Custom models from ONNX files (blackbox)¶

Build an HSSM model directly from an onnx file, via the blackbox route. For our purposes, the onnx file-format provides nice translation layer from deep learning frameworks into a common layer from which we can then reconstruct computation graph to use through PyMC.

New to HSSM's likelihood kinds? Understanding likelihoods in HSSM explains how analytical, approx_differentiable, and blackbox likelihoods differ.

import os

import matplotlib.pyplot as plt
import numpy as np

import hssm

import os import matplotlib.pyplot as plt import numpy as np import hssm

Loading the network¶

# Networks
network_path = os.path.join("data", "race_3_no_bias_lan_no_batch.onnx")

# Networks network_path = os.path.join("data", "race_3_no_bias_lan_no_batch.onnx")

The network we load here does not have dynamic input dimensions, which prevents us from batching computations.

Instead of fixing things behind the scenes and loading a fixed network, we provide a useful snippet below that shows how to rectify this situation.

⚠️ Blackbox route only. The dynamic-axes rewrite below applies only to loglik_kind="blackbox", where the ONNX file runs inside a plain Python function via onnxruntime and HSSM never converts the graph. HSSM's approx_differentiable loader requires the exact opposite — every input dimension concrete — and will reject a file rewritten this way. See The ONNX likelihood contract.

import onnx
import onnxruntime as ort

# Load model from path
onnx_model = onnx.load(network_path)

# Change input and output dimensions to be dynamic to allow for batching
# (in case this is not already done)
for input_tensor in onnx_model.graph.input:
    dim_proto = input_tensor.type.tensor_type.shape.dim[0]
    if not dim_proto.dim_param == "None":
        dim_proto.dim_param = "None"

for output_tensor in onnx_model.graph.output:
    dim_proto = output_tensor.type.tensor_type.shape.dim[0]
    if not dim_proto.dim_param == "None":
        dim_proto.dim_param = "None"

input_name = onnx_model.graph.input[0].name

# Please uncomment the below line to save the adjusted model
# onnx.save(onnx_model, "data/race_3_no_bias_lan_batch.onnx")

import onnx import onnxruntime as ort # Load model from path onnx_model = onnx.load(network_path) # Change input and output dimensions to be dynamic to allow for batching # (in case this is not already done) for input_tensor in onnx_model.graph.input: dim_proto = input_tensor.type.tensor_type.shape.dim[0] if not dim_proto.dim_param == "None": dim_proto.dim_param = "None" for output_tensor in onnx_model.graph.output: dim_proto = output_tensor.type.tensor_type.shape.dim[0] if not dim_proto.dim_param == "None": dim_proto.dim_param = "None" input_name = onnx_model.graph.input[0].name # Please uncomment the below line to save the adjusted model # onnx.save(onnx_model, "data/race_3_no_bias_lan_batch.onnx")

2026-08-28 01:18:36.464080706 [W:onnxruntime:Default, device_discovery.cc:146 GetPciBusId] Skipping pci_bus_id for PCI path at "/sys/devices/LNXSYSTM:00/LNXSYBUS:00/ACPI0004:00/VMBUS:00/5620e0c7-8062-4dce-aeb7-520c7ef76171" because filename "5620e0c7-8062-4dce-aeb7-520c7ef76171" did not match expected pattern of [0-9a-f]+:[0-9a-f]+:[0-9a-f]+[.][0-9a-f]+

Armed with the corrected network, let's test inference speed on a data-batch of $1000$ trials.

# Load model batch ready model
ort_session = ort.InferenceSession("data/race_3_no_bias_lan_batch.onnx")

# Test inference speed
import time

start = time.time()
for i in range(100):
    ort_session.run(
        None, {input_name: np.random.uniform(size=(1000, 8)).astype(np.float32)}
    )
end = time.time()
print(f"Time taken: {(end - start) / 100} seconds")

# Load model batch ready model ort_session = ort.InferenceSession("data/race_3_no_bias_lan_batch.onnx") # Test inference speed import time start = time.time() for i in range(100): ort_session.run( None, {input_name: np.random.uniform(size=(1000, 8)).astype(np.float32)} ) end = time.time() print(f"Time taken: {(end - start) / 100} seconds")

Time taken: 0.0006541347503662109 seconds

Defining the Likelihood¶

The network we loaded corresponds to a LAN, for a Race model with three choice alternatives. This model has three drift parameters v0, v1, v2, a boundary parameter a, a starting point bias z and a non-decision-time t.

Data from this model has the usual rt, choice format.

We use this to construct a simple blackbox likelihood function below. This likelihood function takes the respective data and model parameters as arguments. The function body shapes these input arguments into a matrix and performs a batched forward pass through the loaded network via the onnx.runtime.

def my_blackbox_race_model(data, v0, v1, v2, a, z, t):
    """Calculate log-likelihood for a 3-choice race model.

    Parameters
    ----------
    data : np.ndarray
        Array of shape (n_trials, 2) containing response times in first column
        and choices (0, 1, or 2) in second column
    v0 : float
        Drift rate for accumulator 0
    v1 : float
        Drift rate for accumulator 1
    v2 : float
        Drift rate for accumulator 2
    a : float
        Decision threshold/boundary
    z : float
        Starting point bias
    t : float
        Non-decision time

    Notes
    -----
    HSSM calls blackbox likelihoods positionally, in ``list_params`` order —
    keep the signature and the stacked column order aligned with
    ``list_params`` (here: v0, v1, v2, a, z, t), which is also the order the
    network was trained on.

    Returns
    -------
    np.ndarray
        Array of log-likelihood values for each trial
    """
    data_nrows = data.shape[0]
    data = np.vstack(
        [np.full(data_nrows, param_) for param_ in [v0, v1, v2, a, z, t]]
        + [data[:, 0], data[:, 1]]
    ).T.astype(np.float32)
    return ort_session.run(None, {input_name: data})[0].squeeze()

def my_blackbox_race_model(data, v0, v1, v2, a, z, t): """Calculate log-likelihood for a 3-choice race model. Parameters ---------- data : np.ndarray Array of shape (n_trials, 2) containing response times in first column and choices (0, 1, or 2) in second column v0 : float Drift rate for accumulator 0 v1 : float Drift rate for accumulator 1 v2 : float Drift rate for accumulator 2 a : float Decision threshold/boundary z : float Starting point bias t : float Non-decision time Notes ----- HSSM calls blackbox likelihoods positionally, in ``list_params`` order — keep the signature and the stacked column order aligned with ``list_params`` (here: v0, v1, v2, a, z, t), which is also the order the network was trained on. Returns ------- np.ndarray Array of log-likelihood values for each trial """ data_nrows = data.shape[0] data = np.vstack( [np.full(data_nrows, param_) for param_ in [v0, v1, v2, a, z, t]] + [data[:, 0], data[:, 1]] ).T.astype(np.float32) return ort_session.run(None, {input_name: data})[0].squeeze()

Simulate example data¶

# Set parameters
v0 = 1.0
v1 = 0.5
v2 = 0.25
a = 1.5
t = 0.3
z = 0.5

# simulate some data from the model
obs_race3 = hssm.simulate_data(
    theta=dict(v0=v0, v1=v1, v2=v2, a=a, t=t, z=z), model="race_no_bias_3", size=1000
)

# Set parameters v0 = 1.0 v1 = 0.5 v2 = 0.25 a = 1.5 t = 0.3 z = 0.5 # simulate some data from the model obs_race3 = hssm.simulate_data( theta=dict(v0=v0, v1=v1, v2=v2, a=a, t=t, z=z), model="race_no_bias_3", size=1000 )

Test Likelihood Outputs¶

# Test that outputs are reasonable
for choice in [0, 1, 2]:
    rts = np.linspace(0, 20, 1000)
    choices = np.repeat(choice, 1000)

    data = np.vstack([rts, choices]).T
    out = my_blackbox_race_model(data, v0, v1, v2, a, t, z)

    plt.plot(rts, np.exp(out), label=f"choice: {choice}")
plt.legend()
plt.show()

