Allow k order approximation in Gaussian Mixture Filter (gmf).
Ref. dynare#1673remove-submodule^2
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2498000719
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2250fc39d1
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@ -1,7 +1,7 @@
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function IncrementalWeights = gaussian_mixture_densities(obs,StateMuPrior,StateSqrtPPrior,StateWeightsPrior,...
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StateMuPost,StateSqrtPPost,StateWeightsPost,...
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StateParticles,H,normconst,weigths1,weigths2,ReducedForm,ThreadsOptions)
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%
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function IncrementalWeights = gaussian_mixture_densities(obs, StateMuPrior, StateSqrtPPrior, StateWeightsPrior, ...
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StateMuPost, StateSqrtPPost, StateWeightsPost, StateParticles, H, ...
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ReducedForm, ThreadsOptions, DynareOptions, Model)
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% Elements to calculate the importance sampling ratio
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%
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% INPUTS
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@ -21,7 +21,8 @@ function IncrementalWeights = gaussian_mixture_densities(obs,StateMuPrior,State
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%
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% NOTES
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% The vector "lik" is used to evaluate the jacobian of the likelihood.
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% Copyright (C) 2009-2017 Dynare Team
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% Copyright (C) 2009-2019 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -39,19 +40,16 @@ function IncrementalWeights = gaussian_mixture_densities(obs,StateMuPrior,State
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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% Compute the density of particles under the prior distribution
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[ras,ras,prior] = probability(StateMuPrior,StateSqrtPPrior,StateWeightsPrior,StateParticles) ;
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prior = prior' ;
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[~, ~, prior] = probability(StateMuPrior, StateSqrtPPrior, StateWeightsPrior, StateParticles);
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prior = prior';
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% Compute the density of particles under the proposal distribution
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[ras,ras,proposal] = probability(StateMuPost,StateSqrtPPost,StateWeightsPost,StateParticles) ;
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proposal = proposal' ;
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[~, ~, proposal] = probability(StateMuPost, StateSqrtPPost, StateWeightsPost, StateParticles);
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proposal = proposal';
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% Compute the density of the current observation conditionally to each particle
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yt_t_1_i = measurement_equations(StateParticles,ReducedForm,ThreadsOptions) ;
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%eta_t_i = bsxfun(@minus,obs,yt_t_1_i)' ;
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%yt_t_1 = sum(yt_t_1_i*weigths1,2) ;
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%tmp = bsxfun(@minus,yt_t_1_i,yt_t_1) ;
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%Pyy = bsxfun(@times,weigths2',tmp)*tmp' + H ;
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%sqr_det = sqrt(det(Pyy)) ;
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%foo = (eta_t_i/Pyy).*eta_t_i ;
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%likelihood = exp(-0.5*sum(foo,2))/(normconst*sqr_det) + 1e-99 ;
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likelihood = probability2(obs,sqrt(H),yt_t_1_i) ;
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IncrementalWeights = likelihood.*prior./proposal ;
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yt_t_1_i = measurement_equations(StateParticles, ReducedForm, ThreadsOptions, DynareOptions, Model);
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% likelihood
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likelihood = probability2(obs, sqrt(H), yt_t_1_i);
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IncrementalWeights = likelihood.*prior./proposal;
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@ -1,4 +1,5 @@
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function [LIK,lik] = gaussian_mixture_filter(ReducedForm,Y,start,ParticleOptions,ThreadsOptions)
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function [LIK, lik] = gaussian_mixture_filter(ReducedForm, Y, start, ParticleOptions, ThreadsOptions, DynareOptions, Model)
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% Evaluates the likelihood of a non-linear model approximating the state
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% variables distributions with gaussian mixtures. Gaussian Mixture allows reproducing
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% a wide variety of generalized distributions (when multimodal for instance).
