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)

CPU times: user 3.24 s, sys: 3.2 s, total: 6.43 s
Wall time: 1.58 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 -0.1095 0.05797 ... 0.1161 -0.06526
      x          (chain, draw) float64 32kB 0.4387 0.3546 0.2288 ... 0.3748 0.472
      sigma      (chain, draw) float64 32kB 1.022 0.9304 0.9587 ... 1.117 0.8317
  Attributes:
      created_at:                  2025-09-11T05:42:43.343255+00:00
      arviz_version:               0.21.0
      inference_library:           blackjax
      inference_library_version:   1.2.5
      sampling_time:               0.95643
      tuning_steps:                1000
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

  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
      -0.1095 0.05797 ... 0.1161 -0.06526

      array([[-0.1094889 ,  0.05797331,  0.04327499, ...,  0.02635165,
              -0.13830627,  0.00104827],
             [ 0.09546465,  0.14422123,  0.17937716, ..., -0.03196388,
               0.01466326, -0.00308853],
             [ 0.00708064,  0.02592019, -0.22651361, ..., -0.18330677,
               0.14443859, -0.09957408],
             [-0.05038417, -0.00363555, -0.11476545, ..., -0.16839767,
               0.11608832, -0.06525621]], shape=(4, 1000))

    • x
      (chain, draw)
      float64
      0.4387 0.3546 ... 0.3748 0.472

      array([[0.43868636, 0.35458103, 0.22883553, ..., 0.21580375, 0.53020951,
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             [0.3932748 , 0.41888976, 0.39108326, ..., 0.51356491, 0.32814493,
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             [0.61764884, 0.40933245, 0.3324969 , ..., 0.58869691, 0.33798592,
              0.45778798],
             [0.50581408, 0.15664398, 0.39107814, ..., 0.44492801, 0.37484479,
              0.47195527]], shape=(4, 1000))

    • sigma
      (chain, draw)
      float64
      1.022 0.9304 ... 1.117 0.8317

      array([[1.02249295, 0.93039876, 0.95866223, ..., 0.88608892, 0.98496095,
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             [0.95532592, 0.98018437, 0.95340866, ..., 0.96195203, 0.96736664,
              0.99224465],
             [1.03820238, 0.93303685, 1.07777186, ..., 0.93452843, 1.0088954 ,
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             [1.0961958 , 0.93069349, 0.95455395, ..., 0.85481183, 1.11653091,
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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 :

    2025-09-11T05:42:43.343255+00:00

    arviz_version :

    0.21.0

    inference_library :

    blackjax

    inference_library_version :

    1.2.5

    sampling_time :

    0.95643

    tuning_steps :

    1000

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  
• 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:
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      diverging        (chain, draw) bool 4kB False False False ... False False
      energy           (chain, draw) float64 32kB 146.4 145.1 ... 148.2 147.5
      lp               (chain, draw) float64 32kB -144.6 -144.2 ... -146.1 -146.8
      n_steps          (chain, draw) int64 32kB 3 7 3 7 3 3 3 3 ... 3 7 3 7 7 7 3
      tree_depth       (chain, draw) int64 32kB 2 3 2 3 2 2 2 2 ... 2 3 2 3 3 3 2
  Attributes:
      created_at:                  2025-09-11T05:42:43.346499+00:00
      arviz_version:               0.21.0
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

  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
      0.9694 0.9965 0.9181 ... 1.0 0.9465

      array([[0.96942962, 0.99647961, 0.91811083, ..., 1.        , 0.98018882,
              0.60520171],
             [0.94949465, 0.93596351, 0.96131291, ..., 1.        , 0.97801816,
              0.99745504],
             [0.86815153, 0.88044394, 0.57951349, ..., 0.89414565, 1.        ,
              0.98183615],
             [0.87387052, 0.92847711, 0.95655609, ..., 0.76876559, 1.        ,
              0.94651445]], 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
      146.4 145.1 145.5 ... 148.2 147.5

      array([[146.37825886, 145.11028415, 145.4681003 , ..., 151.27067931,
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             [144.51883526, 145.20079494, 145.65086716, ..., 148.93017407,
              144.41491565, 144.1712155 ],
             [147.22304492, 146.76461467, 147.37431707, ..., 147.97731351,
              146.79408708, 145.24613956],
             [145.82965984, 147.29117213, 147.31911612, ..., 148.39977488,
              148.1837061 , 147.53580811]], shape=(4, 1000))

    • lp
      (chain, draw)
      float64
      -144.6 -144.2 ... -146.1 -146.8

      array([[-144.58471267, -144.24284723, -145.08706253, ..., -146.30490487,
              -145.19220282, -146.51402495],
             [-144.2337965 , -144.74388189, -145.50548095, ..., -144.05182835,
              -144.00234471, -143.90607229],
             [-145.17942066, -143.89356846, -147.11719013, ..., -146.97669959,
              -145.10653408, -144.42727152],
             [-145.38518655, -146.34174825, -144.49976448, ..., -147.52851498,
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    • n_steps
      (chain, draw)
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      3 7 3 7 3 3 3 3 ... 7 3 7 3 7 7 7 3

