1.8694577 , -0.25456891, -1.07982821,
             -0.02821523,  0.59252591,  1.3120998 ,  0.70459244,  0.24956995,
              1.62550659, -1.07740601, -0.51398486, -0.79529742,  0.2627868 ,
             -1.50052774,  0.47906184, -0.47019315, -1.28310684, -0.67156194,
              0.27879211,  0.58211654,  1.74549738,  3.1121092 ,  0.64089167,
             -0.82402974, -2.33483846,  0.33845498, -0.77738494, -0.34871911,
             -0.34655757, -0.0726575 ,  1.27285679,  0.17764106, -0.07053522,
             -0.84328945, -2.11870321, -0.58371719, -0.19711313,  1.57325292,
              0.04643398,  1.43827366, -0.76312913, -0.88989281, -1.47791592,
             -0.82727125,  2.17806337, -0.64275472,  1.05521209, -0.66118073,
              0.82531053,  0.24406448,  0.10480201, -0.09905622, -1.04351111,
              0.10074023, -0.7351563 , -1.07411239, -1.23453802,  0.3829906 ,
              1.44890008,  0.20830137,  0.07198975,  0.19156297,  1.44518896,
              0.01768236, -0.52155594,  0.98996665,  0.06436367,  1.68414482,
              0.04019953, -1.22066186, -1.22166748,  1.78699361,  1.92641993,
             -0.20952942, -0.51217355,  1.43715279, -1.6212053 , -1.33568691,
              0.24027763, -0.69848326,  0.11669617, -0.43935783,  0.22234196])

  • Indexes: (1)
    • __obs__
      PandasIndex

      PandasIndex(Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
             54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,
             72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
             90, 91, 92, 93, 94, 95, 96, 97, 98, 99],
            dtype='int64', name='__obs__'))

  • Attributes: (8)

    created_at :

    2025-09-28T16:00:26.218137+00:00

    arviz_version :

    0.22.0

    inference_library :

    numpyro

    inference_library_version :

    0.19.0

    sampling_time :

    1.23596

    tuning_steps :

    1000

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  

nutpie

nutpie_idata = model.fit(inference_method="nutpie", progressbar=False)

nutpie_idata

arviz.InferenceData

• posterior

  <xarray.Dataset> Size: 136kB
  Dimensions:      (chain: 4, draw: 1000)
  Coordinates:
    * chain        (chain) int64 32B 0 1 2 3
    * draw         (draw) int64 8kB 0 1 2 3 4 5 6 ... 993 994 995 996 997 998 999
  Data variables:
      sigma_log__  (chain, draw) float64 32kB -0.09139 0.02693 ... 0.1097 -0.1576
      Intercept    (chain, draw) float64 32kB 0.03335 -0.01864 ... 0.07132
      x            (chain, draw) float64 32kB 0.3313 0.53 0.3076 ... 0.5508 0.3157
      sigma        (chain, draw) float64 32kB 0.9127 1.027 0.8574 ... 1.116 0.8542
  Attributes:
      created_at:                  2025-09-28T16:00:34.798058+00:00
      arviz_version:               0.22.0
      inference_library:           nutpie
      inference_library_version:   0.15.2
      sampling_time:               0.0895071029663086
      tuning_steps:                1000
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

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

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

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

  • Data variables: (4)
    • sigma_log__
      (chain, draw)
      float64
      -0.09139 0.02693 ... 0.1097 -0.1576

      array([[-0.0913925 ,  0.02693456, -0.15381458, ..., -0.01926776,
              -0.05179212, -0.14672768],
             [-0.04271045, -0.06867495, -0.00665569, ..., -0.02777598,
              -0.0191235 ,  0.00168801],
             [-0.06103663, -0.07701374,  0.09958068, ..., -0.06289853,
               0.0468535 ,  0.07066342],
             [-0.10653042,  0.0335802 ,  0.05127071, ..., -0.10656168,
               0.10972859, -0.1576338 ]], shape=(4, 1000))

