.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/bayesian_swissmetro/plot_b23b_binary_probit.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_bayesian_swissmetro_plot_b23b_binary_probit.py: 23b. Binary probit model ======================== Bayesian estimation of a binary probit model. Two alternatives: Train and Car. All observations such that the Swissmetro was chosen haven been removed from the sample. Michel Bierlaire, EPFL Sat Jun 28 2025, 12:43:40 .. GENERATED FROM PYTHON SOURCE LINES 15-20 .. code-block:: Python from pathlib import Path from IPython.core.display_functions import display .. GENERATED FROM PYTHON SOURCE LINES 21-22 See the data processing script ``swissmetro_binary.py``. .. GENERATED FROM PYTHON SOURCE LINES 22-39 .. code-block:: Python from swissmetro_binary import ( CAR_CO_SCALED, CAR_TT_SCALED, CHOICE, TRAIN_COST_SCALED, TRAIN_TT_SCALED, database, ) from biogeme.bayesian_estimation import ( BayesianResults, BayesianResultsSummary, get_pandas_estimated_parameters, ) from biogeme.biogeme import BIOGEME from biogeme.expressions import Beta, Elem, NormalCdf, log .. GENERATED FROM PYTHON SOURCE LINES 40-41 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 41-47 .. code-block:: Python asc_car = Beta('asc_car', 0, None, None, 0) b_time_car = Beta('b_time_car', 0, None, None, 0) b_time_train = Beta('b_time_train', 0, None, None, 0) b_cost_car = Beta('b_cost_car', 0, None, None, 0) b_cost_train = Beta('b_cost_train', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 48-50 Definition of the utility functions. We estimate a binary probit model. There are only two alternatives. .. GENERATED FROM PYTHON SOURCE LINES 50-53 .. code-block:: Python v_train = b_time_train * TRAIN_TT_SCALED + b_cost_train * TRAIN_COST_SCALED v_car = asc_car + b_time_car * CAR_TT_SCALED + b_cost_car * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 54-55 Associate choice probability with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 55-60 .. code-block:: Python log_probability_dict = { 1: log(NormalCdf(v_train - v_car)), 3: log(NormalCdf(v_car - v_train)), } .. GENERATED FROM PYTHON SOURCE LINES 61-63 Definition of the model. This is the contribution of each observation to the log likelihood function. .. GENERATED FROM PYTHON SOURCE LINES 63-65 .. code-block:: Python log_probability = Elem(log_probability_dict, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 66-67 Create the Biogeme object .. GENERATED FROM PYTHON SOURCE LINES 67-70 .. code-block:: Python the_biogeme = BIOGEME(database, log_probability) the_biogeme.model_name = 'b23b_binary_probit' .. GENERATED FROM PYTHON SOURCE LINES 71-73 Estimate the posterior distribution of the parameters, or read the results if already available. .. GENERATED FROM PYTHON SOURCE LINES 73-80 .. code-block:: Python yaml_file = Path('saved_results') / f'{the_biogeme.model_name}.yaml' try: summary_results = BayesianResultsSummary.from_yaml_file(filename=yaml_file) except FileNotFoundError: results: BayesianResults = the_biogeme.bayesian_estimation() summary_results = results.to_summary() .. GENERATED FROM PYTHON SOURCE LINES 81-83 .. code-block:: Python print(summary_results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Sample size 2232 Sampler NUTS Number of chains 4 Number of draws per chain 2000 Total number of draws 8000 Acceptance rate target 0.9 Run time 0:00:23.657084 Posterior predictive log-likelihood (sum of log mean p) -903.93 Expected log-likelihood E[log L(Y|θ)] -909.41 Best-draw log-likelihood (posterior upper bound) -906.99 LOO (Leave-One-Out Cross-Validation) -916.38 LOO Standard Error 35.24 Effective number of parameters (p_LOO) 12.46 .. GENERATED FROM PYTHON SOURCE LINES 84-85 Present the parameter estimates in a pandas table. .. GENERATED FROM PYTHON SOURCE LINES 85-90 .. code-block:: Python pandas_results = get_pandas_estimated_parameters( estimation_results=summary_results, ) display(pandas_results) .. rst-class:: sphx-glr-script-out .. code-block:: none Name Value (mean) ... ESS (bulk) ESS (tail) 0 b_time_train -0.653399 ... 4968.635600 4587.750187 1 b_cost_train -0.982377 ... 6737.561798 5607.420819 2 asc_car -0.355007 ... 5638.274853 5066.063417 3 b_time_car -0.186200 ... 6589.288526 5320.973731 4 b_cost_car -0.533072 ... 5907.976659 5191.235350 [5 rows x 12 columns] .. GENERATED FROM PYTHON SOURCE LINES 91-92 Report the variables stored in the Bayesian estimation results. .. GENERATED FROM PYTHON SOURCE LINES 92-93 .. code-block:: Python display(summary_results.report_stored_variables()) .. rst-class:: sphx-glr-script-out .. code-block:: none group variable dims shape 0 constant_data CAR_CO_SCALED [obs] [2232] 1 constant_data CAR_TT_SCALED [obs] [2232] 2 constant_data CHOICE [obs] [2232] 3 constant_data TRAIN_COST_SCALED [obs] [2232] 4 constant_data TRAIN_TT_SCALED [obs] [2232] 5 log_likelihood _choice [chain, draw, obs] [4, 2000, 2232] 6 posterior asc_car [chain, draw] [4, 2000] 7 posterior b_cost_car [chain, draw] [4, 2000] 8 posterior b_cost_train [chain, draw] [4, 2000] 9 posterior b_time_car [chain, draw] [4, 2000] 10 posterior b_time_train [chain, draw] [4, 2000] 11 posterior log_like [chain, draw, obs] [4, 2000, 2232] 12 prior asc_car [chain, draw] [1, 2000] 13 prior b_cost_car [chain, draw] [1, 2000] 14 prior b_cost_train [chain, draw] [1, 2000] 15 prior b_time_car [chain, draw] [1, 2000] 16 prior b_time_train [chain, draw] [1, 2000] 17 prior log_like [chain, draw, obs] [1, 2000, 2232] 18 sample_stats acceptance_rate [chain, draw] [4, 2000] 19 sample_stats diverging [chain, draw] [4, 2000] 20 sample_stats energy [chain, draw] [4, 2000] 21 sample_stats lp [chain, draw] [4, 2000] 22 sample_stats n_steps [chain, draw] [4, 2000] 23 sample_stats step_size [chain, draw] [4, 2000] 24 sample_stats tree_depth [chain, draw] [4, 2000] .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.029 seconds) .. _sphx_glr_download_auto_examples_bayesian_swissmetro_plot_b23b_binary_probit.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b23b_binary_probit.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b23b_binary_probit.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b23b_binary_probit.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_