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

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

    2025-09-11T05:42:43.346499+00:00

    arviz_version :

    0.21.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  
• 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:                  2025-09-11T05:42:43.347121+00:00
      arviz_version:               0.21.0
      inference_library:           blackjax
      inference_library_version:   1.2.5
      sampling_time:               0.95643
      tuning_steps:                1000
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

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

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             -0.02821523,  0.59252591,  1.3120998 ,  0.70459244,  0.24956995,
              1.62550659, -1.07740601, -0.51398486, -0.79529742,  0.2627868 ,
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  • Indexes: (1)
    • __obs__
      PandasIndex

      PandasIndex(Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
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  • Attributes: (8)

    created_at :

    2025-09-11T05:42:43.347121+00:00

    arviz_version :

    0.21.0

    inference_library :

    blackjax

    inference_library_version :

    1.2.5

    sampling_time :

    0.95643

    tuning_steps :

    1000

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  

NumPyro

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

CPU times: user 2.23 s, sys: 111 ms, total: 2.34 s
Wall time: 1.11 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:
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      x          (chain, draw) float64 32kB 0.4035 0.4687 0.3535 ... 0.2083 0.2083
      sigma      (chain, draw) float64 32kB 1.0 1.083 1.008 ... 0.9983 0.9983
  Attributes:
      created_at:                  2025-09-11T05:42:47.864004+00:00
      arviz_version:               0.21.0
      inference_library:           numpyro
      inference_library_version:   0.19.0
      sampling_time:               0.923537
      tuning_steps:                1000
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

  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
      -0.09142 0.06636 ... -0.08637

      array([[-0.09141681,  0.06636123, -0.03248716, ..., -0.0635187 ,
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             [-0.06039285, -0.09622093,  0.12447056, ...,  0.03232895,
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    • x
      (chain, draw)
      float64
      0.4035 0.4687 ... 0.2083 0.2083

      array([[0.40345796, 0.46870785, 0.35347158, ..., 0.28432965, 0.4711614 ,
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             [0.33844933, 0.27992427, 0.60713279, ..., 0.47600678, 0.4544052 ,
              0.34880169],
             [0.4474921 , 0.39875618, 0.44548301, ..., 0.06478803, 0.20831615,
              0.20831615]], shape=(4, 1000))

    • sigma
      (chain, draw)
      float64
      1.0 1.083 1.008 ... 0.9983 0.9983

      array([[1.00020089, 1.0834176 , 1.00765785, ..., 0.93956843, 1.03187819,
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             [0.99615802, 0.96764794, 1.07465454, ..., 1.131289  , 0.88905801,
              0.9250503 ],
             [0.88542245, 0.85820435, 1.1420224 , ..., 0.94811522, 1.01607265,
              0.99328951],
             [0.93634661, 0.9504665 , 0.97252178, ..., 0.95104455, 0.99834259,
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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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  • Attributes: (8)

    created_at :

    2025-09-11T05:42:47.864004+00:00

    arviz_version :

    0.21.0

    inference_library :

    numpyro

    inference_library_version :

    0.19.0

    sampling_time :

    0.923537

    tuning_steps :

    1000

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  
• 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 1.0 0.9147 1.0 ... 1.0 0.7743
      step_size        (chain, draw) float64 32kB 0.7985 0.7985 ... 0.8912 0.8912
      diverging        (chain, draw) bool 4kB False False False ... False False
      energy           (chain, draw) float64 32kB 145.8 145.4 ... 147.9 146.7
      n_steps          (chain, draw) int64 32kB 3 3 3 3 3 3 3 3 ... 3 3 3 3 3 1 1
      tree_depth       (chain, draw) int64 32kB 2 2 2 2 2 2 2 2 ... 2 2 2 2 2 1 1
      lp               (chain, draw) float64 32kB 144.2 145.0 ... 145.5 145.5
  Attributes:
      created_at:                  2025-09-11T05:42:47.866678+00:00
      arviz_version:               0.21.0
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

  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
      1.0 0.9147 1.0 ... 1.0 0.7743

      array([[1.        , 0.91472146, 1.        , ..., 0.99221289, 0.93070402,
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             [0.93419014, 0.99889019, 0.87696293, ..., 0.97921621, 0.9966908 ,
              0.96003669],
             [0.99767404, 0.71750308, 0.97651604, ..., 0.72018961, 0.93593063,
              0.86453027],
             [0.8370123 , 0.99930072, 0.94995388, ..., 0.42129211, 1.        ,
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    • step_size
      (chain, draw)
      float64
      0.7985 0.7985 ... 0.8912 0.8912

      array([[0.79854058, 0.79854058, 0.79854058, ..., 0.79854058, 0.79854058,
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             [0.63412331, 0.63412331, 0.63412331, ..., 0.63412331, 0.63412331,
              0.63412331],
             [0.7416543 , 0.7416543 , 0.7416543 , ..., 0.7416543 , 0.7416543 ,
              0.7416543 ],
             [0.89120115, 0.89120115, 0.89120115, ..., 0.89120115, 0.89120115,
              0.89120115]], 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
      145.8 145.4 145.1 ... 147.9 146.7