    • Intercept
      (chain, draw)
      float64
      0.03335 -0.01864 ... 0.07132

      array([[ 0.03334513, -0.01864335, -0.02748844, ..., -0.05269767,
               0.14561869, -0.0642135 ],
             [-0.03949164,  0.01794342,  0.09791452, ...,  0.11473709,
              -0.11054706,  0.14572664],
             [ 0.08824579, -0.09208579, -0.01262223, ...,  0.17717385,
              -0.17686677, -0.05144212],
             [ 0.10122503,  0.01746952,  0.02200477, ...,  0.0018681 ,
              -0.05232931,  0.07131926]], shape=(4, 1000))

    • x
      (chain, draw)
      float64
      0.3313 0.53 ... 0.5508 0.3157

      array([[0.33125212, 0.52998588, 0.30761086, ..., 0.48715872, 0.32870617,
              0.44511311],
             [0.49718604, 0.4436269 , 0.48331041, ..., 0.39328514, 0.45164918,
              0.43853824],
             [0.25476665, 0.50571958, 0.58312337, ..., 0.33812298, 0.56981331,
              0.47924229],
             [0.58184777, 0.31002132, 0.16957778, ..., 0.34789895, 0.55083413,
              0.31565492]], shape=(4, 1000))

    • sigma
      (chain, draw)
      float64
      0.9127 1.027 ... 1.116 0.8542

      array([[0.91265943, 1.02730057, 0.85743099, ..., 0.98091667, 0.94952623,
              0.86352911],
             [0.9581888 , 0.93363011, 0.99336641, ..., 0.97260622, 0.98105819,
              1.00168943],
             [0.94078878, 0.92587713, 1.1047076 , ..., 0.93903876, 1.04796847,
              1.07321994],
             [0.8989477 , 1.03415038, 1.05260781, ..., 0.8989196 , 1.11597515,
              0.85416252]], shape=(4, 1000))

  • 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,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='draw', length=1000))

  • Attributes: (8)

    created_at :

    2025-09-28T16:00:34.798058+00:00

    arviz_version :

    0.22.0

    inference_library :

    nutpie

    inference_library_version :

    0.15.2

    sampling_time :

    0.0895071029663086

    tuning_steps :

    1000

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  
• sample_stats

  <xarray.Dataset> Size: 336kB
  Dimensions:               (chain: 4, draw: 1000)
  Coordinates:
    * chain                 (chain) int64 32B 0 1 2 3
    * draw                  (draw) int64 8kB 0 1 2 3 4 5 ... 995 996 997 998 999
  Data variables:
      depth                 (chain, draw) uint64 32kB 2 2 2 2 2 2 ... 2 2 2 2 2 2
      maxdepth_reached      (chain, draw) bool 4kB False False ... False False
      index_in_trajectory   (chain, draw) int64 32kB 1 -3 2 -2 2 ... 3 -3 -2 2 -3
      logp                  (chain, draw) float64 32kB -144.5 -144.4 ... -146.3
      energy                (chain, draw) float64 32kB 145.0 144.5 ... 146.1 148.9
      diverging             (chain, draw) bool 4kB False False ... False False
      energy_error          (chain, draw) float64 32kB 0.08409 ... -0.05117
      step_size             (chain, draw) float64 32kB 1.097 1.097 ... 1.103 1.103
      step_size_bar         (chain, draw) float64 32kB 1.097 1.097 ... 1.103 1.103
      mean_tree_accept      (chain, draw) float64 32kB 0.8706 1.0 ... 0.8117 0.84
      mean_tree_accept_sym  (chain, draw) float64 32kB 0.9303 0.9425 ... 0.8828
      n_steps               (chain, draw) uint64 32kB 3 3 3 3 3 3 ... 3 3 3 3 3 3
  Attributes:
      created_at:                  2025-09-28T16:00:34.788419+00:00
      arviz_version:               0.22.0
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

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

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

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

  • Data variables: (12)
    • depth
      (chain, draw)
      uint64
      2 2 2 2 2 2 2 2 ... 2 2 2 2 2 2 2 2

      array([[2, 2, 2, ..., 2, 1, 2],
             [2, 2, 2, ..., 2, 2, 2],
             [2, 2, 2, ..., 1, 2, 2],
             [2, 2, 1, ..., 2, 2, 2]], shape=(4, 1000), dtype=uint64)

    • maxdepth_reached
      (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, 1000))

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

      array([[ 1, -3,  2, ...,  3, -1,  1],
             [-3, -2,  1, ...,  3,  3, -3],
             [ 2,  2,  1, ...,  1,  3,  1],
             [ 1,  2,  1, ..., -2,  2, -3]], shape=(4, 1000))