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@ -52,45 +53,33 @@ function [LIK,lik] = gaussian_mixture_filter(ReducedForm,Y,start,ParticleOptions
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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persistent init_flag mf0 mf1
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persistent nodes weights weights_c I J G number_of_particles
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persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
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% Set default
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if isempty(start)
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start = 1;
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end
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% Set persistent variables.
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if isempty(init_flag)
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mf0 = ReducedForm.mf0;
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mf1 = ReducedForm.mf1;
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sample_size = size(Y,2);
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number_of_state_variables = length(mf0);
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number_of_observed_variables = length(mf1);
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number_of_structural_innovations = length(ReducedForm.Q);
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G = ParticleOptions.mixture_state_variables; % number of GM components in state
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number_of_particles = ParticleOptions.number_of_particles;
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init_flag = 1;
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end
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mf0 = ReducedForm.mf0;
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mf1 = ReducedForm.mf1;
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sample_size = size(Y,2);
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number_of_state_variables = length(mf0);
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number_of_observed_variables = length(mf1);
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number_of_structural_innovations = length(ReducedForm.Q);
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G = ParticleOptions.mixture_state_variables; % number of GM components in state
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number_of_particles = ParticleOptions.number_of_particles;
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% compute gaussian quadrature nodes and weights on states and shocks
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if isempty(nodes)
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if ParticleOptions.distribution_approximation.cubature
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[nodes,weights] = spherical_radial_sigma_points(number_of_state_variables);
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weights_c = weights;
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elseif ParticleOptions.distribution_approximation.unscented
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[nodes,weights,weights_c] = unscented_sigma_points(number_of_state_variables,ParticleOptions);
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else
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if ~ParticleOptions.distribution_approximation.montecarlo
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error('Estimation: This approximation for the proposal is not implemented or unknown!')
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end
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if ParticleOptions.distribution_approximation.cubature
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[nodes, weights] = spherical_radial_sigma_points(number_of_state_variables);
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elseif ParticleOptions.distribution_approximation.unscented
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[nodes, weights] = unscented_sigma_points(number_of_state_variables, ParticleOptions);
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else
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if ~ParticleOptions.distribution_approximation.montecarlo
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error('This approximation for the proposal is unknown!')
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end
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end
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if ParticleOptions.distribution_approximation.montecarlo
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set_dynare_seed('default');
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SampleWeights = 1/number_of_particles ;
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end
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% Get covariance matrices
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@ -105,225 +94,133 @@ end
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Q_lower_triangular_cholesky = reduced_rank_cholesky(Q)';
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% Initialize mixtures
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StateWeights = ones(1,G)/G ;
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StateMu = ReducedForm.StateVectorMean ;
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StateSqrtP = zeros(number_of_state_variables,number_of_state_variables,G) ;
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temp = reduced_rank_cholesky(ReducedForm.StateVectorVariance)' ;
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StateMu = bsxfun(@plus,StateMu,bsxfun(@times,diag(temp),(-(G-1)/2:1:(G-1)/2))/10) ;
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StateWeights = ones(1, G)/G;
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StateMu = ReducedForm.StateVectorMean;
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StateSqrtP = zeros(number_of_state_variables, number_of_state_variables, G);
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temp = reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
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StateMu = bsxfun(@plus, StateMu, bsxfun(@times,diag(temp), (-(G-1)/2:1:(G-1)/2))/10);
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for g=1:G
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StateSqrtP(:,:,g) = temp/sqrt(G) ;
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end
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% if ParticleOptions.mixture_structural_shocks==1
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% StructuralShocksMu = zeros(1,number_of_structural_innovations) ;
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% StructuralShocksWeights = 1 ;
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% else
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% if ParticleOptions.proposal_approximation.cubature
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% [StructuralShocksMu,StructuralShocksWeights] = spherical_radial_sigma_points(number_of_structural_innovations);
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% StructuralShocksWeights = ones(size(StructuralShocksMu,1),1)*StructuralShocksWeights ;
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% elseif ParticleOptions.proposal_approximation.unscented
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% [StructuralShocksMu,StructuralShocksWeights,raf] = unscented_sigma_points(number_of_structural_innovations,ParticleOptions);
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% else
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% if ~ParticleOptions.distribution_approximation.montecarlo
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% error('Estimation: This approximation for the proposal is not implemented or unknown!')