      array([[145.76087837, 145.43309732, 145.13850934, ..., 145.64360141,
              145.51712962, 145.98802395],
             [145.77042483, 145.24848789, 148.56071124, ..., 148.00320399,
              147.4210041 , 145.66473142],
             [145.59369613, 146.78835595, 148.5233748 , ..., 147.51154576,
              144.6651266 , 145.83635453],
             [145.73809264, 144.0610579 , 144.28347789, ..., 150.1702842 ,
              147.85366565, 146.65597291]], shape=(4, 1000))

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

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

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

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

    • lp
      (chain, draw)
      float64
      144.2 145.0 144.0 ... 145.5 145.5

      array([[144.23469058, 145.03797838, 144.02790907, ..., 144.65711277,
              144.7726624 , 145.62717825],
             [144.67550759, 144.58512811, 146.77423733, ..., 146.99261186,
              144.74442719, 144.87097192],
             [145.09471725, 146.75562718, 147.34062196, ..., 143.87901908,
              143.99319208, 144.8985619 ],
             [143.98064507, 143.83138732, 143.75135167, ..., 148.56684623,
              145.46516414, 145.46516414]], 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 :

    2025-09-11T05:42:47.866678+00:00

    arviz_version :

    0.21.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  
• 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:                  2025-09-11T05:42:47.867365+00:00
      arviz_version:               0.21.0
      inference_library:           numpyro
      inference_library_version:   0.19.0
      sampling_time:               0.923537
      tuning_steps:                1000
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

  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 :

    2025-09-11T05:42:47.867365+00:00

    arviz_version :

    0.21.0

    inference_library :

    numpyro

    inference_library_version :

    0.19.0

    sampling_time :

    0.923537

    tuning_steps :

    1000

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  

nutpie

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

/Users/gabestechschulte/projects/bambi/.venv/lib/python3.12/site-packages/pymc/sampling/mcmc.py:335: UserWarning: `var_names` are currently ignored by the nutpie sampler
  warnings.warn(

nutpie_idata

arviz.InferenceData

• posterior

  <xarray.Dataset> Size: 3MB
  Dimensions:      (chain: 4, draw: 1000, __obs__: 100)
  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
    * __obs__      (__obs__) int64 800B 0 1 2 3 4 5 6 7 ... 93 94 95 96 97 98 99
  Data variables:
      sigma_log__  (chain, draw) float64 32kB -0.01424 -0.0169 ... -0.06667
      Intercept    (chain, draw) float64 32kB -0.06445 -0.0443 ... 0.09378
      x            (chain, draw) float64 32kB 0.305 0.1792 0.1207 ... 0.6013 0.288
      sigma        (chain, draw) float64 32kB 0.9859 0.9832 ... 0.9713 0.9355
      mu           (chain, draw, __obs__) float64 3MB -0.3816 0.1644 ... -0.01512
  Attributes:
      created_at:                  2025-09-11T05:43:00.405915+00:00
      arviz_version:               0.21.0
      inference_library:           nutpie
      inference_library_version:   0.15.2
      sampling_time:               0.03235673904418945
      tuning_steps:                1000
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
    • __obs__: 100
  • Coordinates: (3)
    • 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,))

    • __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: (5)
    • sigma_log__
      (chain, draw)
      float64
      -0.01424 -0.0169 ... -0.06667

      array([[-0.01423767, -0.01690331, -0.03528526, ..., -0.10493002,
              -0.16896277,  0.15470223],
             [-0.06382911, -0.02098679, -0.04179016, ..., -0.02229496,
               0.01031951, -0.05067574],
             [-0.09337475,  0.04279347, -0.02286234, ..., -0.17351628,
               0.14791986, -0.02604506],
             [-0.05140905,  0.07326899, -0.02576237, ..., -0.07158359,
              -0.02911429, -0.06666944]], shape=(4, 1000))

    • Intercept
      (chain, draw)
      float64
      -0.06445 -0.0443 ... 0.09378

      array([[-0.06444708, -0.04429772, -0.07007824, ..., -0.00390791,
              -0.02269606,  0.03132426],
             [ 0.03082564, -0.02696727,  0.03763238, ..., -0.0471549 ,
              -0.10851039, -0.04572635],
             [ 0.06430399, -0.0135406 ,  0.01901496, ...,  0.11216584,
              -0.12020242, -0.06081789],
             [ 0.01043164, -0.08644282, -0.04250685, ...,  0.15298464,
              -0.08391973,  0.09378189]], shape=(4, 1000))