    • logp
      (chain, draw)
      float64
      -144.5 -144.4 ... -146.0 -146.3

      array([[-144.47277875, -144.36602162, -145.96273757, ..., -144.01627211,
              -145.25450817, -145.51569932],
             [-144.007511  , -143.87372828, -144.27807504, ..., -144.40199493,
              -144.4241424 , -144.79984181],
             [-145.26397013, -144.74429087, -145.89785049, ..., -145.86881466,
              -146.4621213 , -144.8753708 ],
             [-145.72980905, -144.46467827, -146.11488374, ..., -144.53029853,
              -146.03785561, -146.34049747]], shape=(4, 1000))

    • energy
      (chain, draw)
      float64
      145.0 144.5 148.1 ... 146.1 148.9

      array([[145.00753392, 144.52768363, 148.09723791, ..., 146.90858918,
              146.0533817 , 146.93381138],
             [145.29186789, 145.37152703, 144.5342139 , ..., 144.90524079,
              144.4890901 , 145.35357684],
             [147.52810032, 148.18973347, 147.36921955, ..., 146.75499968,
              146.98649257, 146.44530032],
             [147.15820539, 147.8859679 , 146.14283915, ..., 145.14727925,
              146.08908753, 148.90909068]], shape=(4, 1000))

    • 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, 1000))

    • energy_error
      (chain, draw)
      float64
      0.08409 -0.05273 ... -0.05117

      array([[ 0.08408539, -0.05273411,  0.02796588, ..., -0.14077582,
               0.32982076, -0.18439517],
             [-0.2626348 , -0.02059525,  0.1358298 , ..., -0.01368271,
               0.00558624,  0.14315974],
             [-0.07540878,  0.14610241,  0.37201011, ...,  0.36612249,
               0.18773977, -0.31850533],
             [-0.09442304,  0.07654783,  0.38997001, ...,  0.0172061 ,
               0.49793136, -0.05116595]], shape=(4, 1000))

    • step_size
      (chain, draw)
      float64
      1.097 1.097 1.097 ... 1.103 1.103

      array([[1.09721155, 1.09721155, 1.09721155, ..., 1.09721155, 1.09721155,
              1.09721155],
             [1.09107777, 1.09107777, 1.09107777, ..., 1.09107777, 1.09107777,
              1.09107777],
             [1.06358397, 1.06358397, 1.06358397, ..., 1.06358397, 1.06358397,
              1.06358397],
             [1.102844  , 1.102844  , 1.102844  , ..., 1.102844  , 1.102844  ,
              1.102844  ]], shape=(4, 1000))

    • step_size_bar
      (chain, draw)
      float64
      1.097 1.097 1.097 ... 1.103 1.103

      array([[1.09721155, 1.09721155, 1.09721155, ..., 1.09721155, 1.09721155,
              1.09721155],
             [1.09107777, 1.09107777, 1.09107777, ..., 1.09107777, 1.09107777,
              1.09107777],
             [1.06358397, 1.06358397, 1.06358397, ..., 1.06358397, 1.06358397,
              1.06358397],
             [1.102844  , 1.102844  , 1.102844  , ..., 1.102844  , 1.102844  ,
              1.102844  ]], shape=(4, 1000))

    • mean_tree_accept
      (chain, draw)
      float64
      0.8706 1.0 0.5645 ... 0.8117 0.84

      array([[0.87062522, 1.        , 0.56446271, ..., 0.79202635, 0.69426065,
              0.91844745],
             [0.90532811, 0.70746378, 0.85418096, ..., 0.99471293, 0.99814311,
              0.88596996],
             [0.66821574, 0.52417996, 0.72692021, ..., 0.63982648, 0.94294345,
              1.        ],
             [1.        , 0.56583421, 0.67707718, ..., 0.96125674, 0.81169847,
              0.83996597]], shape=(4, 1000))

    • mean_tree_accept_sym
      (chain, draw)
      float64
      0.9303 0.9425 ... 0.8884 0.8828

      array([[0.93032988, 0.94253668, 0.68195963, ..., 0.84743178, 0.81185559,
              0.92575237],
             [0.86523023, 0.80531888, 0.92113759, ..., 0.98490102, 0.95791681,
              0.93101715],
             [0.75040332, 0.65383936, 0.82382796, ..., 0.77813583, 0.91774906,
              0.81530571],
             [0.90394792, 0.69163009, 0.80744904, ..., 0.97998852, 0.88836452,
              0.88277034]], shape=(4, 1000))