# Test that outputs are reasonable for choice in [0, 1, 2]: rts = np.linspace(0, 20, 1000) choices = np.repeat(choice, 1000) data = np.vstack([rts, choices]).T out = my_blackbox_race_model(data, v0, v1, v2, a, t, z) plt.plot(rts, np.exp(out), label=f"choice: {choice}") plt.legend() plt.show()

Build HSSM Model¶

We can now build a simple HSSM model that takes in our new blackbox likelihood.

model = hssm.HSSM(
    data=obs_race3,
    model="race_no_bias_3",  # some name for the model
    model_config={
        "list_params": ["v0", "v1", "v2", "a", "z", "t"],
        "bounds": {
            "v0": (0.0, 2.5),
            "v1": (0.0, 2.5),
            "v2": (0.0, 2.5),
            "a": (1.0, 3.0),
            "z": (0.0, 0.9),
            "t": (0.001, 2),
        },
    },  # minimal specification of model parameters and parameter bounds
    loglik_kind="blackbox",  # use the blackbox loglik
    loglik=my_blackbox_race_model,
    choices=[0, 1, 2],  # list the legal choice options
    z=0.5,
    p_outlier=0,
)

model = hssm.HSSM( data=obs_race3, model="race_no_bias_3", # some name for the model model_config={ "list_params": ["v0", "v1", "v2", "a", "z", "t"], "bounds": { "v0": (0.0, 2.5), "v1": (0.0, 2.5), "v2": (0.0, 2.5), "a": (1.0, 3.0), "z": (0.0, 0.9), "t": (0.001, 2), }, }, # minimal specification of model parameters and parameter bounds loglik_kind="blackbox", # use the blackbox loglik loglik=my_blackbox_race_model, choices=[0, 1, 2], # list the legal choice options z=0.5, p_outlier=0, )

Model initialized successfully.

model.graph()

model.graph()

model.sample(draws=500, tune=200, discard_tuned_samples=False)

model.sample(draws=500, tune=200, discard_tuned_samples=False)

Using default initvals. 

Multiprocess sampling (2 chains in 2 jobs)

CompoundStep

>Slice: [v2]

>Slice: [v1]

>Slice: [a]

>Slice: [t]

>Slice: [v0]

<python-install>/lib/python3.13/multiprocessing/popen_fork.py:73: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.
  self.pid = os.fork()

<python-install>/lib/python3.13/multiprocessing/popen_fork.py:73: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.
  self.pid = os.fork()

Sampling 2 chains for 200 tune and 500 draw iterations (400 + 1_000 draws total) took 32 seconds.

We recommend running at least 4 chains for robust computation of convergence diagnostics

The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details

<xarray.DataTree>
Group: /
├── Group: /warmup_posterior
│       Dimensions:        (chain: 2, draw: 200, v0_mean_dim_0: 1)
│       Coordinates:
│         * chain          (chain) int64 16B 0 1
│         * draw           (draw) int64 2kB 0 1 2 3 4 5 6 ... 194 195 196 197 198 199
│         * v0_mean_dim_0  (v0_mean_dim_0) int64 8B 0
│       Data variables:
│           v2             (chain, draw) float64 3kB 3.345e-41 6.858e-21 ... 0.2001
│           v1             (chain, draw) float64 3kB 5.591e-116 2.514e-24 ... 0.4933
│           a              (chain, draw) float64 3kB 3.0 3.0 3.0 ... 1.419 1.414 1.414
│           t              (chain, draw) float64 3kB 0.001002 0.00137 ... 0.2933 0.2947
│           v0             (chain, draw) float64 3kB 1.451 1.65 1.578 ... 0.9951 1.003
│           v0_mean        (chain, draw, v0_mean_dim_0) float64 3kB 1.451 1.65 ... 1.003
│       Attributes:
│           created_at:                  2026-08-28T01:19:18.195355+00:00
│           creation_library:            ArviZ
│           creation_library_version:    1.3.0
│           creation_library_language:   Python
│           inference_library:           pymc
│           inference_library_version:   6.3.1
│           sample_dims:                 ['chain', 'draw']
│           sampling_time:               32.14871883392334
│           tuning_steps:                200
│           modeling_interface:          bambi
│           modeling_interface_version:  0.20.0
├── Group: /posterior
│       Dimensions:  (chain: 2, draw: 500)
│       Coordinates:
│         * chain    (chain) int64 16B 0 1
│         * draw     (draw) int64 4kB 0 1 2 3 4 5 6 7 ... 493 494 495 496 497 498 499
│       Data variables:
│           a        (chain, draw) float64 8kB 1.327 1.342 1.331 ... 1.432 1.396 1.391
│           v0       (chain, draw) float64 8kB 0.8268 0.8183 0.7995 ... 0.9167 0.9316
│           t        (chain, draw) float64 8kB 0.3049 0.3049 0.3012 ... 0.2988 0.3012
│           v2       (chain, draw) float64 8kB 0.1468 0.2687 0.1719 ... 0.3808 0.3039
│           v1       (chain, draw) float64 8kB 0.3688 0.3202 0.3361 ... 0.586 0.4373
│       Attributes:
│           created_at:                  2026-08-28T01:19:18.199772+00:00
│           creation_library:            ArviZ
│           creation_library_version:    1.3.0
│           creation_library_language:   Python
│           inference_library:           pymc
│           inference_library_version:   6.3.1
│           sample_dims:                 ['chain', 'draw']
│           sampling_time:               32.14871883392334
│           tuning_steps:                200
│           modeling_interface:          bambi
│           modeling_interface_version:  0.20.0
├── Group: /warmup_sample_stats
│       Dimensions:          (chain: 2, draw: 200, nstep_in_dim_0: 5, nstep_out_dim_0: 5)
│       Coordinates:
│         * chain            (chain) int64 16B 0 1
│         * draw             (draw) int64 2kB 0 1 2 3 4 5 6 ... 194 195 196 197 198 199
│         * nstep_in_dim_0   (nstep_in_dim_0) int64 40B 0 1 2 3 4
│         * nstep_out_dim_0  (nstep_out_dim_0) int64 40B 0 1 2 3 4
│       Data variables:
│           nstep_in         (chain, draw, nstep_in_dim_0) int64 16kB 0 0 0 0 ... 2 2 1
│           nstep_out        (chain, draw, nstep_out_dim_0) int64 16kB 379 332 ... 0 0
│       Attributes:
│           created_at:                  2026-08-28T01:19:18.202599+00:00
│           creation_library:            ArviZ
│           creation_library_version:    1.3.0
│           creation_library_language:   Python
│           inference_library:           pymc
│           inference_library_version:   6.3.1
│           sample_dims:                 ['chain', 'draw']
│           sampling_time:               32.14871883392334
│           tuning_steps:                200
│           modeling_interface:          bambi
│           modeling_interface_version:  0.20.0
├── Group: /sample_stats
│       Dimensions:          (chain: 2, draw: 500, nstep_in_dim_0: 5, nstep_out_dim_0: 5)
│       Coordinates:
│         * chain            (chain) int64 16B 0 1
│         * draw             (draw) int64 4kB 0 1 2 3 4 5 6 ... 494 495 496 497 498 499
│         * nstep_in_dim_0   (nstep_in_dim_0) int64 40B 0 1 2 3 4
│         * nstep_out_dim_0  (nstep_out_dim_0) int64 40B 0 1 2 3 4
│       Data variables:
│           nstep_in         (chain, draw, nstep_in_dim_0) int64 40kB 0 3 4 3 ... 6 0 2
│           nstep_out        (chain, draw, nstep_out_dim_0) int64 40kB 0 0 0 0 ... 0 0 0
│       Attributes:
│           created_at:                  2026-08-28T01:19:18.204794+00:00
│           creation_library:            ArviZ
│           creation_library_version:    1.3.0
│           creation_library_language:   Python
│           inference_library:           pymc
│           inference_library_version:   6.3.1
│           sample_dims:                 ['chain', 'draw']
│           sampling_time:               32.14871883392334
│           tuning_steps:                200
│           modeling_interface:          bambi
│           modeling_interface_version:  0.20.0
├── Group: /observed_data
│       Dimensions:                  (__obs__: 1000, rt,response_extra_dim_0: 2)
│       Coordinates:
│         * __obs__                  (__obs__) int64 8kB 0 1 2 3 4 ... 996 997 998 999
│         * rt,response_extra_dim_0  (rt,response_extra_dim_0) int64 16B 0 1
│       Data variables:
│           rt,response              (__obs__, rt,response_extra_dim_0) float64 16kB ...
│       Attributes:
│           created_at:                  2026-08-28T01:19:18.206324+00:00
│           creation_library:            ArviZ
│           creation_library_version:    1.3.0
│           creation_library_language:   Python
│           inference_library:           pymc
│           inference_library_version:   6.3.1
│           sample_dims:                 []
│           modeling_interface:          bambi
│           modeling_interface_version:  0.20.0
└── Group: /log_likelihood
        Dimensions:      (chain: 2, draw: 500, __obs__: 1000)
        Coordinates:
          * chain        (chain) int64 16B 0 1
          * draw         (draw) int64 4kB 0 1 2 3 4 5 6 ... 493 494 495 496 497 498 499
          * __obs__      (__obs__) int64 8kB 0 1 2 3 4 5 6 ... 994 995 996 997 998 999
        Data variables:
            rt,response  (chain, draw, __obs__) float64 8MB 0.2207 -0.3237 ... -2.76
        Attributes:
            modeling_interface:          bambi
            modeling_interface_version:  0.20.0