    • x
      (chain, draw)
      float64
      0.305 0.1792 ... 0.6013 0.288

      array([[0.30500383, 0.17922344, 0.12068655, ..., 0.37835785, 0.37307532,
              0.49203158],
             [0.49477842, 0.27321138, 0.56276515, ..., 0.37487344, 0.55077676,
              0.35273053],
             [0.32406417, 0.37106613, 0.49239642, ..., 0.34624715, 0.5058039 ,
              0.46181868],
             [0.47728897, 0.33783763, 0.30830065, ..., 0.26215322, 0.60132449,
              0.28798811]], shape=(4, 1000))

    • sigma
      (chain, draw)
      float64
      0.9859 0.9832 ... 0.9713 0.9355

      array([[0.98586321, 0.98323875, 0.96533   , ..., 0.90038753, 0.84454034,
              1.16731031],
             [0.93816531, 0.9792319 , 0.95907101, ..., 0.97795174, 1.01037294,
              0.95058686],
             [0.91085209, 1.04372231, 0.97739702, ..., 0.84070347, 1.15941998,
              0.97429119],
             [0.94989004, 1.07601994, 0.97456665, ..., 0.93091846, 0.97130545,
              0.93550439]], shape=(4, 1000))

    • mu
      (chain, draw, __obs__)
      float64
      -0.3816 0.1644 ... -0.167 -0.01512

      array([[[-0.38164622,  0.16444341,  0.22242876, ...,  0.05748559,
               -0.34062166, -0.17978811],
              [-0.23068725,  0.09020072,  0.12427352, ...,  0.02735119,
               -0.20658079, -0.11207331],
              [-0.19559033,  0.02049113,  0.04343527, ..., -0.02183087,
               -0.17935738, -0.11571737],
              ...,
              [-0.39739406,  0.28003119,  0.35196214, ...,  0.14734981,
               -0.34650302, -0.14698868],
              [-0.41068846,  0.25727876,  0.32820543, ...,  0.12644984,
               -0.36050795, -0.16377917],
              [-0.48038077,  0.40056995,  0.49411181, ...,  0.2280258 ,
               -0.41420004, -0.15474366]],
      
             [[-0.48373605,  0.40213269,  0.49619676, ...,  0.2286253 ,
               -0.41718585, -0.15628103],
              [-0.31110276,  0.17806454,  0.23000572, ...,  0.0822556 ,
               -0.27435445, -0.13028558],
              [-0.54763443,  0.45996016,  0.56694942, ...,  0.26261138,
               -0.47193967, -0.17518432],
      ...
              [-0.2479257 ,  0.37200743,  0.4378337 , ...,  0.25058653,
               -0.20135371, -0.01877187],
              [-0.64623044,  0.25937872,  0.35553888, ...,  0.08200494,
               -0.57819726, -0.31147852],
              [-0.54110198,  0.28575449,  0.37355247, ...,  0.12380532,
               -0.47898503, -0.23546042]],
      
             [[-0.4859413 ,  0.36861372,  0.45935281, ...,  0.20123947,
               -0.42174353, -0.17006117],
              [-0.43778858,  0.16708784,  0.23131534, ...,  0.04861596,
               -0.39234771, -0.21420036],
              [-0.36313462,  0.18885774,  0.24746986, ...,  0.0807438 ,
               -0.32166663, -0.15909461],
              ...,
              [-0.11965054,  0.34971784,  0.39955671, ...,  0.25778675,
               -0.08438961,  0.05384811],
              [-0.70928765,  0.36734495,  0.48166486, ...,  0.1564743 ,
               -0.62840647, -0.31131814],
              [-0.20572117,  0.30990291,  0.36465334, ...,  0.20891211,
               -0.16698531, -0.01512443]]], shape=(4, 1000, 100))

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

    • __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 :

    2025-09-11T05:43:00.405915+00:00

    arviz_version :

    0.21.0

    inference_library :

    nutpie

    inference_library_version :

    0.15.2

    sampling_time :

    0.03235673904418945

    tuning_steps :

    1000

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  
• 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 1 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 2 1 -1 2 -3 ... 2 -2 -1 2 -2
      logp                  (chain, draw) float64 32kB -144.3 -145.6 ... -145.0
      energy                (chain, draw) float64 32kB 145.0 145.7 ... 146.6 145.5
      diverging             (chain, draw) bool 4kB False False ... False False
      energy_error          (chain, draw) float64 32kB -0.1328 0.3533 ... -0.02633
      step_size             (chain, draw) float64 32kB 1.052 1.052 ... 1.088 1.088
      step_size_bar         (chain, draw) float64 32kB 1.052 1.052 ... 1.088 1.088
      mean_tree_accept      (chain, draw) float64 32kB 1.0 0.9008 ... 1.0 1.0
      mean_tree_accept_sym  (chain, draw) float64 32kB 0.94 0.9265 ... 0.9042
      n_steps               (chain, draw) uint64 32kB 3 3 1 3 3 3 ... 3 3 3 3 3 3
  Attributes:
      created_at:                  2025-09-11T05:43:00.401014+00:00
      arviz_version:               0.21.0
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

