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function IncrementalWeights = gaussian_mixture_densities(obs,StateMuPrior,StateSqrtPPrior,StateWeightsPrior,...
StateMuPost,StateSqrtPPost,StateWeightsPost,...
StateParticles,H,normconst,weigths1,weigths2,ReducedForm,DynareOptions)
%
% 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 (C) 2009-2012 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 <http://www.gnu.org/licenses/>.
% Compute the density of particles under the prior distribution
[ras,ras,prior] = probability(StateMuPrior,StateSqrtPPrior,StateWeightsPrior,StateParticles) ;
prior = prior' ;
% Compute the density of particles under the proposal distribution
[ras,ras,proposal] = probability(StateMuPost,StateSqrtPPost,StateWeightsPost,StateParticles) ;
proposal = proposal' ;
% Compute the density of the current observation conditionally to each particle
yt_t_1_i = measurement_equations(StateParticles,ReducedForm,DynareOptions) ;
eta_t_i = bsxfun(@minus,obs,yt_t_1_i)' ;
yt_t_1 = sum(yt_t_1_i*weigths1,2) ;
tmp = bsxfun(@minus,yt_t_1_i,yt_t_1) ;
Pyy = bsxfun(@times,weigths2',tmp)*tmp' + H ;
sqr_det = sqrt(det(Pyy)) ;
foo = (eta_t_i/Pyy).*eta_t_i ;
likelihood = exp(-0.5*sum(foo,2))/(normconst*sqr_det) + 1e-99 ;
IncrementalWeights = likelihood.*prior./proposal ;
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