xarray.DataTree

• /warmup_posterior(20)

  • Dimensions:
    • chain: 2
    • draw: 200
    • v0_mean_dim_0: 1
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0 1

      array([0, 1])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 195 196 197 198 199

      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, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181,182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195,196, 197, 198, 199])

    • v0_mean_dim_0
      (v0_mean_dim_0)
      int64
      0

      array([0])

  • Data variables: (6)
    • v2
      (chain, draw)
      float64
      3.345e-41 6.858e-21 ... 0.2001

      array([[3.34496645e-41, 6.85834751e-21, 5.66048869e-12, 1.03997816e-11,1.39414029e-03, 1.55022392e-02, 1.17288715e-01, 2.17207627e-01,2.63355353e-01, 2.91963154e-01, 1.36126954e+00, 1.16161293e+00,1.15946486e+00, 1.17553737e+00, 1.12640659e+00, 1.26055040e+00,1.22330650e+00, 9.99056523e-01, 9.95109154e-01, 1.05615198e+00,1.06881569e+00, 9.33230498e-01, 9.05904629e-01, 1.08378982e+00,8.91487680e-01, 1.02963734e+00, 1.03833249e+00, 9.05311818e-01,9.62543659e-01, 9.99309262e-01, 9.97599578e-01, 7.86224249e-01,7.72387016e-01, 7.13909690e-01, 7.46156238e-01, 7.32247654e-01,7.38579437e-01, 7.86812016e-01, 5.96914879e-01, 6.78115814e-01,7.61319517e-01, 7.44377221e-01, 7.46406157e-01, 7.92875108e-01,7.96491900e-01, 7.31855838e-01, 7.58310134e-01, 7.36773094e-01,7.20267729e-01, 5.14196758e-01, 4.45884231e-01, 5.67687496e-01,3.41441243e-01, 3.24755058e-01, 3.60065540e-01, 2.98713048e-01,2.31050988e-01, 2.95968019e-01, 3.00416018e-01, 3.69309783e-01,3.64169207e-01, 3.36317469e-01, 4.82619285e-01, 3.86281511e-01,3.60429453e-01, 4.05472485e-01, 3.98319807e-01, 2.83779686e-01,2.75311763e-01, 2.72339989e-01, 3.33554672e-01, 3.94844918e-01,4.09119495e-01, 3.82008100e-01, 4.95621049e-01, 4.90010852e-01,4.96660377e-01, 5.27025792e-01, 1.45562056e-01, 1.49479302e-01,...3.07595894e-01, 3.67402776e-01, 3.73449023e-01, 2.47625771e-01,3.11731653e-01, 3.11480626e-01, 4.47408060e-01, 4.37107360e-01,3.44733437e-01, 3.55417866e-01, 4.35228067e-01, 3.90826371e-01,3.72535112e-01, 2.76056844e-01, 3.10937899e-01, 5.14919173e-01,4.43865015e-01, 3.83019013e-01, 4.14481873e-01, 3.64901637e-01,3.99846763e-01, 4.12223872e-01, 3.21955386e-01, 3.23644209e-01,2.83357295e-01, 3.56071483e-01, 3.13054727e-01, 2.59070835e-01,2.02075820e-01, 3.09768788e-01, 2.48885746e-01, 4.20342622e-01,2.99626908e-01, 3.89100398e-01, 2.43986609e-01, 2.72953577e-01,2.77876158e-01, 4.12618947e-01, 3.80975980e-01, 3.69458796e-01,4.47499892e-01, 3.27425406e-01, 3.99744169e-01, 2.91675777e-01,4.12228737e-01, 2.79168175e-01, 4.07827059e-01, 3.79771958e-01,3.39162810e-01, 3.22561782e-01, 3.86073992e-01, 2.05950486e-01,2.82137078e-01, 3.99423838e-01, 4.17243203e-01, 2.46318325e-01,2.35897280e-01, 2.18681311e-01, 3.30342010e-01, 2.94492472e-01,3.26746018e-01, 2.82500269e-01, 3.39548127e-01, 2.84822605e-01,1.96856544e-01, 2.03154681e-01, 2.43337852e-01, 4.29488680e-01,3.21147774e-01, 3.27199703e-01, 2.44154113e-01, 2.87985038e-01,2.51691913e-01, 2.27435780e-01, 3.56559215e-01, 3.89854556e-01,3.27966465e-01, 3.24642270e-01, 2.42107179e-01, 2.00050952e-01]])

    • v1
      (chain, draw)
      float64
      5.591e-116 2.514e-24 ... 0.4933

      array([[5.59137243e-116, 2.51386229e-024, 4.25694020e-019,2.81152918e-013, 1.84756401e-004, 4.86759427e-001,1.35115843e+000, 1.33111013e+000, 1.24201360e+000,1.44134520e+000, 1.22779557e+000, 1.39511506e+000,1.39237417e+000, 1.30683223e+000, 1.21375655e+000,1.28095204e+000, 1.27324157e+000, 1.21033659e+000,1.21562524e+000, 1.14856823e+000, 1.19390351e+000,1.18187843e+000, 1.10457118e+000, 1.07218531e+000,1.12580424e+000, 1.14114126e+000, 1.03541248e+000,1.06645105e+000, 1.08896535e+000, 9.50597849e-001,1.02136871e+000, 1.04923938e+000, 1.03474625e+000,9.08860956e-001, 7.87121112e-001, 1.02214363e+000,6.94630324e-001, 7.78598817e-001, 8.85491191e-001,8.17826976e-001, 8.16801474e-001, 9.37223795e-001,9.81795236e-001, 8.10651642e-001, 9.29188211e-001,9.67351387e-001, 7.78443612e-001, 7.53627379e-001,8.45050553e-001, 6.99410615e-001, 8.13856122e-001,7.50701597e-001, 4.82682548e-001, 4.79487529e-001,4.65637589e-001, 4.45248389e-001, 3.67907370e-001,4.25055596e-001, 4.88904434e-001, 4.99960864e-001,...6.15247754e-001, 4.33656183e-001, 6.09181473e-001,6.00095240e-001, 3.83104850e-001, 4.23021075e-001,4.58547656e-001, 4.87902109e-001, 5.48112826e-001,4.95763557e-001, 5.15749230e-001, 5.58713525e-001,4.75260896e-001, 5.62552910e-001, 5.35286787e-001,4.78249154e-001, 4.89049734e-001, 5.73585311e-001,5.48659507e-001, 6.80226081e-001, 5.07095185e-001,5.93978382e-001, 5.19611727e-001, 5.58056379e-001,4.84187520e-001, 5.48689615e-001, 5.50336875e-001,6.11128145e-001, 5.28811553e-001, 5.03400761e-001,5.70417057e-001, 4.64222258e-001, 6.64974393e-001,4.38032877e-001, 4.20524692e-001, 4.09960777e-001,4.15712136e-001, 4.94874076e-001, 4.23383646e-001,4.76044292e-001, 4.75023000e-001, 5.80740740e-001,4.33623870e-001, 4.07455171e-001, 4.92319761e-001,4.80615754e-001, 5.49138763e-001, 4.91571817e-001,3.80998979e-001, 5.89524305e-001, 4.65379965e-001,5.15383607e-001, 4.57558795e-001, 4.06199781e-001,6.04642693e-001, 4.68964436e-001, 5.08150117e-001,4.85832204e-001, 4.93293848e-001]])