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% end
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% end
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% end
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% I = size(StructuralShocksWeights,1) ;
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% StructuralShocksMu = Q_lower_triangular_cholesky*(StructuralShocksMu') ;
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% StructuralShocksSqrtP = zeros(number_of_structural_innovations,number_of_structural_innovations,I) ;
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% for i=1:I
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% StructuralShocksSqrtP(:,:,i) = Q_lower_triangular_cholesky/sqrt(StructuralShocksWeights(i)) ;
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% end
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%
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% if ParticleOptions.mixture_measurement_shocks==1
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% ObservationShocksMu = zeros(1,number_of_observed_variables) ;
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% ObservationShocksWeights = 1 ;
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% else
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% if ParticleOptions.proposal_approximation.cubature
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% [ObservationShocksMu,ObservationShocksWeights] = spherical_radial_sigma_points(number_of_observed_variables);
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% ObservationShocksWeights = ones(size(ObservationShocksMu,1),1)*ObservationShocksWeights;
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% elseif ParticleOptions.proposal_approximation.unscented
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% [ObservationShocksMu,ObservationShocksWeights,raf] = unscented_sigma_points(number_of_observed_variables,ParticleOptions);
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% else
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% if ~ParticleOptions.distribution_approximation.montecarlo
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% error('Estimation: This approximation for the proposal is not implemented or unknown!')
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% end
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% end
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% end
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% J = size(ObservationShocksWeights,1) ;
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% ObservationShocksMu = H_lower_triangular_cholesky*(ObservationShocksMu') ;
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% ObservationShocksSqrtP = zeros(number_of_observed_variables,number_of_observed_variables,J) ;
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% for j=1:J
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% ObservationShocksSqrtP(:,:,j) = H_lower_triangular_cholesky/sqrt(ObservationShocksWeights(j)) ;
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% end
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if ParticleOptions.mixture_structural_shocks==0
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StructuralShocksMu = zeros(1,number_of_structural_innovations) ;
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StructuralShocksWeights = 1 ;
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I = 1 ;
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StructuralShocksMu = Q_lower_triangular_cholesky*(StructuralShocksMu') ;
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StructuralShocksSqrtP = zeros(number_of_structural_innovations,number_of_structural_innovations,I) ;
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StructuralShocksSqrtP(:,:,1) = Q_lower_triangular_cholesky ;
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if ~ParticleOptions.mixture_structural_shocks
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StructuralShocksMu = zeros(1, number_of_structural_innovations);
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StructuralShocksWeights = 1;
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I = 1;
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StructuralShocksMu = Q_lower_triangular_cholesky*StructuralShocksMu';
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StructuralShocksSqrtP = zeros(number_of_structural_innovations, number_of_structural_innovations, I);
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StructuralShocksSqrtP(:,:,1) = Q_lower_triangular_cholesky;
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elseif ParticleOptions.mixture_structural_shocks==1
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if ParticleOptions.proposal_approximation.cubature
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[StructuralShocksMu,StructuralShocksWeights] = spherical_radial_sigma_points(number_of_structural_innovations);
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StructuralShocksWeights = ones(size(StructuralShocksMu,1),1)*StructuralShocksWeights ;
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[StructuralShocksMu, StructuralShocksWeights] = spherical_radial_sigma_points(number_of_structural_innovations);
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StructuralShocksWeights = ones(size(StructuralShocksMu, 1), 1)*StructuralShocksWeights;
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elseif ParticleOptions.proposal_approximation.unscented
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[StructuralShocksMu,StructuralShocksWeights,raf] = unscented_sigma_points(number_of_structural_innovations,ParticleOptions);
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[StructuralShocksMu, StructuralShocksWeights] = unscented_sigma_points(number_of_structural_innovations, ParticleOptions);
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else
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if ~ParticleOptions.distribution_approximation.montecarlo
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error('Estimation: This approximation for the proposal is not implemented or unknown!')