    • n_steps
      (chain, draw)
      uint64
      3 3 3 3 3 3 3 3 ... 3 3 3 3 3 3 3 3

      array([[3, 3, 3, ..., 3, 3, 3],
             [3, 3, 3, ..., 3, 3, 3],
             [3, 3, 3, ..., 3, 3, 3],
             [3, 3, 1, ..., 3, 3, 3]], shape=(4, 1000), dtype=uint64)

  • 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,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='draw', length=1000))

  • Attributes: (4)

    created_at :

    2025-09-28T16:00:34.788419+00:00

    arviz_version :

    0.22.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  
• observed_data

  <xarray.Dataset> Size: 2kB
  Dimensions:  (__obs__: 100)
  Coordinates:
    * __obs__  (__obs__) int64 800B 0 1 2 3 4 5 6 7 8 ... 92 93 94 95 96 97 98 99
  Data variables:
      y        (__obs__) float64 800B 0.9823 -0.1276 1.024 ... -0.4394 0.2223
  Attributes:
      created_at:                  2025-09-28T16:00:34.797508+00:00
      arviz_version:               0.22.0
      inference_library:           pymc
      inference_library_version:   3.9.2+2907.g7a3db78e6
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • __obs__: 100
  • Coordinates: (1)
    • __obs__
      (__obs__)
      int64
      0 1 2 3 4 5 6 ... 94 95 96 97 98 99

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
             54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,
             72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
             90, 91, 92, 93, 94, 95, 96, 97, 98, 99])

  • Data variables: (1)
    • y
      (__obs__)
      float64
      0.9823 -0.1276 ... -0.4394 0.2223

      array([ 0.98232738, -0.12758867,  1.0241217 , -1.52813143, -0.60223389,
             -0.9110669 , -0.4353976 ,  0.83518854, -1.98725748,  0.70239123,
              0.47474209, -0.57402927, -1.10256821,  0.21458759, -0.7913338 ,
              0.34504087, -0.27033576,  1.8694577 , -0.25456891, -1.07982821,
             -0.02821523,  0.59252591,  1.3120998 ,  0.70459244,  0.24956995,
              1.62550659, -1.07740601, -0.51398486, -0.79529742,  0.2627868 ,
             -1.50052774,  0.47906184, -0.47019315, -1.28310684, -0.67156194,
              0.27879211,  0.58211654,  1.74549738,  3.1121092 ,  0.64089167,
             -0.82402974, -2.33483846,  0.33845498, -0.77738494, -0.34871911,
             -0.34655757, -0.0726575 ,  1.27285679,  0.17764106, -0.07053522,
             -0.84328945, -2.11870321, -0.58371719, -0.19711313,  1.57325292,
              0.04643398,  1.43827366, -0.76312913, -0.88989281, -1.47791592,
             -0.82727125,  2.17806337, -0.64275472,  1.05521209, -0.66118073,
              0.82531053,  0.24406448,  0.10480201, -0.09905622, -1.04351111,
              0.10074023, -0.7351563 , -1.07411239, -1.23453802,  0.3829906 ,
              1.44890008,  0.20830137,  0.07198975,  0.19156297,  1.44518896,
              0.01768236, -0.52155594,  0.98996665,  0.06436367,  1.68414482,
              0.04019953, -1.22066186, -1.22166748,  1.78699361,  1.92641993,
             -0.20952942, -0.51217355,  1.43715279, -1.6212053 , -1.33568691,
              0.24027763, -0.69848326,  0.11669617, -0.43935783,  0.22234196])

  • Indexes: (1)
    • __obs__
      PandasIndex

      PandasIndex(Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
             54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,
             72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
             90, 91, 92, 93, 94, 95, 96, 97, 98, 99],
            dtype='int64', name='__obs__'))

  • Attributes: (6)

    created_at :

    2025-09-28T16:00:34.797508+00:00

    arviz_version :

    0.22.0

    inference_library :

    pymc

    inference_library_version :