    • a
      (chain, draw)
      float64
      3.0 3.0 3.0 ... 1.419 1.414 1.414

      array([[3.        , 3.        , 3.        , 2.60272972, 2.59196446,2.58877964, 2.62855204, 2.61309369, 2.58379418, 2.55168837,2.51702077, 2.49032226, 2.46211756, 2.34772696, 2.34317864,2.36059708, 2.35778521, 2.27054534, 2.22534182, 2.20316411,2.21393261, 2.20464167, 2.14709068, 2.14841743, 2.11137354,2.0597993 , 2.09131827, 2.05545639, 2.00028861, 1.9507304 ,1.94732044, 1.89536786, 1.88836642, 1.83487328, 1.84219779,1.82925019, 1.83932156, 1.79693627, 1.79929799, 1.85100411,1.83951573, 1.84932792, 1.85659723, 1.80417604, 1.79446454,1.74205206, 1.73048638, 1.70182723, 1.68724158, 1.61082607,1.58363795, 1.51858659, 1.48204866, 1.46231269, 1.40371996,1.36955392, 1.380909  , 1.42303906, 1.46971555, 1.46157106,1.46325752, 1.47329385, 1.43417026, 1.47010542, 1.46742681,1.46976806, 1.43171482, 1.42880925, 1.40616959, 1.41264989,1.41934442, 1.45129763, 1.52544925, 1.49587723, 1.5255446 ,1.53950264, 1.5356009 , 1.44657115, 1.48321354, 1.46980018,1.49062064, 1.52123498, 1.5133717 , 1.51897675, 1.48611179,1.48685195, 1.49128259, 1.46141744, 1.4458245 , 1.46927341,1.4520016 , 1.42389753, 1.44893741, 1.45200015, 1.39745652,1.42448067, 1.36342936, 1.35109283, 1.34338917, 1.36886897,...1.3685824 , 1.39172709, 1.403028  , 1.44628705, 1.46100719,1.4735264 , 1.45162945, 1.42678271, 1.45567513, 1.42721557,1.37487935, 1.45274295, 1.4820235 , 1.47649986, 1.47777088,1.52492424, 1.5053029 , 1.51674344, 1.53450554, 1.52016917,1.51772303, 1.50144371, 1.44125622, 1.42178515, 1.46808998,1.49034185, 1.50345426, 1.52365551, 1.52713133, 1.53561224,1.50982057, 1.53839149, 1.53351884, 1.53597736, 1.53396583,1.53739029, 1.53643886, 1.52906279, 1.47749997, 1.46682052,1.46252514, 1.50668835, 1.47408151, 1.47253196, 1.37997822,1.33289007, 1.32995769, 1.40053529, 1.44947153, 1.44356613,1.4511731 , 1.47276652, 1.4639201 , 1.45804515, 1.44976096,1.41563328, 1.44015348, 1.50042777, 1.49998392, 1.53963489,1.49754091, 1.47820252, 1.46308101, 1.47264001, 1.46770189,1.47784707, 1.47055084, 1.50896102, 1.52133754, 1.47560441,1.44562301, 1.44914879, 1.46377584, 1.48065392, 1.45867757,1.37964447, 1.39724981, 1.41129186, 1.39894654, 1.42311487,1.43481679, 1.45210495, 1.41562946, 1.37550494, 1.40944437,1.4320882 , 1.42630329, 1.42267058, 1.4001541 , 1.39996858,1.39066055, 1.38904364, 1.35850094, 1.37906265, 1.42833599,1.45663515, 1.42953746, 1.41881097, 1.41412313, 1.41407058]])

    • t
      (chain, draw)
      float64
      0.001002 0.00137 ... 0.2933 0.2947

      array([[0.00100177, 0.00136956, 0.00189589, 0.00320057, 0.03776009,0.044659  , 0.09388058, 0.11575353, 0.16280798, 0.16706846,0.18804347, 0.18463351, 0.17850761, 0.18700842, 0.20033067,0.19756437, 0.19334184, 0.19792357, 0.19974614, 0.21169238,0.20983108, 0.20960064, 0.20705801, 0.22343515, 0.22597662,0.22763169, 0.22891428, 0.22835024, 0.23996748, 0.24080192,0.24676092, 0.24863127, 0.24376406, 0.25833304, 0.25808053,0.25275251, 0.25242151, 0.25185544, 0.25179796, 0.24608688,0.25461939, 0.24933722, 0.2544302 , 0.25767382, 0.26421317,0.26645149, 0.26445652, 0.27579099, 0.27684814, 0.27751712,0.28990174, 0.2898662 , 0.28827641, 0.29385085, 0.29991753,0.30052016, 0.29528967, 0.28717059, 0.28332832, 0.28791608,0.28903455, 0.29348493, 0.29319074, 0.28966082, 0.29284613,0.29278216, 0.29655408, 0.29034197, 0.29814199, 0.29665029,0.29572859, 0.28988349, 0.27866217, 0.27936681, 0.28516853,0.28835184, 0.29040358, 0.29141553, 0.29519088, 0.2851017 ,0.28684334, 0.29102874, 0.28464197, 0.28630042, 0.28908122,0.29173204, 0.29130073, 0.29534868, 0.29492329, 0.28911769,0.28623905, 0.28925929, 0.29322465, 0.28772118, 0.29310285,0.29558672, 0.30350274, 0.30353808, 0.30406219, 0.30097697,...0.30410587, 0.29629038, 0.29681166, 0.29601232, 0.29147563,0.29443434, 0.29271269, 0.29418748, 0.29062854, 0.29661577,0.29831248, 0.28893965, 0.29134469, 0.29150945, 0.28487586,0.28581903, 0.28551578, 0.28043384, 0.28253816, 0.28310854,0.28180478, 0.29224756, 0.292984  , 0.29195793, 0.29182427,0.2861662 , 0.28894307, 0.28398352, 0.28599771, 0.28659536,0.28673465, 0.28546396, 0.28202491, 0.28062896, 0.28511827,0.28237136, 0.28228485, 0.29103721, 0.28776336, 0.2890819 ,0.28906181, 0.28349609, 0.28174998, 0.29371808, 0.30293925,0.30310967, 0.30280256, 0.29163899, 0.29013036, 0.28967985,0.29122965, 0.28912457, 0.29212332, 0.28975018, 0.29661923,0.29506966, 0.28921292, 0.28977712, 0.28060671, 0.28608118,0.28945578, 0.29039637, 0.28737202, 0.28846973, 0.28454501,0.28720348, 0.2857542 , 0.28951852, 0.28073247, 0.28268911,0.28448685, 0.28926368, 0.29062994, 0.28748009, 0.29409581,0.29310427, 0.29011739, 0.29616819, 0.29565829, 0.2911276 ,0.29035881, 0.2921815 , 0.29399986, 0.29381211, 0.29171923,0.29267341, 0.29424268, 0.29346434, 0.29729653, 0.29512436,0.29534418, 0.30011329, 0.30115989, 0.2993777 , 0.29651983,0.29259211, 0.29584019, 0.29605512, 0.29326976, 0.29470735]])

