.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/inference/mle/regression_model.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_inference_mle_regression_model.py>`
        to download the full example code or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_inference_mle_regression_model.py:


Regression model
==============================================

Here a model is defined that is of the form

.. math:: y=f(θ) + \epsilon

where f consists in running :class:`.RunModel`. In particular, here
:math:`f(θ)=θ_{0} x + θ_{1} x^{2}` is a
regression model.

.. GENERATED FROM PYTHON SOURCE LINES 18-19

Initially we have to import the necessary modules.

.. GENERATED FROM PYTHON SOURCE LINES 22-32

.. code-block:: default

    import shutil

    import numpy as np

    from UQpy import PythonModel
    from UQpy.inference import ComputationalModel, MLE
    from UQpy.distributions import Normal
    from UQpy.inference import MinimizeOptimizer
    from UQpy.run_model.RunModel import RunModel


.. GENERATED FROM PYTHON SOURCE LINES 33-34

First we generate synthetic data, and add some noise to it.

.. GENERATED FROM PYTHON SOURCE LINES 37-56

.. code-block:: default


    # Generate data

    param_true = np.array([1.0, 2.0]).reshape((1, -1))
    print('Shape of true parameter vector: {}'.format(param_true.shape))

    model = PythonModel(model_script='local_pfn_models.py', model_object_name='model_quadratic', delete_files=True,
                        var_names=['theta_0', 'theta_1'])
    h_func = RunModel(model=model)
    h_func.run(samples=param_true)

    # Add noise
    error_covariance = 1.
    data_clean = np.array(h_func.qoi_list[0])
    noise = Normal(loc=0., scale=np.sqrt(error_covariance)).rvs(nsamples=50).reshape((50,))
    data_3 = data_clean + noise
    print('Shape of data: {}'.format(data_3.shape))



.. GENERATED FROM PYTHON SOURCE LINES 57-59

Then we create an instance of the Model class, using model_type='python', and we perform maximum likelihood estimation
of the two parameters.

.. GENERATED FROM PYTHON SOURCE LINES 62-69

.. code-block:: default


    candidate_model = ComputationalModel(n_parameters=2, runmodel_object=h_func, error_covariance=error_covariance)

    optimizer = MinimizeOptimizer(method='nelder-mead')
    ml_estimator = MLE(inference_model=candidate_model, data=data_3, n_optimizations=1)
    print('fitted parameters: theta_0={0:.3f} (true=1.), and theta_1={1:.3f} (true=2.)'.format(
        ml_estimator.mle[0], ml_estimator.mle[1]))


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_inference_mle_regression_model.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/inference/mle/regression_model.ipynb
        :alt: Launch binder
        :width: 150 px



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

      :download:`Download Python source code: regression_model.py <regression_model.py>`

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

      :download:`Download Jupyter notebook: regression_model.ipynb <regression_model.ipynb>`


.. only:: html

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

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