jpt.distributions.multivariate
==============================

.. py:module:: jpt.distributions.multivariate

.. autoapi-nested-parse::

   © Copyright 2021, Mareike Picklum, Daniel Nyga.



Classes
-------

.. autoapisummary::

   jpt.distributions.multivariate.MultiVariateGaussian


Module Contents
---------------

.. py:class:: MultiVariateGaussian(mean=None, cov=None, data=None, ignore=-6000000)

   Bases: :py:obj:`jpt.distributions.univariate.Gaussian`


   Extension of :class:`dnutils.stats.Gaussian`

   A Multivariate Gaussian distribution that can be incrementally updated with new samples
           


   .. py:attribute:: ignore
      :value: -6000000



   .. py:method:: cdf(intervals)

      Computes the CDF for a multivariate normal distribution.

      :param intervals: the boundaries of the integral
      :type intervals: list of matcalo.utils.utils.Interval



   .. py:method:: pdf()


   .. py:property:: mvg

      Computes the multivariate Gaussian distribution.
              



   .. py:property:: dim

      Returns the dimension of the distribution.
              



   .. py:property:: cov_

      Returns the covariance matrix for prettyprinting (precision .2).
              



   .. py:property:: mean_

      Returns the mean vector for prettyprinting (precision .2).
              



   .. py:method:: conditional(evidence)

      Returns a distribution conditioning on the variables in ``evidence`` following the calculations described
      in `Conditional distributions <https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Conditional_distributions>`_,
      i.e., after determining the partitions of :math:`\mu`, i.e. :math:`\mu_{1}` and :math:`\mu_{2}` as well as
      the partitions of :math:`\Sigma`, i.e. :math:`\Sigma_{11}, \Sigma_{12}, \Sigma_{21} \text{ and } \Sigma_{22}`, we
      calculate the multivariate normal :math:`N(\overline\mu,\overline\Sigma)` using

      .. math::
          \overline\mu = \mu_{1} + \Sigma_{12}\Sigma_{22}^{-1}(a-\mu_{2})
          :label: mu

      .. math::
          \overline\Sigma = \Sigma_{11} + \Sigma_{12}\Sigma_{22}^{-1}\Sigma_{21}
          :label: sigma

      :param evidence: the variables the returned distribution conditions on (mapping indices to values or Intervals of values)
      :type evidence: dict



   .. py:method:: plot(engine=None, **kwargs) -> Any

      Plots the distribution using the given engine.

      :param engine:  Can be either one of
          ``["plotly", "matplotlib"]``, or an instance of a
          rendering engine subclassing
          ``DistributionRendering``.
      :param kwargs:  The keyword arguments to pass to the
          engine as defined in the
          ``.plot_multivariate()`` function of
          ``DistributionRendering`` or its respective
          subclass defined by ``engine``.
      :return:        the figure object of the plotting engine