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error('This approximation for the proposal is unknown!')
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end
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end
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I = size(StructuralShocksWeights,1) ;
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StructuralShocksMu = Q_lower_triangular_cholesky*(StructuralShocksMu') ;
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StructuralShocksSqrtP = zeros(number_of_structural_innovations,number_of_structural_innovations,I) ;
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I = size(StructuralShocksWeights, 1);
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StructuralShocksMu = Q_lower_triangular_cholesky*StructuralShocksMu';
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StructuralShocksSqrtP = zeros(number_of_structural_innovations, number_of_structural_innovations, I);
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for i=1:I
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StructuralShocksSqrtP(:,:,i) = Q_lower_triangular_cholesky ;
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StructuralShocksSqrtP(:,:,i) = Q_lower_triangular_cholesky;
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end
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else
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if ParticleOptions.proposal_approximation.cubature
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[StructuralShocksMu,StructuralShocksWeights] = spherical_radial_sigma_points(number_of_structural_innovations);
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StructuralShocksWeights = ones(size(StructuralShocksMu,1),1)*StructuralShocksWeights ;
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[StructuralShocksMu, StructuralShocksWeights] = spherical_radial_sigma_points(number_of_structural_innovations);
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StructuralShocksWeights = ones(size(StructuralShocksMu, 1), 1)*StructuralShocksWeights ;
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elseif ParticleOptions.proposal_approximation.unscented
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[StructuralShocksMu,StructuralShocksWeights,raf] = unscented_sigma_points(number_of_structural_innovations,ParticleOptions);
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[StructuralShocksMu, StructuralShocksWeights] = unscented_sigma_points(number_of_structural_innovations, ParticleOptions);
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else
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if ~ParticleOptions.distribution_approximation.montecarlo
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error('Estimation: This approximation for the proposal is not implemented or unknown!')
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error('This approximation for the proposal is unknown!')
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end
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end
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I = size(StructuralShocksWeights,1) ;
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StructuralShocksMu = Q_lower_triangular_cholesky*(StructuralShocksMu') ;
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StructuralShocksSqrtP = zeros(number_of_structural_innovations,number_of_structural_innovations,I) ;
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I = size(StructuralShocksWeights, 1);
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StructuralShocksMu = Q_lower_triangular_cholesky*StructuralShocksMu';
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StructuralShocksSqrtP = zeros(number_of_structural_innovations, number_of_structural_innovations, I);
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for i=1:I
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StructuralShocksSqrtP(:,:,i) = Q_lower_triangular_cholesky/sqrt(StructuralShocksWeights(i)) ;
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StructuralShocksSqrtP(:,:,i) = Q_lower_triangular_cholesky/sqrt(StructuralShocksWeights(i));
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end
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end
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ObservationShocksMu = zeros(1,number_of_observed_variables) ;
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ObservationShocksWeights = 1 ;
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ObservationShocksWeights = 1;
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J = 1 ;
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ObservationShocksMu = H_lower_triangular_cholesky*(ObservationShocksMu') ;
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ObservationShocksSqrtP = zeros(number_of_observed_variables,number_of_observed_variables,J) ;
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ObservationShocksSqrtP(:,:,1) = H_lower_triangular_cholesky ;
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% if ParticleOptions.mixture_measurement_shocks==0
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% ObservationShocksMu = zeros(1,number_of_observed_variables) ;
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% ObservationShocksWeights = 1 ;
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% J = 1 ;
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% ObservationShocksMu = H_lower_triangular_cholesky*(ObservationShocksMu') ;
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% ObservationShocksSqrtP = zeros(number_of_observed_variables,number_of_observed_variables,J) ;
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% ObservationShocksSqrtP(:,:,1) = H_lower_triangular_cholesky ;
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% elseif ParticleOptions.mixture_measurement_shocks==1
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% if ParticleOptions.proposal_approximation.cubature
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% [ObservationShocksMu,ObservationShocksWeights] = spherical_radial_sigma_points(number_of_observed_variables);
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% ObservationShocksWeights = ones(size(ObservationShocksMu,1),1)*ObservationShocksWeights;
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% elseif ParticleOptions.proposal_approximation.unscented
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% [ObservationShocksMu,ObservationShocksWeights,raf] = unscented_sigma_points(number_of_observed_variables,ParticleOptions);
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% else
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% if ~ParticleOptions.distribution_approximation.montecarlo
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% error('Estimation: This approximation for the proposal is not implemented or unknown!')