    • v0
      (chain, draw)
      float64
      1.451 1.65 1.578 ... 0.9951 1.003

      array([[1.4505605 , 1.65025004, 1.57781383, 1.29392707, 1.29964162,1.27418256, 1.72844135, 1.71679033, 1.82717146, 1.90664566,1.91171429, 1.75229113, 1.65204775, 1.59620193, 1.78327404,1.59567964, 1.70848276, 1.50754613, 1.49938068, 1.49013855,1.65944947, 1.57851654, 1.43292938, 1.52426356, 1.59847446,1.64370175, 1.5518302 , 1.42164716, 1.42402306, 1.44883556,1.48886261, 1.32211118, 1.26910122, 1.45402029, 1.37172224,1.28069297, 1.3313103 , 1.22943035, 1.33808461, 1.36383823,1.32681995, 1.36174159, 1.39142543, 1.39104019, 1.33241891,1.31376771, 1.27812946, 1.23921324, 1.20700229, 1.20480509,1.23770572, 1.10989344, 0.99767501, 1.00966058, 0.92877308,0.8969926 , 0.94498131, 0.86399923, 0.78578865, 0.96051146,0.99833443, 0.97474554, 1.03701274, 1.02145409, 1.08099322,0.98175695, 0.98427507, 0.96650962, 0.90059446, 1.01025362,1.00382291, 1.06806073, 0.99177872, 0.99278378, 1.15802731,1.13924546, 0.98575423, 1.03341849, 1.05282664, 1.06371716,1.02483424, 1.06761588, 1.04812657, 0.93852257, 0.97389568,1.09833388, 1.04233972, 0.96717025, 1.0798815 , 0.88030355,0.91720758, 0.90100458, 0.93083896, 0.99056323, 0.90803553,0.85719526, 0.93366343, 0.86994555, 0.93377694, 0.92973647,...0.98993139, 0.96823367, 0.97695128, 1.0016066 , 1.07195708,1.06448454, 0.96714866, 0.94186724, 0.94829059, 0.97794357,1.04011641, 1.00884408, 1.0497489 , 0.94245086, 0.99655295,1.09593139, 0.99321202, 1.07356033, 1.07885594, 0.9556834 ,1.06671337, 0.99891359, 0.96620858, 0.97543774, 1.03575179,0.93549476, 1.06398921, 1.01732892, 1.10205673, 1.0551672 ,1.16349646, 1.07728892, 1.13742715, 1.12905008, 1.12035776,0.99530562, 0.99745008, 1.01018384, 0.9777059 , 1.02423764,0.95273937, 0.93475381, 0.87664382, 0.86037776, 0.85855635,0.82138631, 0.88774116, 0.9055629 , 0.99528025, 0.94733253,1.05925404, 1.01210457, 0.97075608, 1.02762139, 1.07658524,0.91909229, 0.99427822, 0.99303442, 1.03263331, 1.03985615,1.03718189, 0.94380774, 0.90601313, 0.88834178, 0.92938487,0.92907396, 1.05085743, 1.0552084 , 1.01046624, 1.02893695,0.92548978, 0.99901493, 1.00503445, 0.94803435, 0.99114369,0.91663811, 0.90793105, 0.94709495, 0.9645072 , 0.85022418,0.87715719, 0.8474822 , 0.87007116, 0.85697859, 0.96080432,0.96635116, 0.94155281, 0.92148947, 0.95264495, 0.98096682,0.88830403, 0.94791917, 0.86929428, 0.98205939, 0.99917808,0.98853828, 0.86485152, 0.96073123, 0.99507413, 1.00327984]])

    • v0_mean
      (chain, draw, v0_mean_dim_0)
      float64
      1.451 1.65 1.578 ... 0.9951 1.003

      array([[[1.4505605 ],[1.65025004],[1.57781383],[1.29392707],[1.29964162],[1.27418256],[1.72844135],[1.71679033],[1.82717146],[1.90664566],[1.91171429],[1.75229113],[1.65204775],[1.59620193],[1.78327404],[1.59567964],[1.70848276],[1.50754613],[1.49938068],[1.49013855],...[0.87715719],[0.8474822 ],[0.87007116],[0.85697859],[0.96080432],[0.96635116],[0.94155281],[0.92148947],[0.95264495],[0.98096682],[0.88830403],[0.94791917],[0.86929428],[0.98205939],[0.99917808],[0.98853828],[0.86485152],[0.96073123],[0.99507413],[1.00327984]]])

  • Attributes: (11)

    created_at :

    2026-08-28T01:19:18.195355+00:00

    creation_library :

    ArviZ

    creation_library_version :

    1.3.0

    creation_library_language :

    Python

    inference_library :

    pymc

    inference_library_version :

    6.3.1

    sample_dims :

    ['chain', 'draw']

    sampling_time :

    32.14871883392334

    tuning_steps :

    200

    modeling_interface :

    bambi

    modeling_interface_version :

    0.20.0

  /posterior(18)

  • Dimensions:
    • chain: 2
    • draw: 500
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1

      array([0, 1])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499], shape=(500,))

  • Data variables: (5)
    • a
      (chain, draw)
      float64
      1.327 1.342 1.331 ... 1.396 1.391

      array([[1.32681591, 1.34204825, 1.33052784, 1.37302157, 1.37143027,1.40537352, 1.35797462, 1.33736081, 1.30062681, 1.33263512,1.31018822, 1.29037084, 1.35499837, 1.36224789, 1.36920743,1.37280368, 1.36582382, 1.31495948, 1.36932085, 1.4037793 ,1.43363951, 1.51657718, 1.49153092, 1.5020836 , 1.50202408,1.49475382, 1.52857041, 1.51713764, 1.52526635, 1.55978123,1.50786769, 1.51523539, 1.5236787 , 1.55375216, 1.52475842,1.55868415, 1.52283198, 1.51959054, 1.51110211, 1.52386809,1.50425954, 1.50729487, 1.55144328, 1.4821911 , 1.50151924,1.49223533, 1.49079571, 1.45097495, 1.42937377, 1.45264875,1.40225221, 1.46099133, 1.436326  , 1.41300022, 1.44829924,1.41426921, 1.45540963, 1.4423845 , 1.44477132, 1.41731081,1.4081432 , 1.45453879, 1.44404199, 1.3904273 , 1.43743693,1.36464045, 1.35100913, 1.35474822, 1.3409114 , 1.3500411 ,1.3755971 , 1.38787088, 1.3667317 , 1.36929006, 1.37607819,1.32114513, 1.3723657 , 1.33911939, 1.33800558, 1.35692534,1.39045467, 1.39707078, 1.37266358, 1.36559158, 1.35784752,1.38217559, 1.40366425, 1.4283337 , 1.45312272, 1.44006057,1.4579309 , 1.46763052, 1.49254817, 1.43821926, 1.42708304,1.41464064, 1.43377272, 1.46667832, 1.40848957, 1.38203103,...1.33906442, 1.37803139, 1.3788042 , 1.3535659 , 1.36140118,1.40022274, 1.44147462, 1.42605474, 1.45129109, 1.42536851,1.41753563, 1.44323064, 1.42749925, 1.45357496, 1.51005987,1.46007753, 1.45833254, 1.44943275, 1.458987  , 1.42518688,1.42179392, 1.42459308, 1.37862988, 1.3625158 , 1.3691503 ,1.40709326, 1.40577088, 1.38652721, 1.38549862, 1.41889246,1.4324016 , 1.46910586, 1.45786449, 1.47930633, 1.4664659 ,1.47352205, 1.45134483, 1.42486337, 1.42188704, 1.41748522,1.43116405, 1.44830921, 1.44588569, 1.51380938, 1.51323281,1.52342738, 1.52084703, 1.47669381, 1.45831202, 1.46577443,1.42751658, 1.49403623, 1.48265356, 1.44711331, 1.45451615,1.44136701, 1.41718339, 1.41542246, 1.43216163, 1.39920944,1.42124862, 1.47097201, 1.47806865, 1.4875158 , 1.46021635,1.4697641 , 1.46505115, 1.47983636, 1.48109613, 1.44861939,1.44000173, 1.41175934, 1.44623767, 1.43079752, 1.41643305,1.41836135, 1.40879686, 1.39225784, 1.40132708, 1.38739993,1.3917051 , 1.39991467, 1.46926558, 1.45126604, 1.44801089,1.42148405, 1.49398517, 1.49166072, 1.48776006, 1.51098783,1.51109539, 1.5147512 , 1.48477955, 1.50535398, 1.46935494,1.44824238, 1.42182241, 1.43159956, 1.39586926, 1.39124252]])