  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 1 2 2 2 2 2 ... 2 2 2 2 2 2 2 2

      array([[2, 2, 1, ..., 2, 1, 2],
             [2, 2, 2, ..., 2, 2, 2],
             [2, 2, 2, ..., 2, 2, 1],
             [2, 2, 2, ..., 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
      2 1 -1 2 -3 3 ... -1 2 -2 -1 2 -2

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

    • logp
      (chain, draw)
      float64
      -144.3 -145.6 ... -145.2 -145.0

      array([[-144.34380059, -145.6177586 , -146.81154455, ..., -144.36736343,
              -145.97751854, -146.86945692],
             [-144.01567809, -144.43288502, -144.37520172, ..., -143.8939164 ,
              -145.02243695, -144.0173637 ],
             [-144.74363876, -144.2868325 , -143.85462934, ..., -147.1446513 ,
              -147.30029598, -143.97387932],
             [-143.83774493, -145.19854651, -144.19645796, ..., -146.23312493,
              -145.1977827 , -145.01491514]], shape=(4, 1000))

    • energy
      (chain, draw)
      float64
      145.0 145.7 147.2 ... 146.6 145.5

      array([[144.96768042, 145.71896235, 147.1920356 , ..., 145.38066772,
              146.0733165 , 148.8284128 ],
             [144.82576056, 144.68415237, 145.88222989, ..., 147.97524471,
              146.02646771, 149.44302988],
             [145.15181906, 145.44367857, 144.45467619, ..., 148.53440854,
              149.19478072, 147.18947601],
             [144.07940858, 145.37345438, 145.26955123, ..., 146.79274616,
              146.55714312, 145.54046694]], 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
      -0.1328 0.3533 ... -0.2799 -0.02633

      array([[-0.13279618,  0.35326399,  0.40202685, ..., -0.16731691,
               0.56860668,  0.54905812],
             [-0.15481295,  0.10796993, -0.07980555, ...,  0.        ,
               0.32688207, -0.27817506],
             [ 0.10805124, -0.09720589, -0.14546899, ...,  0.03132533,
              -0.01554497, -0.83632895],
             [-0.06791538,  0.41121064, -0.24749701, ...,  0.34861328,
              -0.27987241, -0.0263325 ]], shape=(4, 1000))

    • step_size
      (chain, draw)
      float64
      1.052 1.052 1.052 ... 1.088 1.088

      array([[1.05194764, 1.05194764, 1.05194764, ..., 1.05194764, 1.05194764,
              1.05194764],
             [1.09107225, 1.09107225, 1.09107225, ..., 1.09107225, 1.09107225,
              1.09107225],
             [1.06962045, 1.06962045, 1.06962045, ..., 1.06962045, 1.06962045,
              1.06962045],
             [1.08796434, 1.08796434, 1.08796434, ..., 1.08796434, 1.08796434,
              1.08796434]], shape=(4, 1000))

    • step_size_bar
      (chain, draw)
      float64
      1.052 1.052 1.052 ... 1.088 1.088

      array([[1.05194764, 1.05194764, 1.05194764, ..., 1.05194764, 1.05194764,
              1.05194764],
             [1.09107225, 1.09107225, 1.09107225, ..., 1.09107225, 1.09107225,
              1.09107225],
             [1.06962045, 1.06962045, 1.06962045, ..., 1.06962045, 1.06962045,
              1.06962045],
             [1.08796434, 1.08796434, 1.08796434, ..., 1.08796434, 1.08796434,
              1.08796434]], shape=(4, 1000))

    • mean_tree_accept
      (chain, draw)
      float64
      1.0 0.9008 0.669 ... 0.9019 1.0 1.0

      array([[1.        , 0.90079725, 0.66896278, ..., 0.93879719, 0.56631395,
              0.61271814],
             [0.93522928, 0.89462375, 0.82827774, ..., 0.28121004, 0.71815978,
              0.46317387],
             [0.93897189, 0.93809703, 0.95286802, ..., 0.98972007, 0.97597648,
              0.97049426],
             [1.        , 0.78547494, 1.        , ..., 0.90188866, 1.        ,
              1.        ]], shape=(4, 1000))

    • mean_tree_accept_sym
      (chain, draw)
      float64
      0.94 0.9265 ... 0.8407 0.9042

      array([[0.93999578, 0.92652403, 0.80165093, ..., 0.93968757, 0.72311678,
              0.75673643],
             [0.940194  , 0.94420945, 0.88785141, ..., 0.43596329, 0.82612764,
              0.48914261],
             [0.96058998, 0.95133661, 0.95120103, ..., 0.88823272, 0.91562092,
              0.73862137],
             [0.96964759, 0.8744303 , 0.92187683, ..., 0.90926903, 0.84067767,
              0.9042355 ]], shape=(4, 1000))

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

      array([[3, 3, 1, ..., 3, 1, 3],
             [3, 3, 3, ..., 3, 3, 3],
             [3, 3, 3, ..., 3, 3, 3],
             [3, 3, 3, ..., 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 :

    2025-09-11T05:43:00.401014+00:00

    arviz_version :

