pastas.objective_functions.GaussianLikelihood
=============================================

.. toctree::
   :hidden:

   /api/pastas/objective_functions/GaussianLikelihood.get_init_parameters
   /api/pastas/objective_functions/GaussianLikelihood.compute

.. py:class:: pastas.objective_functions.GaussianLikelihood

   
   Gaussian likelihood function for homoscedastic, uncorrelated errors.

   .. rubric:: Notes

   The Gaussian log-likelihood function :cite:p:`smith_modeling_2015` is defined as:

   .. math::

       \log(L) = -\frac{N}{2}\log(2\pi\sigma^2) -
       \frac{\sum_{t=1}^N \epsilon_t^2}{2\sigma^2}

   where :math:`N` is the number of observations, :math:`\sigma^2` is the variance of
   the residuals, and :math:`\epsilon_t` is the residual at time :math:`t`. The
   parameter :math:`\sigma^2` needs to be estimated.

   The current implementation is valid for equidistant time series only.















   ..
       !! processed by numpydoc !!
Methods
-------

.. autoapisummary::

   pastas.objective_functions.GaussianLikelihood.get_init_parameters
   pastas.objective_functions.GaussianLikelihood.compute