.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/bayesian_swissmetro/plot_b25_triangular_mixture.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_b25_triangular_mixture.py: 25. Triangular mixture of logit =============================== Bayesian estimation of a mixture of logit models. The mixing distribution is specified by the user. Here, a triangular distribution. Michel Bierlaire, EPFL Tue Nov 18 2025, 12:35:26 .. GENERATED FROM PYTHON SOURCE LINES 14-26 .. code-block:: Python from functools import partial import biogeme.biogeme_logging as blog import pymc as pm from IPython.core.display_functions import display from biogeme.bayesian_estimation import BayesianResults, get_pandas_estimated_parameters from biogeme.biogeme import BIOGEME from biogeme.draws import PyMcDistributionFactory from biogeme.expressions import Beta, DistributedParameter, Draws from biogeme.models import loglogit .. GENERATED FROM PYTHON SOURCE LINES 27-28 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 28-45 .. code-block:: Python from swissmetro_data import ( CAR_AV_SP, CAR_CO_SCALED, CAR_TT_SCALED, CHOICE, SM_AV, SM_COST_SCALED, SM_TT_SCALED, TRAIN_AV_SP, TRAIN_COST_SCALED, TRAIN_TT_SCALED, database, ) logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b25_triangular_mixture.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b25_triangular_mixture.py .. GENERATED FROM PYTHON SOURCE LINES 46-47 The scale parameters must stay away from zero. We define a small but positive lower bound .. GENERATED FROM PYTHON SOURCE LINES 47-49 .. code-block:: Python POSITIVE_LOWER_BOUND = 1.0e-5 .. GENERATED FROM PYTHON SOURCE LINES 50-51 Parameters to be estimated. .. GENERATED FROM PYTHON SOURCE LINES 51-56 .. 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_cost = Beta('b_cost', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 57-63 Define a random parameter with a triangular distribution. The triangular distribution is not directly available from Biogeme. It has to be generated by a function provided by the user, based on PyMC available distributions. See the PyMC documentation: https://www.pymc.io/projects/docs/en/stable/api/distributions.html .. GENERATED FROM PYTHON SOURCE LINES 65-66 Mean of the distribution. .. GENERATED FROM PYTHON SOURCE LINES 66-68 .. code-block:: Python b_time = Beta('b_time', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 69-71 Scale of the distribution. It is advised not to use 0 as starting value for the following parameter. .. GENERATED FROM PYTHON SOURCE LINES 71-73 .. code-block:: Python b_time_s = Beta('b_time_s', 1, POSITIVE_LOWER_BOUND, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 74-76 Distribution of the draws. The user must define a function that takes a `str` as argument (corresponding to the name of the random variable) and return a `pymc.distributions.Distribution` .. GENERATED FROM PYTHON SOURCE LINES 76-83 .. code-block:: Python triangular_factory: PyMcDistributionFactory = partial( pm.Triangular, lower=-1.0, c=0.0, upper=1.0, ) .. GENERATED FROM PYTHON SOURCE LINES 84-85 Associate the function with a name .. GENERATED FROM PYTHON SOURCE LINES 85-88 .. code-block:: Python DISTRIBUTIONS = {'TRIANGULAR': triangular_factory} .. GENERATED FROM PYTHON SOURCE LINES 89-91 Define a random parameter with a triangular distribution, designed to be used for Monte-Carlo simulation. .. GENERATED FROM PYTHON SOURCE LINES 91-97 .. code-block:: Python b_time_rnd = DistributedParameter( 'b_time_rnd', b_time + b_time_s * Draws('b_time_eps', 'TRIANGULAR', dict_of_distributions=DISTRIBUTIONS), ) .. GENERATED FROM PYTHON SOURCE LINES 98-99 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 99-103 .. code-block:: Python v_train = asc_train + b_time_rnd * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED v_swissmetro = asc_sm + b_time_rnd * SM_TT_SCALED + b_cost * SM_COST_SCALED v_car = asc_car + b_time_rnd * CAR_TT_SCALED + b_cost * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 104-105 Associate utility functions with the numbering of alternatives .. GENERATED FROM PYTHON SOURCE LINES 105-107 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 108-109 Associate the availability conditions with the alternatives .. GENERATED FROM PYTHON SOURCE LINES 109-111 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 112-113 Conditional to b_time_rnd, we have a logit model (called the kernel) .. GENERATED FROM PYTHON SOURCE LINES 113-115 .. code-block:: Python conditional_log_probability = loglogit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 116-117 Create the Biogeme object. .. GENERATED FROM PYTHON SOURCE LINES 117-123 .. code-block:: Python the_biogeme = BIOGEME( database, conditional_log_probability, ) the_biogeme.model_name = 'b25_triangular' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 124-125 Estimate the parameters. .. GENERATED FROM PYTHON SOURCE LINES 125-132 .. code-block:: Python try: bayesian_results = BayesianResults.from_netcdf( filename=f'saved_results/{the_biogeme.model_name}.nc' ) except FileNotFoundError: bayesian_results = the_biogeme.bayesian_estimation() .. rst-class:: sphx-glr-script-out .. code-block:: none Loaded NetCDF file size: 1.8 GB load finished in 9624 ms (9.62 s) .. GENERATED FROM PYTHON SOURCE LINES 133-134 Get the results in a pandas table .. GENERATED FROM PYTHON SOURCE LINES 134-138 .. code-block:: Python pandas_results = get_pandas_estimated_parameters( estimation_results=bayesian_results, ) display(pandas_results) .. rst-class:: sphx-glr-script-out .. code-block:: none Diagnostics computation took 75.8 seconds (cached). Name Value (mean) Value (median) ... R hat ESS (bulk) ESS (tail) 0 asc_train -0.393645 -0.393730 ... 1.000042 6129.449492 6131.566807 1 b_time -2.282075 -2.280289 ... 1.001155 1696.593924 3441.429131 2 b_cost -1.284068 -1.282969 ... 1.000366 7710.204636 6241.910672 3 asc_car 0.141109 0.140517 ... 1.000087 3587.630483 5766.455070 4 b_time_s 4.013062 4.006510 ... 1.002735 1169.172079 2912.845359 [5 rows x 12 columns] .. rst-class:: sphx-glr-timing **Total running time of the script:** (1 minutes 25.536 seconds) .. _sphx_glr_download_auto_examples_bayesian_swissmetro_plot_b25_triangular_mixture.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b25_triangular_mixture.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b25_triangular_mixture.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b25_triangular_mixture.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_