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 estimate_model().

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

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]

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)