compute incremental weights for gaussian filters.

matlab/particle/gaussian_densities.m

+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,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) 2009-2010 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/>.
+
+% 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,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 ;