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% end
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% end
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% J = size(ObservationShocksWeights,1) ;
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% ObservationShocksMu = H_lower_triangular_cholesky*(ObservationShocksMu') ;
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% ObservationShocksSqrtP = zeros(number_of_observed_variables,number_of_observed_variables,J) ;
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% for j=1:J
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% ObservationShocksSqrtP(:,:,j) = H_lower_triangular_cholesky ;
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% end
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% else
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% if ParticleOptions.proposal_approximation.cubature
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% [ObservationShocksMu,ObservationShocksWeights] = spherical_radial_sigma_points(number_of_observed_variables);
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% ObservationShocksWeights = ones(size(ObservationShocksMu,1),1)*ObservationShocksWeights;
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% elseif ParticleOptions.proposal_approximation.unscented
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% [ObservationShocksMu,ObservationShocksWeights,raf] = unscented_sigma_points(number_of_observed_variables,ParticleOptions);
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% else
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% if ~ParticleOptions.distribution_approximation.montecarlo
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% error('Estimation: This approximation for the proposal is not implemented or unknown!')
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% end
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% end
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% J = size(ObservationShocksWeights,1) ;
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% ObservationShocksMu = H_lower_triangular_cholesky*(ObservationShocksMu') ;
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% ObservationShocksSqrtP = zeros(number_of_observed_variables,number_of_observed_variables,J) ;
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% for j=1:J
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% ObservationShocksSqrtP(:,:,j) = H_lower_triangular_cholesky/sqrt(ObservationShocksWeights(j)) ;
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% end
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% end
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Gprime = G*I;
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Gsecond = G*I*J;
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SampleWeights = ones(Gsecond, 1)/Gsecond;
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Gprime = G*I ;
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Gsecond = G*I*J ;
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SampleWeights = ones(Gsecond,1)/Gsecond ;
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StateWeightsPrior = zeros(1,Gprime);
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StateMuPrior = zeros(number_of_state_variables,Gprime);
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StateSqrtPPrior = zeros(number_of_state_variables, number_of_state_variables, Gprime);
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StateWeightsPrior = zeros(1,Gprime) ;
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StateMuPrior = zeros(number_of_state_variables,Gprime) ;
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StateSqrtPPrior = zeros(number_of_state_variables,number_of_state_variables,Gprime) ;
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StateWeightsPost = zeros(1, Gsecond);
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StateMuPost = zeros(number_of_state_variables, Gsecond);
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StateSqrtPPost = zeros(number_of_state_variables, number_of_state_variables, Gsecond);
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StateWeightsPost = zeros(1,Gsecond) ;
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StateMuPost = zeros(number_of_state_variables,Gsecond) ;
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StateSqrtPPost = zeros(number_of_state_variables,number_of_state_variables,Gsecond) ;
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const_lik = (2*pi)^(.5*number_of_observed_variables);
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const_lik = (2*pi)^(.5*number_of_observed_variables) ;
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lik = NaN(sample_size,1);
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lik = NaN(sample_size, 1);
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LIK = NaN;
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for t=1:sample_size
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% Build the proposal joint quadratures of Gaussian on states, structural
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% shocks and observation shocks based on each combination of mixtures
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for i=1:I
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for j=1:J
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for g=1:G ;
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gprime = g + (i-1)*G ;
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gsecond = gprime + (j-1)*Gprime ;
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[StateMuPrior(:,gprime),StateSqrtPPrior(:,:,gprime),StateWeightsPrior(1,gprime),...
