pastas.solver.likelihood.GaussianLikelihood
===========================================

.. toctree::
   :hidden:

   /api/pastas/solver/likelihood/GaussianLikelihood.get_init_parameters
   /api/pastas/solver/likelihood/GaussianLikelihood.compute

.. py:class:: pastas.solver.likelihood.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 !!

   .. py:property:: nparam
      :type: int


      
      Number of parameters in the log-likelihood function.
















      ..
          !! processed by numpydoc !!

Methods
-------

.. autoapisummary::

   pastas.solver.likelihood.GaussianLikelihood.get_init_parameters
   pastas.solver.likelihood.GaussianLikelihood.compute