.. _sphx_glr_auto_examples_bayesian_swissmetro:

Biogeme examples for Bayesian inference with the Swissmetro data
****************************************************************

You find here several examples of models that illustrate how to specify models to be estimated with Biogeme using
Bayesian inference. To the extent possible, we have used the same examples illustrating the maximum
likelihood estimation. The names of the files should correspond too.




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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Calculation of the individual level parameters for the model defined in plot_b05_normal_mixture.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b19_individual_level_parameters_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b19_individual_level_parameters`

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      <div class="sphx-glr-thumbnail-title">19. Calculation of individual level parameters</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of an ordinal logit model.  This is just to illustrate the syntax, as the data are not ordered.  But the example assume, for the sake of it, that the alternatives are ordered as 1-&gt;2-&gt;3">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b18a_ordinal_logit_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b18a_ordinal_logit`

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      <div class="sphx-glr-thumbnail-title">18a. Ordinal logit model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of an ordinal probit model.  This is just to illustrate the syntax, as the data are not ordered.  But the example assume, for the sake of it, that the alternatives are ordered as 1-&gt;2-&gt;3">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b18b_ordinal_probit_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b18b_ordinal_probit`

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      <div class="sphx-glr-thumbnail-title">18. Ordinal probit model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Example of the out-of-sample validation of a logit model in a Bayesian estimation context.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b04_validation_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b04_validation`

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      <div class="sphx-glr-thumbnail-title">4. Out-of-sample validation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a binary logit model. Two alternatives: Train and Car.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b23a_binary_logit_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b23a_binary_logit`

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      <div class="sphx-glr-thumbnail-title">23a. Binary logit model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="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.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b23b_binary_probit_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b23b_binary_probit`

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      <div class="sphx-glr-thumbnail-title">23b. Binary probit model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the Bayesian estimation of a logit model using Biogeme and the Swissmetro stated-preference dataset.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b01a_logit_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b01a_logit`

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      <div class="sphx-glr-thumbnail-title">1a. Estimation of a logit model (Bayesian)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Example of a uniform mixture of logit models, using Bayesian inference.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b06_unif_mixture_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b06_unif_mixture`

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      <div class="sphx-glr-thumbnail-title">6. Mixture of logit models: uniform distribution</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Example of simulation with a logit model">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b01c_logit_simul_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b01c_logit_simul`

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      <div class="sphx-glr-thumbnail-title">1c. Simulation of a logit model (traditional and Bayesian)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Although normalizing the scale to 1 is a common practice in random utility models, it is sometimes preferable to normalize another parameter. For instance, normalizing the cost coefficient to -1 sets the units of the utility function as currency units (CHF here), and the estimated coefficients are easily interpreted as willingness to pay. In that case, the scale must be estimated.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b03_scale_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b03_scale`

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      <div class="sphx-glr-thumbnail-title">3. Moneymetric and heteroscedastic specification</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a mixture of logit models. The mixing distribution is distributed as a log normal.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b17_lognormal_mixture_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b17_lognormal_mixture`

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      <div class="sphx-glr-thumbnail-title">17. Mixture with lognormal distribution</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a logit model, with a Box-Cox transform of variables.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b08_boxcox_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b08_boxcox`

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      <div class="sphx-glr-thumbnail-title">8. Box-Cox transforms</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Example of a normal mixture of logit models, using Bayesian inference.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b05_normal_mixture_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b05_normal_mixture`

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      <div class="sphx-glr-thumbnail-title">5. Mixture of logit models: normal distribution</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a nested logit model where the normalization is done at the  bottom level.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b10_nested_bottom_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b10_nested_bottom`

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      <div class="sphx-glr-thumbnail-title">10. Nested logit model normalized from bottom</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a discrete mixture of logit (or latent class model).">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b07_discrete_mixture_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b07_discrete_mixture`

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      <div class="sphx-glr-thumbnail-title">7. Latent class model</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a nested logit model.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b09_nested_thumb.png
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  :doc:`/auto_examples/bayesian_swissmetro/plot_b09_nested`

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      <div class="sphx-glr-thumbnail-title">9. Nested logit model</div>
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    <div class="sphx-glr-thumbcontainer" tooltip=" Example of a logit model with a weighted sample">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b02_weight_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b02_weight`