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StateMuPost(:,gsecond),StateSqrtPPost(:,:,gsecond),StateWeightsPost(1,gsecond)] =...
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gaussian_mixture_filter_bank(ReducedForm,Y(:,t),StateMu(:,g),StateSqrtP(:,:,g),StateWeights(g),...
|
||||
StructuralShocksMu(:,i),StructuralShocksSqrtP(:,:,i),StructuralShocksWeights(i),...
|
||||
ObservationShocksMu(:,j),ObservationShocksSqrtP(:,:,j),ObservationShocksWeights(j),...
|
||||
H,H_lower_triangular_cholesky,const_lik,ParticleOptions,ThreadsOptions) ;
|
||||
for g=1:G
|
||||
gprime = g + (i-1)*G;
|
||||
gsecond = gprime + (j-1)*Gprime;
|
||||
[StateMuPrior(:,gprime), StateSqrtPPrior(:,:,gprime), StateWeightsPrior(1,gprime), ...
|
||||
StateMuPost(:,gsecond), StateSqrtPPost(:,:,gsecond), StateWeightsPost(1,gsecond)] = ...
|
||||
gaussian_mixture_filter_bank(ReducedForm,Y(:,t), StateMu(:,g), StateSqrtP(:,:,g), StateWeights(g),...
|
||||
StructuralShocksMu(:,i), StructuralShocksSqrtP(:,:,i), StructuralShocksWeights(i),...
|
||||
ObservationShocksWeights(j), H, H_lower_triangular_cholesky, const_lik, ...
|
||||
ParticleOptions, ThreadsOptions, DynareOptions, Model);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
% Normalize weights
|
||||
StateWeightsPrior = StateWeightsPrior/sum(StateWeightsPrior,2) ;
|
||||
StateWeightsPost = StateWeightsPost/sum(StateWeightsPost,2) ;
|
||||
StateWeightsPrior = StateWeightsPrior/sum(StateWeightsPrior, 2);
|
||||
StateWeightsPost = StateWeightsPost/sum(StateWeightsPost, 2);
|
||||
|
||||
if ParticleOptions.distribution_approximation.cubature || ParticleOptions.distribution_approximation.unscented
|
||||
for i=1:Gsecond
|
||||
StateParticles = bsxfun(@plus,StateMuPost(:,i),StateSqrtPPost(:,:,i)*nodes') ;
|
||||
IncrementalWeights = gaussian_mixture_densities(Y(:,t),StateMuPrior,StateSqrtPPrior,StateWeightsPrior,...
|
||||
StateMuPost,StateSqrtPPost,StateWeightsPost,...
|
||||
StateParticles,H,const_lik,weights,weights_c,ReducedForm,ThreadsOptions) ;
|
||||
SampleWeights(i) = sum(StateWeightsPost(i)*weights.*IncrementalWeights) ;
|
||||
StateParticles = bsxfun(@plus, StateMuPost(:,i), StateSqrtPPost(:,:,i)*nodes');
|
||||
IncrementalWeights = gaussian_mixture_densities(Y(:,t), StateMuPrior, StateSqrtPPrior, StateWeightsPrior, ...
|
||||
StateMuPost, StateSqrtPPost, StateWeightsPost, StateParticles, H, ...