    • v0
      (chain, draw)
      float64
      0.8268 0.8183 ... 0.9167 0.9316

      array([[0.82678716, 0.81830194, 0.79946894, 0.8564103 , 0.87380439,0.91102856, 0.80569623, 0.75932081, 0.82768218, 0.83122789,0.8703338 , 0.89749451, 0.83364762, 0.89704379, 0.90581741,0.92521601, 0.69508999, 0.94741438, 0.81845387, 0.82177525,1.05898955, 1.0611246 , 0.97999673, 1.07659972, 1.10551384,1.07520523, 1.03390259, 0.94553608, 1.08319297, 1.08048968,1.14161612, 0.95030306, 1.14208438, 1.15068956, 1.10064966,1.12820526, 0.96854245, 0.9181667 , 1.08798416, 1.06197151,1.11140092, 1.12117736, 1.01436391, 0.89555324, 1.10248403,1.07701992, 1.0680349 , 0.99279263, 0.95370964, 1.105172  ,1.08889453, 1.0079359 , 1.05643479, 0.99256918, 0.93982191,1.00861871, 0.99212787, 0.94753252, 1.01399533, 0.91308522,0.96866514, 0.94629354, 0.8581237 , 0.89703757, 0.90965596,0.95812606, 0.95233206, 0.89188834, 0.9249419 , 0.90406853,0.88553227, 1.05605039, 0.96281226, 0.86173051, 0.83817259,0.8491386 , 0.80341069, 0.87064429, 0.81815927, 0.81087668,0.74334845, 0.80211674, 0.93525052, 0.79523088, 0.90591271,0.8216343 , 0.95309872, 1.01392818, 0.94252231, 0.92870507,1.10108985, 0.90962063, 0.9354794 , 0.92959369, 0.97639624,0.95718371, 0.95095986, 0.96615986, 0.83907186, 0.71113531,...0.81882734, 0.95947267, 0.79572966, 0.91582267, 0.8974329 ,0.98348162, 1.01781146, 1.01116237, 0.92485393, 0.87471867,0.85678768, 0.98091425, 0.98920117, 1.08223899, 1.00932787,0.97872677, 1.03658539, 0.9550228 , 0.95763061, 1.02073814,0.97068476, 0.94954126, 0.93546196, 0.89021423, 0.88718808,0.91898186, 0.91824958, 0.98488824, 0.96545411, 1.02386721,1.00842002, 0.93190649, 0.92901428, 0.97215795, 0.90010579,1.05309855, 1.01132973, 1.00865472, 0.80318275, 0.85440598,0.9572809 , 0.91818491, 1.00447485, 1.0910307 , 1.10393091,1.16509247, 1.12495026, 0.9606554 , 0.91025238, 0.89578306,0.96113184, 1.00255212, 1.03653597, 1.01106264, 0.96642212,0.96354608, 0.96808481, 0.92544079, 0.93593012, 0.95389998,0.94138606, 1.00631815, 1.06966859, 1.03727051, 0.91414501,0.97074474, 1.02537912, 0.9544945 , 1.01691538, 1.01158647,0.90220337, 0.92747849, 0.9575894 , 1.02605133, 0.93624786,0.95352218, 0.94709486, 0.99603922, 0.83887496, 0.92143769,0.91703123, 0.88613383, 1.05673666, 0.99481228, 0.95999291,0.98250898, 1.03417198, 1.03302418, 1.00847637, 1.03359686,1.06042183, 1.04234419, 1.18759834, 1.02259724, 1.05483442,0.98841831, 0.90781589, 0.88234028, 0.91665791, 0.93163486]])

    • t
      (chain, draw)
      float64
      0.3049 0.3049 ... 0.2988 0.3012

      array([[0.3049296 , 0.30490568, 0.30115263, 0.29591405, 0.30062008,0.29343861, 0.30269607, 0.30127758, 0.30672763, 0.29957973,0.31400882, 0.30354118, 0.30104602, 0.3007288 , 0.30340718,0.29888095, 0.29937843, 0.30165859, 0.29332105, 0.29321738,0.29228057, 0.28919951, 0.28713361, 0.28717503, 0.2893721 ,0.28712946, 0.28179256, 0.2791175 , 0.27875309, 0.28574036,0.29228586, 0.28485092, 0.28481858, 0.28497232, 0.28082605,0.28194638, 0.27935998, 0.28033659, 0.27981279, 0.28653641,0.29152459, 0.28561589, 0.28386152, 0.28393564, 0.28493432,0.29304   , 0.29121381, 0.29633653, 0.29668814, 0.29934989,0.29624667, 0.29169058, 0.29886486, 0.2966394 , 0.2951702 ,0.29807084, 0.29611828, 0.29210321, 0.2939285 , 0.29774237,0.29815344, 0.29133222, 0.29143673, 0.29151346, 0.29275245,0.30453372, 0.29920782, 0.30099407, 0.3033137 , 0.3027597 ,0.29717354, 0.3048963 , 0.30513242, 0.29652067, 0.30151146,0.30392327, 0.29837858, 0.30304304, 0.30321888, 0.30115765,0.29344386, 0.30001831, 0.30167961, 0.29974188, 0.2965627 ,0.29490746, 0.29736965, 0.29132155, 0.2901283 , 0.29432072,0.2915736 , 0.29022272, 0.29171744, 0.29788103, 0.30114332,0.29914454, 0.29047079, 0.28890665, 0.28768997, 0.28788883,...0.29932994, 0.29926213, 0.29736088, 0.29848488, 0.29792736,0.29857002, 0.29786879, 0.2951791 , 0.2907178 , 0.29155442,0.29421232, 0.29444191, 0.2944409 , 0.29042324, 0.29469135,0.29139016, 0.29421974, 0.29020151, 0.29676599, 0.29672541,0.29876508, 0.29845311, 0.30214413, 0.30065879, 0.29994139,0.29365725, 0.29466161, 0.30117024, 0.29464284, 0.29707208,0.29386639, 0.29182959, 0.28658663, 0.2865732 , 0.28946636,0.28755943, 0.29479072, 0.2939534 , 0.29296152, 0.29078228,0.29089305, 0.29473566, 0.28901599, 0.28480849, 0.28722726,0.28567353, 0.29074949, 0.29407116, 0.29008823, 0.28821946,0.28819238, 0.28725082, 0.29027217, 0.29602496, 0.2912627 ,0.29147248, 0.29591237, 0.29332319, 0.29604266, 0.29406784,0.29321631, 0.28732911, 0.28714394, 0.29121209, 0.29359418,0.28306861, 0.29366935, 0.28663193, 0.292501  , 0.29164601,0.28916701, 0.28878015, 0.29529189, 0.2909817 , 0.30053351,0.29714233, 0.29635006, 0.30169847, 0.29408728, 0.29467997,0.29428635, 0.29091593, 0.28959915, 0.29114884, 0.29507093,0.29217772, 0.28412942, 0.2840841 , 0.28695695, 0.29007023,0.28748548, 0.28643078, 0.29223246, 0.29333167, 0.29231138,0.29594305, 0.29202819, 0.29869678, 0.29876672, 0.30121036]])

