.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/hybrid_choice/plot_b04_choice_only_bayes.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_hybrid_choice_plot_b04_choice_only_bayes.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_hybrid_choice_plot_b04_choice_only_bayes.py:


4. Choice model only - Bayesian estimation
==========================================

This script estimates a **standard discrete choice model** without any latent
variables using **Bayesian estimation** in Biogeme.

It serves as the Bayesian counterpart of the choice-only maximum likelihood
specification and provides a baseline for comparison with:

- the Bayesian hybrid choice model, and
- the corresponding maximum likelihood estimates.

The configuration is defined locally in this file and passed to the generic
estimation pipeline via :func:`estimate_model`.

Michel Bierlaire
Thu Dec 25 2025, 08:27:04

.. GENERATED FROM PYTHON SOURCE LINES 20-38




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 
    Loaded NetCDF file size: 1.1 GB 
    load finished in 5868 ms (5.87 s)
    Results are read from the file saved_results/b04_choice_only_bayes.nc.
    posterior_predictive_loglike finished in 342 ms
    expected_log_likelihood finished in 15 ms
    best_draw_log_likelihood finished in 15 ms
    /Users/bierlair/python_envs/venv313/lib/python3.13/site-packages/arviz/stats/stats.py:1667: UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. 
    See http://arxiv.org/abs/1507.04544 for details
      warnings.warn(
    waic_res finished in 894 ms
    waic finished in 894 ms
    loo_res finished in 10878 ms (10.88 s)
    loo finished in 10878 ms (10.88 s)
    Sample size                                              896
    Sampler                                                  NUTS
    Number of chains                                         4
    Number of draws per chain                                20000
    Total number of draws                                    80000
    Acceptance rate target                                   0.9
    Run time                                                 0:01:48.594689
    Posterior predictive log-likelihood (sum of log mean p)  -509.25
    Expected log-likelihood E[log L(Y|θ)]                    -516.04
    Best-draw log-likelihood (posterior upper bound)         -512.56
    WAIC (Widely Applicable Information Criterion)           -523.52
    WAIC Standard Error                                      27.35
    Effective number of parameters (p_WAIC)                  14.26
    LOO (Leave-One-Out Cross-Validation)                     -523.57
    LOO Standard Error                                       27.37
    Effective number of parameters (p_LOO)                   14.32
    Diagnostics computation took 33.7 seconds (cached). 
                                  Name  Value (mean)  ...    ESS (bulk)    ESS (tail)
    0                    choice_asc_pt     -0.680088  ...  29694.589536  40554.824942
    1                   choice_asc_car     -0.264857  ...  27725.976971  38426.823096
    2          choice_beta_time_pt_ref     -0.965795  ...  33348.740556  36408.843240
    3                 choice_beta_cost     -0.080881  ...  47738.336216  42031.206892
    4         choice_beta_time_car_ref     -2.053416  ...  34740.385276  38711.164989
    5            choice_beta_dist_work     -0.209783  ...  32861.169315  43327.888783
    6  choice_beta_dist_other_purposes     -0.332450  ...  33112.393040  43404.599078

    [7 rows x 12 columns]






|

.. code-block:: Python


    import biogeme.biogeme_logging as blog

    from config import Config
    from estimate import estimate_model

    logger = blog.get_screen_logger(level=blog.INFO)

    the_config = Config(
        name='b04_choice_only_bayes',
        latent_variables="zero",
        choice_model="yes",
        estimation="bayes",
        number_of_bayesian_draws_per_chain=20_000,
        number_of_monte_carlo_draws=20_000,
    )

    estimate_model(config=the_config)


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 53.505 seconds)


.. _sphx_glr_download_auto_examples_hybrid_choice_plot_b04_choice_only_bayes.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_b04_choice_only_bayes.ipynb <plot_b04_choice_only_bayes.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_b04_choice_only_bayes.py <plot_b04_choice_only_bayes.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_b04_choice_only_bayes.zip <plot_b04_choice_only_bayes.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_