function IncrementalWeights = gaussian_densities(obs,mut_t,sqr_Pss_t_t,st_t_1,sqr_Pss_t_t_1,particles,H,normconst,weigths1,weigths2,ReducedForm,ThreadsOptions,options_, M_)
% IncrementalWeights = gaussian_densities(obs,mut_t,sqr_Pss_t_t,st_t_1,sqr_Pss_t_t_1,particles,H,normconst,weigths1,weigths2,ReducedForm,ThreadsOptions,options_, M_)
% Elements to calculate the importance sampling ratio
%
% INPUTS
%    reduced_form_model     [structure] Matlab's structure describing the reduced form model.
%                                       reduced_form_model.measurement.H   [double]   (pp x pp) variance matrix of measurement errors.
%                                       reduced_form_model.state.Q         [double]   (qq x qq) variance matrix of state errors.
%                                       reduced_form_model.state.dr        [structure] output of resol.m.
%    Y                      [double]    pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
%    start                  [integer]   scalar, likelihood evaluation starts at 'start'.
%    smolyak_accuracy       [integer]   scalar.
%
% OUTPUTS
%    LIK        [double]    scalar, likelihood
%    lik        [double]    vector, density of observations in each period.
%
% REFERENCES
%
% NOTES
%   The vector "lik" is used to evaluate the jacobian of the likelihood.

% Copyright © 2009-2023 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare.  If not, see <https://www.gnu.org/licenses/>.

% proposal density
proposal = probability2(mut_t, sqr_Pss_t_t, particles);

% prior density
prior = probability2(st_t_1, sqr_Pss_t_t_1, particles);

% likelihood
yt_t_1_i = measurement_equations(particles, ReducedForm, ThreadsOptions, options_, M_);
likelihood = probability2(obs, sqrt(H), yt_t_1_i);

IncrementalWeights = likelihood.*prior./proposal;