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      <div class="sphx-glr-thumbnail-title">2. Logit and sample with weights (Bayesian)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip=" Bayesian estimation of a mixture of logit models.  The mixing distribution is specified by the user. Here, a triangular  distribution.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b25_triangular_mixture_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b25_triangular_mixture`

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      <div class="sphx-glr-thumbnail-title">25. Triangular mixture of logit</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example estimates the same Bayesian logit model as in Example 1a, but illustrates how to specify custom prior distributions for the model parameters.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b01b_logit_thumb.png
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  :doc:`/auto_examples/bayesian_swissmetro/plot_b01b_logit`

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      <div class="sphx-glr-thumbnail-title">1b. Estimation of a logit model with custom priors (Bayesian)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a mixture of logit models. The datafile is organized as panel data. Note that, with Bayesian estimation, there is no need to calculate a Monte-Carlo integration.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b12_panel_thumb.png
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  :doc:`/auto_examples/bayesian_swissmetro/plot_b12_panel`

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      <div class="sphx-glr-thumbnail-title">12. Mixture of logit with panel data</div>
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    <div class="sphx-glr-thumbcontainer" tooltip=" Bayesian estimation of a mixture of logit models.  The mixing distribution is user-defined (triangular, here).  The datafile is organized as panel data.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b26triangular_panel_mixture_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b26triangular_panel_mixture`

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      <div class="sphx-glr-thumbnail-title">26. Triangular mixture with panel data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip=" Bayesian estimation of a cross-nested logit model with two nests:">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b11_cnl_thumb.png
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  :doc:`/auto_examples/bayesian_swissmetro/plot_b11_cnl`

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      <div class="sphx-glr-thumbnail-title">11. Cross-nested logit</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a discrete mixture of logit models, also called latent class model.  The datafile is organized as panel data.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b15_panel_discrete_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b15_panel_discrete`

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      <div class="sphx-glr-thumbnail-title">15. Discrete mixture with panel data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian estimation of a discrete mixture of logit models, also called latent class model. The class membership model includes socio-economic variables. The datafile is organized as panel data.">

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  .. image:: /auto_examples/bayesian_swissmetro/images/thumb/sphx_glr_plot_b16_panel_discrete_socio_eco_thumb.png
    :alt:

  :doc:`/auto_examples/bayesian_swissmetro/plot_b16_panel_discrete_socio_eco`

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      <div class="sphx-glr-thumbnail-title">16. Latent class model with panel data</div>
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    </div>


.. toctree::
   :hidden:

   /auto_examples/bayesian_swissmetro/plot_b19_individual_level_parameters
   /auto_examples/bayesian_swissmetro/plot_b18a_ordinal_logit
   /auto_examples/bayesian_swissmetro/plot_b18b_ordinal_probit
   /auto_examples/bayesian_swissmetro/plot_b04_validation
   /auto_examples/bayesian_swissmetro/plot_b23a_binary_logit
   /auto_examples/bayesian_swissmetro/plot_b23b_binary_probit
   /auto_examples/bayesian_swissmetro/plot_b01a_logit
   /auto_examples/bayesian_swissmetro/plot_b06_unif_mixture
   /auto_examples/bayesian_swissmetro/plot_b01c_logit_simul
   /auto_examples/bayesian_swissmetro/plot_b03_scale
   /auto_examples/bayesian_swissmetro/plot_b17_lognormal_mixture
   /auto_examples/bayesian_swissmetro/plot_b08_boxcox
   /auto_examples/bayesian_swissmetro/plot_b05_normal_mixture
   /auto_examples/bayesian_swissmetro/plot_b10_nested_bottom
   /auto_examples/bayesian_swissmetro/plot_b07_discrete_mixture
   /auto_examples/bayesian_swissmetro/plot_b09_nested
   /auto_examples/bayesian_swissmetro/plot_b02_weight
   /auto_examples/bayesian_swissmetro/plot_b25_triangular_mixture
   /auto_examples/bayesian_swissmetro/plot_b01b_logit
   /auto_examples/bayesian_swissmetro/plot_b12_panel
   /auto_examples/bayesian_swissmetro/plot_b26triangular_panel_mixture
   /auto_examples/bayesian_swissmetro/plot_b11_cnl
   /auto_examples/bayesian_swissmetro/plot_b15_panel_discrete
   /auto_examples/bayesian_swissmetro/plot_b16_panel_discrete_socio_eco