.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/bayesian_swissmetro/plot_b02_weight.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_b02_weight.py: 2. Logit and sample with weights (Bayesian) =========================================== Example of a logit model with a weighted sample Michel Bierlaire, EPFL Thu Oct 30 2025, 10:15:17 .. GENERATED FROM PYTHON SOURCE LINES 11-19 .. code-block:: Python from IPython.core.display_functions import display from biogeme.bayesian_estimation import BayesianResults, get_pandas_estimated_parameters from biogeme.biogeme import BIOGEME from biogeme.expressions import Beta from biogeme.models import loglogit .. GENERATED FROM PYTHON SOURCE LINES 20-21 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 21-36 .. code-block:: Python from swissmetro_data import ( CAR_AV_SP, CAR_CO_SCALED, CAR_TT_SCALED, CHOICE, GROUP, SM_AV, SM_COST_SCALED, SM_TT_SCALED, TRAIN_AV_SP, TRAIN_COST_SCALED, TRAIN_TT_SCALED, database, ) .. GENERATED FROM PYTHON SOURCE LINES 37-39 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 39-45 .. code-block:: Python asc_car = Beta('asc_car', 0, None, None, 0) asc_train = Beta('asc_train', 0, None, None, 0) asc_sm = Beta('asc_sm', 0, None, None, 1) b_time = Beta('b_time', 0, None, None, 0) b_cost = Beta('b_cost', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 46-48 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 48-52 .. code-block:: Python v_train = asc_train + b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED v_swissmetro = asc_sm + b_time * SM_TT_SCALED + b_cost * SM_COST_SCALED v_car = asc_car + b_time * CAR_TT_SCALED + b_cost * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 53-55 Associate utility functions with the numbering of alternatives. .. GENERATED FROM PYTHON SOURCE LINES 55-57 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 58-60 Associate the availability conditions with the alternatives. .. GENERATED FROM PYTHON SOURCE LINES 60-62 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 63-67 Definition of the model. This is the contribution of each observation to the log likelihood function. .. GENERATED FROM PYTHON SOURCE LINES 67-69 .. code-block:: Python logprob = loglogit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 70-71 Definition of the weight. .. GENERATED FROM PYTHON SOURCE LINES 71-76 .. code-block:: Python WEIGHT_GROUP_2 = 8.890991e-01 WEIGHT_GROUP_3 = 1.2 weight = WEIGHT_GROUP_2 * (GROUP == 2) + WEIGHT_GROUP_3 * (GROUP == 3) .. GENERATED FROM PYTHON SOURCE LINES 77-78 These notes will be included as such in the report file. .. GENERATED FROM PYTHON SOURCE LINES 78-85 .. code-block:: Python USER_NOTES = ( 'Example of a logit model with three alternatives: ' 'Train, Car and Swissmetro.' ' Weighted Exogenous Sample Maximum Likelihood estimator (WESML)' ) .. GENERATED FROM PYTHON SOURCE LINES 86-90 Create the Biogeme object. It is possible to control the generation of the HTML and the yaml files. Note that these parameters can also be modified in the .TOML configuration file. .. GENERATED FROM PYTHON SOURCE LINES 90-113 .. code-block:: Python formulas = {'log_like': logprob, 'weight': weight} the_biogeme = BIOGEME( database, formulas, mcmc_sampling_strategy='pymc', user_notes=USER_NOTES, generate_html=True, generate_yaml=False, ) the_biogeme.model_name = 'b02_weight' ## %% # Estimate the parameters. try: results = BayesianResults.from_netcdf( filename=f'saved_results/{the_biogeme.model_name}.nc' ) except FileNotFoundError: results = the_biogeme.bayesian_estimation() ## %% print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none load finished in 4343 ms (4.34 s) posterior_predictive_loglike finished in 250 ms expected_log_likelihood finished in 12 ms best_draw_log_likelihood finished in 11 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 643 ms waic finished in 643 ms loo_res finished in 7607 ms (7.61 s) loo finished in 7607 ms (7.61 s) Sample size 6768 Sampler NUTS Number of chains 4 Number of draws per chain 2000 Total number of draws 8000 Acceptance rate target 0.9 Run time 0:01:08.123196 Posterior predictive log-likelihood (sum of log mean p) -5667.46 Expected log-likelihood E[log L(Y|θ)] -5671.10 Best-draw log-likelihood (posterior upper bound) -5669.09 WAIC (Widely Applicable Information Criterion) -5674.75 WAIC Standard Error 63.97 Effective number of parameters (p_WAIC) 7.29 LOO (Leave-One-Out Cross-Validation) -5674.75 LOO Standard Error 63.97 Effective number of parameters (p_LOO) 7.30 .. GENERATED FROM PYTHON SOURCE LINES 114-115 Get the results in a pandas table .. GENERATED FROM PYTHON SOURCE LINES 115-117 .. code-block:: Python pandas_results = get_pandas_estimated_parameters(estimation_results=results) display(pandas_results) .. rst-class:: sphx-glr-script-out .. code-block:: none Name Value (mean) Value (median) ... R hat ESS (bulk) ESS (tail) 0 asc_train -0.795184 -0.794658 ... 1.000254 3965.997402 4158.713468 1 b_time -1.347826 -1.347359 ... 1.000156 3807.078668 4421.493905 2 b_cost -1.141865 -1.141583 ... 1.000357 5604.456149 5152.311844 3 asc_car -0.090900 -0.091456 ... 0.999939 4252.924344 4418.206056 [4 rows x 12 columns] .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 37.246 seconds) .. _sphx_glr_download_auto_examples_bayesian_swissmetro_plot_b02_weight.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b02_weight.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b02_weight.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b02_weight.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_