    3.9.2+2907.g7a3db78e6

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  
• warmup_posterior

  <xarray.Dataset> Size: 136kB
  Dimensions:      (chain: 4, draw: 1000)
  Coordinates:
    * chain        (chain) int64 32B 0 1 2 3
    * draw         (draw) int64 8kB 0 1 2 3 4 5 6 ... 993 994 995 996 997 998 999
  Data variables:
      sigma_log__  (chain, draw) float64 32kB -0.6403 -0.6403 ... -0.1866 -0.1695
      Intercept    (chain, draw) float64 32kB -0.7069 -0.7069 ... -0.06133
      x            (chain, draw) float64 32kB -0.6089 -0.6089 ... 0.5059 0.5003
      sigma        (chain, draw) float64 32kB 0.5271 0.5271 ... 0.8298 0.8441
  Attributes:
      created_at:                  2025-09-28T16:00:34.783875+00:00
      arviz_version:               0.22.0
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

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

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

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

  • Data variables: (4)
    • sigma_log__
      (chain, draw)
      float64
      -0.6403 -0.6403 ... -0.1866 -0.1695

      array([[-0.64031042, -0.64031042, -0.58697007, ...,  0.1369976 ,
              -0.17321066,  0.02065661],
             [-0.03655889, -0.03655889, -0.03417751, ...,  0.12047646,
              -0.15781504,  0.01728873],
             [ 0.34481534,  0.34481534,  0.32232358, ..., -0.06585357,
               0.00119091, -0.06441009],
             [ 0.27491724,  0.27491724,  0.27491724, ..., -0.18660609,
              -0.18660609, -0.16946566]], shape=(4, 1000))

    • Intercept
      (chain, draw)
      float64
      -0.7069 -0.7069 ... -0.06133

      array([[-0.70692427, -0.70692427, -0.6206744 , ...,  0.01390273,
              -0.03922895, -0.03577979],
             [ 0.23581111,  0.23581111,  0.22376263, ...,  0.01389254,
              -0.07421712,  0.0991392 ],
             [ 0.97195642,  0.97195642,  0.93889415, ..., -0.04137669,
               0.04667493, -0.08410599],
             [ 0.34682803,  0.34682803,  0.34682803, ..., -0.07576052,
              -0.07576052, -0.06132872]], shape=(4, 1000))

    • x
      (chain, draw)
      float64
      -0.6089 -0.6089 ... 0.5059 0.5003

      array([[-0.60893851, -0.60893851, -0.54620464, ...,  0.32905225,
               0.51070467,  0.33396698],
             [ 0.68555955,  0.68555955,  0.66883271, ...,  0.56799823,
               0.23175333,  0.35687578],
             [-0.14155374, -0.14155374, -0.07812364, ...,  0.49874524,
               0.37617113,  0.49093921],
             [ 0.42176107,  0.42176107,  0.42176107, ...,  0.50591277,
               0.50591277,  0.50032231]], shape=(4, 1000))

    • sigma
      (chain, draw)
      float64
      0.5271 0.5271 ... 0.8298 0.8441

      array([[0.52712877, 0.52712877, 0.5560094 , ..., 1.14682539, 0.84096044,
              1.02087143],
             [0.96410131, 0.96410131, 0.96639994, ..., 1.12803419, 0.85400773,
              1.01743905],
             [1.4117292 , 1.4117292 , 1.38033135, ..., 0.93626795, 1.00119162,
              0.93762041],
             [1.31642172, 1.31642172, 1.31642172, ..., 0.82977052, 0.82977052,
              0.84411574]], shape=(4, 1000))

  • 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,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='draw', length=1000))

  • Attributes: (4)

    created_at :

    2025-09-28T16:00:34.783875+00:00

    arviz_version :

    0.22.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  
• warmup_sample_stats