    0.21.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  
• 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:                  2025-09-11T05:43:00.405522+00:00
      arviz_version:               0.21.0
      inference_library:           pymc
      inference_library_version:   5.23.0
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

  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 :

    2025-09-11T05:43:00.405522+00:00

    arviz_version :

    0.21.0

    inference_library :

    pymc

    inference_library_version :

    5.23.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  
• warmup_posterior

  <xarray.Dataset> Size: 3MB
  Dimensions:      (chain: 4, draw: 1000, __obs__: 100)
  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
    * __obs__      (__obs__) int64 800B 0 1 2 3 4 5 6 7 ... 93 94 95 96 97 98 99
  Data variables:
      sigma_log__  (chain, draw) float64 32kB -0.6316 -0.6316 ... 0.02711
      Intercept    (chain, draw) float64 32kB 0.4837 0.4837 ... 0.09586 -0.04978
      x            (chain, draw) float64 32kB -0.9797 -0.9797 ... 0.4696 0.3999
      sigma        (chain, draw) float64 32kB 0.5317 0.5317 7.545 ... 0.9999 1.027
      mu           (chain, draw, __obs__) float64 3MB 1.447 -0.3075 ... -0.1782
  Attributes:
      created_at:                  2025-09-11T05:43:00.398914+00:00
      arviz_version:               0.21.0
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
    • __obs__: 100
  • Coordinates: (3)
    • 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,))

    • __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: (5)
    • sigma_log__
      (chain, draw)
      float64
      -0.6316 -0.6316 ... 0.02711

      array([[-6.31602586e-01, -6.31602586e-01,  2.02085796e+00, ...,
              -6.79296961e-02,  4.81619598e-02, -9.66358794e-02],
             [-6.02586886e-01, -6.02586886e-01, -3.60805780e-01, ...,
              -3.51470203e-02,  1.42242545e-02,  1.67896096e-02],
             [ 7.65432659e-01,  7.65432659e-01,  3.36741994e-01, ...,
               7.23249279e-02,  1.95159645e-02, -1.09212073e-02],
             [ 5.46032766e-01,  5.46032766e-01,  3.16643128e-03, ...,
              -7.76781141e-02, -7.31673186e-05,  2.71134411e-02]],
            shape=(4, 1000))

    • Intercept
      (chain, draw)
      float64
      0.4837 0.4837 ... 0.09586 -0.04978

      array([[ 0.4837156 ,  0.4837156 , -1.87396621, ...,  0.00538542,
              -0.08860544,  0.05429767],
             [ 0.88779185,  0.88779185,  0.67897433, ..., -0.05087092,
              -0.03781194, -0.12952053],
             [-0.0299484 , -0.0299484 , -0.09983608, ...,  0.04322752,
               0.16851274, -0.12308524],
             [ 0.16442588,  0.16442588, -0.12090552, ..., -0.12835917,
               0.09586213, -0.04977877]], shape=(4, 1000))

    • x
      (chain, draw)
      float64
      -0.9797 -0.9797 ... 0.4696 0.3999

      array([[-0.97973487, -0.97973487,  2.66784052, ...,  0.52915062,
               0.34060638,  0.50867264],
             [ 0.7031206 ,  0.7031206 ,  0.47243793, ...,  0.51012372,
               0.31613494,  0.44276578],
             [-0.66424383, -0.66424383,  0.09526789, ...,  0.39906532,
               0.3264891 ,  0.49433037],
             [ 0.48185439,  0.48185439,  0.40487875, ...,  0.42266244,
               0.46963947,  0.39985407]], shape=(4, 1000))

    • sigma
      (chain, draw)
      float64
      0.5317 0.5317 ... 0.9999 1.027

      array([[0.53173896, 0.53173896, 7.54479532, ..., 0.93432616, 1.04934059,
              0.90788653],
             [0.54739376, 0.54739376, 0.69711438, ..., 0.96546346, 1.0143259 ,
              1.01693135],
             [2.14992436, 2.14992436, 1.40037771, ..., 1.07500459, 1.01970765,
              0.98913821],
             [1.72639042, 1.72639042, 1.00317145, ..., 0.92526221, 0.99992684,
              1.02748436]], shape=(4, 1000))

    • mu
      (chain, draw, __obs__)
      float64
      1.447 -0.3075 ... -0.389 -0.1782

      array([[[ 1.44668299, -0.30746891, -0.49372976, ...,  0.03610155,
                1.3149037 ,  0.79827334],
              [ 1.44668299, -0.30746891, -0.49372976, ...,  0.03610155,
                1.3149037 ,  0.79827334],
              [-4.4961485 ,  0.28044735,  0.7876399 , ..., -0.65510288,
               -4.13731047, -2.73051414],
              ...,
              [-0.51470915,  0.43270079,  0.53329948, ...,  0.24713986,
               -0.44353572, -0.16450587],
              [-0.42338258,  0.18645112,  0.25120499, ...,  0.0670083 ,
               -0.3775693 , -0.19796193],
              [-0.44566939,  0.46507606,  0.5617816 , ...,  0.28669628,
               -0.37725035, -0.10901887]],
      