    • v2
      (chain, draw)
      float64
      0.1468 0.2687 ... 0.3808 0.3039

      array([[0.14675658, 0.26867419, 0.17185231, 0.215905  , 0.2324922 ,0.29828703, 0.20941596, 0.29871385, 0.21332242, 0.22043612,0.21388605, 0.06341996, 0.15611808, 0.31862084, 0.1265721 ,0.23079054, 0.23329884, 0.24265762, 0.11165249, 0.18046815,0.27107918, 0.3504139 , 0.35730321, 0.38743968, 0.38506587,0.39989105, 0.43634796, 0.45670918, 0.26302802, 0.4497927 ,0.49638357, 0.52927538, 0.35720497, 0.4487412 , 0.447733  ,0.37656886, 0.31872357, 0.26708268, 0.41532385, 0.41981988,0.44000093, 0.27020733, 0.34729692, 0.42563735, 0.40749924,0.36375748, 0.47234041, 0.38625056, 0.34738237, 0.38907334,0.31229426, 0.2365603 , 0.26354923, 0.27351528, 0.33097699,0.40015286, 0.34133361, 0.2706027 , 0.34766782, 0.31772808,0.29904599, 0.36928484, 0.40351731, 0.2634036 , 0.26668028,0.27812349, 0.30258505, 0.16061681, 0.23764927, 0.16614685,0.29172528, 0.28182756, 0.30591425, 0.22735204, 0.21205455,0.22000123, 0.29172261, 0.14807604, 0.18789483, 0.31475037,0.31140689, 0.33545042, 0.30009181, 0.26409437, 0.25823652,0.18058198, 0.26685275, 0.31000112, 0.33386221, 0.27991968,0.34928908, 0.36533377, 0.33657974, 0.3394739 , 0.37969437,0.31248088, 0.31515709, 0.37480764, 0.23422287, 0.23485152,...0.16089224, 0.24331971, 0.24554286, 0.24867251, 0.32039887,0.28741814, 0.35648234, 0.32618123, 0.33091967, 0.36031057,0.35329484, 0.30427439, 0.44718152, 0.29473081, 0.43415832,0.47381698, 0.4564712 , 0.28589321, 0.34713056, 0.50604515,0.3115017 , 0.39473855, 0.32315472, 0.25248049, 0.25489215,0.2867016 , 0.34291836, 0.25780668, 0.23159305, 0.26399138,0.26070814, 0.31977926, 0.42199204, 0.41496483, 0.3780443 ,0.36024535, 0.32859693, 0.28367466, 0.26949576, 0.34895926,0.33244339, 0.4459969 , 0.25790379, 0.39266727, 0.45792105,0.39901489, 0.47064237, 0.5020493 , 0.37177064, 0.32235885,0.30655657, 0.34390107, 0.37365404, 0.39312913, 0.37844038,0.28134533, 0.29466367, 0.22250564, 0.26300625, 0.32269781,0.15117352, 0.28449533, 0.31382911, 0.41028392, 0.40262709,0.29436002, 0.19447279, 0.30647737, 0.38014609, 0.3466236 ,0.32495398, 0.14913006, 0.28920851, 0.44160541, 0.17038475,0.46942896, 0.30513896, 0.21355179, 0.17821152, 0.27066829,0.31402449, 0.23058992, 0.2796213 , 0.47573498, 0.35594184,0.38432489, 0.34642093, 0.23621912, 0.21338218, 0.5808647 ,0.28466778, 0.47846597, 0.36500989, 0.48331782, 0.36836034,0.40352889, 0.36911324, 0.37731418, 0.38076851, 0.30393326]])

    • v1
      (chain, draw)
      float64
      0.3688 0.3202 ... 0.586 0.4373

      array([[0.36881767, 0.32019835, 0.33607647, 0.35437939, 0.36394076,0.47790679, 0.23921022, 0.32503808, 0.24474096, 0.28370531,0.37574384, 0.36533426, 0.44463857, 0.43025255, 0.45283408,0.54468838, 0.30255209, 0.35641872, 0.37968209, 0.48288934,0.40898228, 0.58315452, 0.52183776, 0.5316092 , 0.54589476,0.63939434, 0.63224709, 0.56793872, 0.62566666, 0.52687815,0.62354162, 0.59297196, 0.6919332 , 0.66666119, 0.61788756,0.63831204, 0.61488812, 0.56075489, 0.59307567, 0.60191243,0.55301641, 0.518111  , 0.67000112, 0.58620157, 0.50581677,0.5129092 , 0.60499425, 0.55183496, 0.59008109, 0.63031506,0.52591287, 0.5420876 , 0.50583912, 0.51513187, 0.51325623,0.51496534, 0.59591447, 0.62885919, 0.533265  , 0.45193575,0.45589053, 0.64033015, 0.47895689, 0.46601446, 0.35492614,0.30633964, 0.3425763 , 0.35879632, 0.41048455, 0.36727035,0.41454084, 0.413061  , 0.45326369, 0.43758606, 0.50955209,0.41813719, 0.38240751, 0.49318938, 0.32002815, 0.41572032,0.46936231, 0.42156714, 0.43661045, 0.57133803, 0.32424717,0.37899175, 0.36091256, 0.51091957, 0.5213402 , 0.52779746,0.53517447, 0.50203549, 0.55554479, 0.52770391, 0.59243182,0.5778496 , 0.61117457, 0.3985524 , 0.46405949, 0.3127183 ,...0.34286414, 0.33665449, 0.54951891, 0.37574825, 0.39451957,0.45363308, 0.51418002, 0.53145037, 0.49415974, 0.39817408,0.56161348, 0.52456091, 0.60317366, 0.58785808, 0.59278741,0.7076978 , 0.41132507, 0.36813649, 0.58916437, 0.58488108,0.5431232 , 0.43064004, 0.46337387, 0.49003608, 0.3792718 ,0.52978607, 0.37521201, 0.34865386, 0.38311535, 0.43454961,0.54353739, 0.52940363, 0.57308255, 0.4531211 , 0.49484877,0.62251473, 0.42265651, 0.36711542, 0.45034609, 0.50779794,0.47848219, 0.60758451, 0.48910643, 0.46894848, 0.64442109,0.59779422, 0.58630075, 0.52176222, 0.58319483, 0.57028668,0.51739011, 0.54943939, 0.56114899, 0.44513668, 0.52330817,0.56118186, 0.44179907, 0.42169501, 0.57541109, 0.46533805,0.5184801 , 0.60169484, 0.48918954, 0.51857284, 0.62510588,0.45540198, 0.49073973, 0.64480928, 0.48267683, 0.49046268,0.45859451, 0.42723299, 0.42616888, 0.35877156, 0.55579232,0.54167294, 0.51373814, 0.45239094, 0.52487329, 0.43415399,0.45694254, 0.50411881, 0.49255732, 0.4865086 , 0.56010211,0.49874827, 0.49424913, 0.54686997, 0.49973212, 0.51166836,0.57336474, 0.66399727, 0.66855727, 0.56780087, 0.62966422,0.50006884, 0.55694019, 0.53472476, 0.58598044, 0.43729975]])

  • Attributes: (11)

    created_at :

    2026-08-28T01:19:18.199772+00:00

    creation_library :

    ArviZ

    creation_library_version :

    1.3.0

    creation_library_language :

    Python

    inference_library :

    pymc

    inference_library_version :

    6.3.1

    sample_dims :

    ['chain', 'draw']

    sampling_time :

    32.14871883392334

    tuning_steps :

    200

    modeling_interface :

    bambi

    modeling_interface_version :

    0.20.0

  /warmup_sample_stats(17)

  • Dimensions:
    • chain: 2
    • draw: 200
    • nstep_in_dim_0: 5
    • nstep_out_dim_0: 5
  • Coordinates: (4)
    • chain
      (chain)
      int64
      0 1

      array([0, 1])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 195 196 197 198 199

      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, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181,182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195,196, 197, 198, 199])

    • nstep_in_dim_0
      (nstep_in_dim_0)
      int64
      0 1 2 3 4

      array([0, 1, 2, 3, 4])

    • nstep_out_dim_0
      (nstep_out_dim_0)
      int64
      0 1 2 3 4

      array([0, 1, 2, 3, 4])