  <xarray.Dataset> Size: 336kB
  Dimensions:               (chain: 4, draw: 1000)
  Coordinates:
    * chain                 (chain) int64 32B 0 1 2 3
    * draw                  (draw) int64 8kB 0 1 2 3 4 5 ... 995 996 997 998 999
  Data variables:
      depth                 (chain, draw) uint64 32kB 3 0 1 2 1 0 ... 2 2 2 2 1 1
      maxdepth_reached      (chain, draw) bool 4kB False False ... False False
      index_in_trajectory   (chain, draw) int64 32kB 0 0 -1 -2 0 ... 2 -3 -2 0 -1
      logp                  (chain, draw) float64 32kB -401.7 -401.7 ... -146.2
      energy                (chain, draw) float64 32kB 402.3 402.8 ... 152.4 147.0
      diverging             (chain, draw) bool 4kB False True ... False False
      energy_error          (chain, draw) float64 32kB 0.0 0.0 ... 0.0 -0.1304
      step_size             (chain, draw) float64 32kB 3.736 0.3684 ... 1.103
      step_size_bar         (chain, draw) float64 32kB 3.736 0.9423 ... 1.103
      mean_tree_accept      (chain, draw) float64 32kB 1.58e-34 0.0 ... 1.0
      mean_tree_accept_sym  (chain, draw) float64 32kB 3.16e-34 0.0 ... 0.9349
      n_steps               (chain, draw) uint64 32kB 7 1 1 3 1 1 ... 3 3 3 3 1 1
  Attributes:
      created_at:                  2025-09-28T16:00:34.792568+00:00
      arviz_version:               0.22.0
      modeling_interface:          bambi
      modeling_interface_version:  0.14.1.dev56+gd93591cd2.d20250927

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

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

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

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

  • Data variables: (12)
    • depth
      (chain, draw)
      uint64
      3 0 1 2 1 0 2 1 ... 2 2 2 2 2 2 1 1

      array([[3, 0, 1, ..., 2, 2, 2],
             [4, 1, 1, ..., 2, 2, 2],
             [1, 1, 2, ..., 2, 2, 2],
             [1, 0, 0, ..., 2, 1, 1]], shape=(4, 1000), dtype=uint64)

    • maxdepth_reached
      (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, 1000))

    • index_in_trajectory
      (chain, draw)
      int64
      0 0 -1 -2 0 0 1 ... 3 2 -3 -2 0 -1

      array([[  0,   0,  -1, ...,  -3,  -3,   2],
             [-15,   0,   1, ...,   1,   3,  -2],
             [  0,   0,   2, ...,   2,  -2,   3],
             [  1,   0,   0, ...,  -2,   0,  -1]], shape=(4, 1000))

    • logp
      (chain, draw)
      float64
      -401.7 -401.7 ... -147.0 -146.2

      array([[-401.72718231, -401.72718231, -339.62991572, ..., -146.46396444,
              -146.3140243 , -144.18500188],
             [-149.4535143 , -149.4535143 , -148.82837345, ..., -146.30069406,
              -147.19592796, -144.73759264],
             [-184.50408756, -184.50408756, -181.92536355, ..., -144.04358829,
              -144.0852368 , -144.19839762],
             [-155.33830768, -155.33830768, -155.33830768, ..., -146.95360262,
              -146.95360262, -146.20863035]], shape=(4, 1000))

    • energy
      (chain, draw)
      float64
      402.3 402.8 396.0 ... 152.4 147.0

      array([[402.25580912, 402.7725382 , 395.99061091, ..., 149.18161602,
              146.78288341, 146.3568912 ],
             [173.56049036, 151.0000366 , 149.63118747, ..., 150.2407165 ,
              149.29067226, 148.21815365],
             [186.10548316, 186.61377226, 185.92502857, ..., 145.35696417,
              148.56392124, 144.73657482],
             [164.18283783, 156.51934316, 155.37523676, ..., 148.43039234,
              152.41970738, 147.02025649]], shape=(4, 1000))

    • diverging
      (chain, draw)
      bool
      False True False ... False False

      array([[False,  True, False, ..., False, False, False],
             [False,  True, False, ..., False, False, False],
             [ True, False, False, ..., False, False, False],
             [False,  True,  True, ..., False, False, False]], shape=(4, 1000))

    • energy_error
      (chain, draw)
      float64
      0.0 0.0 -6.561 ... 0.0 -0.1304

      array([[ 0.00000000e+00,  0.00000000e+00, -6.56114873e+00, ...,
               4.04266016e-01,  2.48292158e-02, -5.35956855e-01],
             [-8.93640309e-02,  0.00000000e+00, -6.43466051e-02, ...,
               1.20599701e-01, -7.69016780e-02, -4.60979696e-01],
             [ 0.00000000e+00,  0.00000000e+00, -6.78649349e-03, ...,
              -2.77189925e-02,  2.34115741e-01,  5.57172081e-03],
             [-9.51579661e-01,  0.00000000e+00,  0.00000000e+00, ...,
               2.71923951e-01,  0.00000000e+00, -1.30427658e-01]],
            shape=(4, 1000))