             [[ 0.19670466,  1.45559661,  1.58926934, ...,  1.20902841,
                0.29127794,  0.66204503],
              [ 0.19670466,  1.45559661,  1.58926934, ...,  1.20902841,
                0.29127794,  0.66204503],
              [ 0.21462184,  1.06049139,  1.15030823, ...,  0.89481829,
                0.27816713,  0.52729145],
      ...
              [-0.34900808,  0.36549256,  0.44136028, ...,  0.22554954,
               -0.29533178, -0.08489805],
              [-0.15238874,  0.43216888,  0.49423888, ...,  0.31767667,
               -0.1084743 ,  0.06368879],
              [-0.60895549,  0.27611105,  0.37008994, ...,  0.10276078,
               -0.54246556, -0.281797  ]],
      
             [[-0.3091819 ,  0.55354721,  0.64515424, ...,  0.38457197,
               -0.24437006,  0.00971972],
              [-0.3091819 ,  0.55354721,  0.64515424, ...,  0.38457197,
               -0.24437006,  0.00971972],
              [-0.51885505,  0.20605415,  0.28302707, ...,  0.0640725 ,
               -0.46439682, -0.25089757],
              ...,
              [-0.54378804,  0.21296172,  0.29331556, ...,  0.06474373,
               -0.4869378 , -0.26406092],
              [-0.36573978,  0.4751193 ,  0.56440411, ...,  0.31042756,
               -0.3025709 , -0.05492226],
              [-0.44278962,  0.27312323,  0.34914089, ...,  0.13290361,
               -0.38900723, -0.17815758]]], shape=(4, 1000, 100))

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

    • __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: (4)

    created_at :

    2025-09-11T05:43:00.398914+00:00

    arviz_version :

    0.21.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  
• 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 6 5 1 0 ... 1 2 1 2 2 2
      maxdepth_reached      (chain, draw) bool 4kB False False ... False False
      index_in_trajectory   (chain, draw) int64 32kB 0 0 -14 -6 0 ... -2 1 -2 2 2
      logp                  (chain, draw) float64 32kB -453.4 -453.4 ... -144.1
      energy                (chain, draw) float64 32kB 453.6 455.3 ... 144.8 145.3
      diverging             (chain, draw) bool 4kB False True ... False False
      energy_error          (chain, draw) float64 32kB 0.0 0.0 ... -0.0436 -0.2045
      step_size             (chain, draw) float64 32kB 3.736 0.3684 ... 1.088
      step_size_bar         (chain, draw) float64 32kB 3.736 0.9423 ... 1.088
      mean_tree_accept      (chain, draw) float64 32kB 1.312e-28 0.0 ... 0.9112
      mean_tree_accept_sym  (chain, draw) float64 32kB 2.624e-28 0.0 ... 0.9075
      n_steps               (chain, draw) uint64 32kB 7 1 63 31 1 1 ... 3 3 3 3 3
  Attributes:
      created_at:                  2025-09-11T05:43:00.403552+00:00
      arviz_version:               0.21.0
      modeling_interface:          bambi
      modeling_interface_version:  0.15.1.dev17+g2db951a93.d20250910

  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 6 5 1 0 3 3 ... 2 2 1 2 1 2 2 2

      array([[3, 0, 6, ..., 1, 2, 2],
             [2, 0, 2, ..., 2, 2, 2],
             [3, 1, 3, ..., 2, 2, 2],
             [1, 0, 3, ..., 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
      0 0 -14 -6 0 0 -7 ... 1 -2 1 -2 2 2

      array([[  0,   0, -14, ...,  -1,   2,   3],
             [  0,   0,  -2, ...,  -2,   2,   2],
             [ -4,   0,   4, ...,  -3,   1,  -3],
             [  0,   0,   6, ...,  -2,   2,   2]], shape=(4, 1000))

    • logp
      (chain, draw)
      float64
      -453.4 -453.4 ... -144.5 -144.1

      array([[-453.43193838, -453.43193838, -310.01340866, ..., -144.26377661,
              -144.67362299, -144.76761589],
             [-339.3503542 , -339.3503542 , -208.1507837 , ..., -143.98526029,
              -144.23491578, -144.48986104],
             [-191.67214587, -191.67214587, -156.28326603, ..., -144.87324152,
              -145.93150692, -144.41777392],
             [-167.99402922, -167.99402922, -144.31083451, ..., -144.60723853,
              -144.52829065, -144.06573562]], shape=(4, 1000))

    • energy
      (chain, draw)
      float64
      453.6 455.3 449.5 ... 144.8 145.3

      array([[453.64838517, 455.26452125, 449.51117347, ..., 144.40176761,
              148.20055003, 145.51294082],
             [342.48160125, 340.06905936, 330.33875561, ..., 144.87134226,
              145.12616908, 146.53739474],
             [194.30719406, 192.56055955, 192.77995897, ..., 145.58556412,
              146.75477095, 146.98575503],
             [168.39030312, 169.16148739, 169.67721023, ..., 145.63759485,
              144.80350967, 145.3344773 ]], 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],
             [False, False, False, ..., False, False, False],
             [False,  True, False, ..., False, False, False]], shape=(4, 1000))