  • Data variables: (2)
    • nstep_in
      (chain, draw, nstep_in_dim_0)
      int64
      0 0 0 0 1 3 1 1 ... 6 6 2 6 1 2 2 1

      array([[[ 0,  0,  0,  0,  1],[ 3,  1,  1,  0,  1],[ 4,  2,  1,  1,  5],...,[ 4,  4,  9,  4,  0],[ 1,  3,  8, 10,  6],[ 6,  3,  7,  5,  4]],[[ 0,  0,  0,  0,  1],[ 4,  1,  1,  0,  4],[ 0,  1,  2,  2,  0],...,[10,  8,  5,  1,  2],[ 8,  5,  6,  6,  2],[ 6,  1,  2,  2,  1]]], shape=(2, 200, 5))

    • nstep_out
      (chain, draw, nstep_out_dim_0)
      int64
      379 332 249 11 1 1 ... 0 0 0 0 0 0

      array([[[379, 332, 249,  11,   1],[  1,   1,   1,   1,   0],[  0,   0,   1,   0,   1],...,[  1,   1,   0,   0,   0],[  0,   0,   0,   0,   0],[  1,   0,   0,   0,   0]],[[379, 332, 248,  11,   1],[  1,   1,   1,   0,   0],[  1,   0,   0,   1,   0],...,[  0,   0,   0,   0,   0],[  0,   0,   0,   0,   0],[  0,   0,   0,   0,   0]]], shape=(2, 200, 5))

  • Attributes: (11)

    created_at :

    2026-08-28T01:19:18.202599+00:00

    creation_library :

    ArviZ

    creation_library_version :

    1.3.0

    creation_library_language :

    Python

    inference_library :

    pymc

    inference_library_version :

    6.3.1

    sample_dims :

    ['chain', 'draw']

    sampling_time :

    32.14871883392334

    tuning_steps :

    200

    modeling_interface :

    bambi

    modeling_interface_version :

    0.20.0

  /sample_stats(17)

  • Dimensions:
    • chain: 2
    • draw: 500
    • nstep_in_dim_0: 5
    • nstep_out_dim_0: 5
  • Coordinates: (4)
    • chain
      (chain)
      int64
      0 1

      array([0, 1])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499], shape=(500,))

    • nstep_in_dim_0
      (nstep_in_dim_0)
      int64
      0 1 2 3 4

      array([0, 1, 2, 3, 4])

    • nstep_out_dim_0
      (nstep_out_dim_0)
      int64
      0 1 2 3 4

      array([0, 1, 2, 3, 4])

  • Data variables: (2)
    • nstep_in
      (chain, draw, nstep_in_dim_0)
      int64
      0 3 4 3 0 6 3 10 ... 7 4 4 7 6 0 2

      array([[[ 0,  3,  4,  3,  0],[ 6,  3, 10,  6,  3],[ 2,  5,  4,  5,  3],...,[ 2,  4,  3,  5,  1],[ 5,  5,  6,  7,  2],[ 2,  7,  4,  6,  2]],[[ 3,  7,  5,  5,  4],[ 6,  4,  7,  7,  0],[ 0,  5,  7,  6,  0],...,[ 5,  3, 12,  0,  4],[ 3,  4,  5,  7,  4],[ 4,  7,  6,  0,  2]]], shape=(2, 500, 5))

    • nstep_out
      (chain, draw, nstep_out_dim_0)
      int64
      0 0 0 0 1 0 0 0 ... 0 0 0 0 1 0 0 0

      array([[[0, 0, 0, 0, 1],[0, 0, 0, 0, 0],[0, 0, 0, 0, 0],...,[0, 0, 0, 0, 0],[0, 0, 0, 0, 0],[0, 0, 0, 0, 1]],[[0, 0, 0, 0, 1],[0, 0, 1, 0, 0],[0, 0, 0, 0, 1],...,[0, 0, 0, 0, 1],[0, 0, 0, 0, 0],[0, 1, 0, 0, 0]]], shape=(2, 500, 5))

  • Attributes: (11)

    created_at :

    2026-08-28T01:19:18.204794+00:00

    creation_library :

    ArviZ

    creation_library_version :

    1.3.0

    creation_library_language :

    Python

    inference_library :

    pymc

    inference_library_version :

    6.3.1

    sample_dims :

    ['chain', 'draw']

    sampling_time :

    32.14871883392334

    tuning_steps :

    200

    modeling_interface :

    bambi

    modeling_interface_version :

    0.20.0

  /observed_data(12)

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

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

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

      array([0, 1])

  • Data variables: (1)
    • rt,response
      (__obs__, rt,response_extra_dim_0)
      float64
      0.478 0.0 0.5345 ... 0.0 1.249 0.0

      array([[0.47798058, 0.        ],[0.53446436, 1.        ],[0.78802198, 0.        ],...,[0.44450322, 0.        ],[0.38095433, 0.        ],[1.24947262, 0.        ]], shape=(1000, 2))

  • Attributes: (9)

    created_at :

    2026-08-28T01:19:18.206324+00:00

    creation_library :

    ArviZ

    creation_library_version :

    1.3.0

    creation_library_language :

    Python

    inference_library :

    pymc

    inference_library_version :

    6.3.1

    sample_dims :

    []

    modeling_interface :

    bambi

    modeling_interface_version :

    0.20.0

  /log_likelihood(6)

  • Dimensions:
    • chain: 2
    • draw: 500
    • __obs__: 1000
  • Coordinates: (3)
    • chain
      (chain)
      int64
      0 1

      array([0, 1])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499], shape=(500,))

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

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

  • Data variables: (1)
    • rt,response
      (chain, draw, __obs__)
      float64
      0.2207 -0.3237 ... -0.3951 -2.76

      array([[[ 0.22067067, -0.32365215, -1.12100112, ...,  0.25615215,-0.32640797, -2.70146704],[ 0.20330802, -0.36673662, -1.12670672, ...,  0.23056683,-0.38640448, -2.71664405],[ 0.19413872, -0.35937136, -1.13545907, ...,  0.23815043,-0.27097118, -2.69180274],...,[ 0.22699967, -0.34850013, -1.10591519, ...,  0.25372592,-0.29675949, -2.80008245],[ 0.22645462, -0.33830801, -1.10334694, ...,  0.25007349,-0.3218815 , -2.79233336],[ 0.26120707, -0.3751713 , -1.00050449, ...,  0.26182461,-0.35919431, -2.71896982]],[[ 0.19155569, -0.26888168, -1.11642599, ...,  0.20898506,-0.37733629, -2.78983402],[ 0.14202757, -0.2896392 , -1.17505372, ...,  0.16304646,-0.4134973 , -2.83556581],[ 0.24574021, -0.3252911 , -1.1127516 , ...,  0.27148119,-0.33847019, -2.79908204],...,[ 0.15609415, -0.27624175, -1.13303506, ...,  0.15777963,-0.51170957, -2.80811954],[ 0.19147401, -0.25266334, -1.19290519, ...,  0.21927463,-0.36376208, -2.94032788],[ 0.22562961, -0.32937714, -1.09739625, ...,  0.24174617,-0.39508462, -2.76015759]]], shape=(2, 500, 1000))

  • Attributes: (2)

    modeling_interface :

    bambi

    modeling_interface_version :

    0.20.0

import arviz as az

az.plot_trace(model.traces, var_names=["~v0_mean"])
plt.tight_layout()

import arviz as az az.plot_trace(model.traces, var_names=["~v0_mean"]) plt.tight_layout()

<environment>/site-packages/arviz_base/utils.py:149: UserWarning: Items starting with ~: ['v0_mean'] have not been found and will be ignored
  warnings.warn(

az.plot_pair(model.traces, var_names=["~v0_mean"])
plt.tight_layout()

az.plot_pair(model.traces, var_names=["~v0_mean"]) plt.tight_layout()

<environment>/site-packages/arviz_base/utils.py:149: UserWarning: Items starting with ~: ['v0_mean'] have not been found and will be ignored
  warnings.warn(