    • step_size
      (chain, draw)
      float64
      3.736 0.3684 ... 0.6813 1.103

      array([[ 3.73610367,  0.36837736,  0.38366625, ...,  0.98388775,
               1.03343453,  1.09721155],
             [ 1.43587041,  0.24252961,  1.6       , ...,  0.86722582,
               0.88333926,  1.09107777],
             [ 1.86805308,  0.18418884,  0.09535425, ...,  1.1326495 ,
               0.89755218,  1.06358397],
             [11.50840808,  1.94493388,  0.19183312, ...,  1.11279303,
               0.68132026,  1.102844  ]], shape=(4, 1000))

    • step_size_bar
      (chain, draw)
      float64
      3.736 0.9423 0.6353 ... 1.105 1.103

      array([[ 3.73610367,  0.94226449,  0.63531196, ...,  1.09770865,
               1.09733485,  1.09721155],
             [ 1.43587041,  0.49873852,  1.6       , ...,  1.09353059,
               1.0922148 ,  1.09107777],
             [ 1.86805308,  0.47113261,  0.23376407, ...,  1.06496243,
               1.06393795,  1.06358397],
             [11.50840808,  3.99867083,  1.0550797 , ...,  1.10835849,
               1.10531837,  1.102844  ]], shape=(4, 1000))

    • mean_tree_accept
      (chain, draw)
      float64
      1.58e-34 0.0 1.0 ... 0.007978 1.0

      array([[1.58024939e-34, 0.00000000e+00, 1.00000000e+00, ...,
              6.06432697e-01, 9.91825498e-01, 9.94586995e-01],
             [9.98974174e-01, 1.84410615e-53, 1.00000000e+00, ...,
              7.08022396e-01, 8.85605279e-01, 1.00000000e+00],
             [3.67605149e-07, 0.00000000e+00, 7.37670427e-01, ...,
              7.07564402e-01, 3.40582141e-01, 9.61213889e-01],
             [1.00000000e+00, 0.00000000e+00, 0.00000000e+00, ...,
              8.54173574e-01, 7.97765200e-03, 1.00000000e+00]], shape=(4, 1000))

    • mean_tree_accept_sym
      (chain, draw)
      float64
      3.16e-34 0.0 ... 0.01583 0.9349

      array([[3.16049879e-34, 0.00000000e+00, 2.82452574e-03, ...,
              7.53978519e-01, 8.74991049e-01, 8.60633000e-01],
             [9.74633465e-01, 3.68821231e-53, 9.67837794e-01, ...,
              8.22378448e-01, 8.27055512e-01, 8.41501639e-01],
             [7.35209758e-07, 0.00000000e+00, 8.31932732e-01, ...,
              8.03152094e-01, 4.27130732e-01, 9.75368764e-01],
             [5.57134501e-01, 0.00000000e+00, 0.00000000e+00, ...,
              8.96109222e-01, 1.58290255e-02, 9.34878462e-01]], shape=(4, 1000))

    • n_steps
      (chain, draw)
      uint64
      7 1 1 3 1 1 3 1 ... 3 3 3 3 3 3 1 1

      array([[ 7,  1,  1, ...,  3,  3,  3],
             [31,  2,  1, ...,  3,  3,  3],
             [ 2,  1,  3, ...,  3,  3,  3],
             [ 1,  1,  1, ...,  3,  1,  1]], shape=(4, 1000), dtype=uint64)

  • 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,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='draw', length=1000))

  • Attributes: (4)

    created_at :

    2025-09-28T16:00:34.792568+00:00

    arviz_version :

    0.22.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.14.1.dev56+gd93591cd2.d20250927

  
  

%load_ext watermark
%watermark -n -u -v -iv -w

Last updated: Sun Sep 28 2025

Python implementation: CPython
Python version       : 3.13.7
IPython version      : 9.4.0

numpy : 2.3.3
pandas: 2.3.2
bambi : 0.14.1.dev56+gd93591cd2.d20250927

Watermark: 2.5.0