    • energy_error
      (chain, draw)
      float64
      0.0 0.0 -7.05 ... -0.0436 -0.2045

      array([[ 0.00000000e+00,  0.00000000e+00, -7.04953287e+00, ...,
               8.35937394e-02,  9.81405823e-01,  5.53408067e-02],
             [ 0.00000000e+00,  0.00000000e+00, -9.44301672e+00, ...,
               1.69642779e-03,  1.60533547e-01,  1.36001619e-01],
             [ 2.16825320e-03,  0.00000000e+00, -4.83430172e-01, ...,
               2.02481606e-01,  1.21420684e-01, -4.92424486e-01],
             [ 0.00000000e+00,  0.00000000e+00, -1.97703253e+00, ...,
               1.16965481e-01, -4.36015864e-02, -2.04474529e-01]],
            shape=(4, 1000))

    • step_size
      (chain, draw)
      float64
      3.736 0.3684 0.3837 ... 1.233 1.088

      array([[3.73610367, 0.36837736, 0.38366625, ..., 1.29875288, 0.96155004,
              1.05194764],
             [3.73610367, 0.36837736, 0.38366625, ..., 1.34845424, 1.29740556,
              1.09107225],
             [1.43504234, 0.24234831, 0.1       , ..., 0.86834966, 0.94735201,
              1.06962045],
             [1.95014425, 0.19474941, 0.09689406, ..., 1.12782322, 1.2331121 ,
              1.08796434]], shape=(4, 1000))

    • step_size_bar
      (chain, draw)
      float64
      3.736 0.9423 0.6353 ... 1.087 1.088

      array([[3.73610367, 0.94226449, 0.63531196, ..., 1.05230356, 1.05176798,
              1.05194764],
             [3.73610367, 0.94226449, 0.63531196, ..., 1.08942721, 1.09050213,
              1.09107225],
             [1.43504234, 0.49840022, 0.42127578, ..., 1.07081384, 1.07007587,
              1.06962045],
             [1.95014425, 0.49557799, 0.24219271, ..., 1.08598907, 1.08676817,
              1.08796434]], shape=(4, 1000))

    • mean_tree_accept
      (chain, draw)
      float64
      1.312e-28 0.0 1.0 ... 1.0 0.9112

      array([[1.31222524e-28, 0.00000000e+00, 1.00000000e+00, ...,
              9.19804861e-01, 2.03600672e-01, 9.79245894e-01],
             [1.37286188e-19, 0.00000000e+00, 1.00000000e+00, ...,
              7.56911153e-01, 6.01978197e-01, 5.35307272e-01],
             [9.98656893e-01, 1.83596678e-40, 9.96203517e-01, ...,
              8.02007829e-01, 8.93392413e-01, 9.53635693e-01],
             [2.36539918e-02, 0.00000000e+00, 7.20028478e-01, ...,
              7.53604329e-01, 1.00000000e+00, 9.11178391e-01]], shape=(4, 1000))

    • mean_tree_accept_sym
      (chain, draw)
      float64
      2.624e-28 0.0 ... 0.9401 0.9075

      array([[2.62445049e-28, 0.00000000e+00, 1.40221384e-03, ...,
              9.58227453e-01, 3.18598903e-01, 9.88450084e-01],
             [2.74572377e-19, 0.00000000e+00, 5.34127691e-03, ...,
              8.51260221e-01, 7.36035869e-01, 6.68288775e-01],
             [9.98333015e-01, 3.67193356e-40, 8.52834052e-01, ...,
              8.89371353e-01, 9.38877720e-01, 8.73600346e-01],
             [4.62148187e-02, 0.00000000e+00, 6.51604983e-01, ...,
              8.50848092e-01, 9.40099372e-01, 9.07488720e-01]], shape=(4, 1000))

    • n_steps
      (chain, draw)
      uint64
      7 1 63 31 1 1 15 ... 3 3 3 3 3 3 3

      array([[ 7,  1, 63, ...,  1,  3,  3],
             [ 3,  1,  3, ...,  3,  3,  3],
             [ 7,  1,  7, ...,  3,  3,  3],
             [ 1,  1,  7, ...,  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 :

    2025-09-11T05:43:00.403552+00:00

    arviz_version :

    0.21.0

    modeling_interface :

    bambi

    modeling_interface_version :

    0.15.1.dev17+g2db951a93.d20250910

  
  

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

The watermark extension is already loaded. To reload it, use:
  %reload_ext watermark
Last updated: Thu Sep 11 2025

Python implementation: CPython
Python version       : 3.12.5
IPython version      : 9.5.0

pandas: 2.3.0
numpy : 2.2.6
arviz : 0.21.0
bambi : 0.15.1.dev17+g2db951a93.d20250910

Watermark: 2.5.0