:orphan:

Maximum Likelihood Estimation Examples
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

These notebooks illustrate the use of the Inference Model alternatives to create a model for inference, and the MLE class to perform maximum likelihood estimation of the parameters of that model. Recall that a maximum likelihood estimate is simply the parameter vector that maximizes the likelihood:

.. math:: \theta_{ML} = argmax_{\theta} \quad p(data \vert \theta)



.. raw:: html

    <div class="sphx-glr-thumbnails">


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Here a model is defined that is of the form">

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  .. image:: /auto_examples/inference/mle/images/thumb/sphx_glr_regression_model_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_inference_mle_regression_model.py`

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      <div class="sphx-glr-thumbnail-title">Regression model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In the following we learn the mean and covariance of a univariate gaussian distribution from da...">

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  .. image:: /auto_examples/inference/mle/images/thumb/sphx_glr_plot_learn_distribution_model_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_inference_mle_plot_learn_distribution_model.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Simple probability distribution model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Here we define a bivariate probability model, with a dependence structure defined using a gumbe...">

.. only:: html

  .. image:: /auto_examples/inference/mle/images/thumb/sphx_glr_plot_complex_probability_model_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_inference_mle_plot_complex_probability_model.py`

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      <div class="sphx-glr-thumbnail-title">Complex probability distribution model</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /auto_examples/inference/mle/regression_model
   /auto_examples/inference/mle/plot_learn_distribution_model
   /auto_examples/inference/mle/plot_complex_probability_model


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download all examples in Python source code: mle_python.zip </auto_examples/inference/mle/mle_python.zip>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download all examples in Jupyter notebooks: mle_jupyter.zip </auto_examples/inference/mle/mle_jupyter.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_