|
||||
ReducedForm, ThreadsOptions, DynareOptions, Model);
|
||||
SampleWeights(i) = sum(StateWeightsPost(i)*weights.*IncrementalWeights);
|
||||
end
|
||||
SumSampleWeights = sum(SampleWeights) ;
|
||||
lik(t) = log(SumSampleWeights) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
[ras,SortedRandomIndx] = sort(rand(1,Gsecond));
|
||||
SumSampleWeights = sum(SampleWeights);
|
||||
lik(t) = log(SumSampleWeights);
|
||||
SampleWeights = SampleWeights./SumSampleWeights;
|
||||
[~, SortedRandomIndx] = sort(rand(1,Gsecond));
|
||||
SortedRandomIndx = SortedRandomIndx(1:G);
|
||||
indx = resample(0,SampleWeights,ParticleOptions) ;
|
||||
indx = indx(SortedRandomIndx) ;
|
||||
indx = resample(0,SampleWeights,ParticleOptions);
|
||||
indx = indx(SortedRandomIndx);
|
||||
StateMu = StateMuPost(:,indx);
|
||||
StateSqrtP = StateSqrtPPost(:,:,indx);
|
||||
StateWeights = ones(1,G)/G ;
|
||||
StateWeights = ones(1,G)/G;
|
||||
else
|
||||
% Sample particle in the proposal distribution, ie the posterior state GM
|
||||
StateParticles = importance_sampling(StateMuPost,StateSqrtPPost,StateWeightsPost',number_of_particles) ;
|
||||
IncrementalWeights = gaussian_mixture_densities(Y(:,t),StateMuPrior,StateSqrtPPrior,StateWeightsPrior,...
|
||||
StateMuPost,StateSqrtPPost,StateWeightsPost,...
|
||||
StateParticles,H,const_lik,1/number_of_particles,...
|
||||
1/number_of_particles,ReducedForm,ThreadsOptions) ;
|
||||
SampleWeights = IncrementalWeights/number_of_particles ;
|
||||
SumSampleWeights = sum(SampleWeights,1) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
lik(t) = log(SumSampleWeights) ;
|
||||
StateParticles = importance_sampling(StateMuPost,StateSqrtPPost,StateWeightsPost',number_of_particles);
|
||||
IncrementalWeights = gaussian_mixture_densities(Y(:,t), StateMuPrior, StateSqrtPPrior, StateWeightsPrior, ...
|
||||
StateMuPost, StateSqrtPPost, StateWeightsPost, StateParticles, H, ...
|
||||
ReducedForm, ThreadsOptions, DynareOptions, Model);
|
||||
SampleWeights = IncrementalWeights/number_of_particles;
|
||||
SumSampleWeights = sum(SampleWeights,1);
|
||||
SampleWeights = SampleWeights./SumSampleWeights;
|
||||
lik(t) = log(SumSampleWeights);
|
||||
if (ParticleOptions.resampling.status.generic && neff(SampleWeights)<ParticleOptions.resampling.threshold*sample_size) || ParticleOptions.resampling.status.systematic
|
||||
StateParticles = resample(StateParticles',SampleWeights',ParticleOptions)';
|
||||
SampleWeights = ones(number_of_particles,1)/number_of_particles;
|
||||
end
|
||||
[StateMu,StateSqrtP,StateWeights] = fit_gaussian_mixture(StateParticles,SampleWeights',StateMu,StateSqrtP,StateWeights,0.001,10,1) ;
|
||||
[StateMu, StateSqrtP, StateWeights] = fit_gaussian_mixture(StateParticles, SampleWeights', StateMu, StateSqrtP, StateWeights, 0.001, 10, 1);
|
||||
end
|
||||
end
|
||||
|
||||
LIK = -sum(lik(start:end)) ;
|
||||
LIK = -sum(lik(start:end));
|
||||
|
|
@ -1,9 +1,9 @@
|
|||
function [StateMuPrior,StateSqrtPPrior,StateWeightsPrior,StateMuPost,StateSqrtPPost,StateWeightsPost] =...
|
||||
gaussian_mixture_filter_bank(ReducedForm,obs,StateMu,StateSqrtP,StateWeights,...
|
||||
StructuralShocksMu,StructuralShocksSqrtP,StructuralShocksWeights,...
|
||||
ObservationShocksMu,ObservationShocksSqrtP,ObservationShocksWeights,...
|
||||
H,H_lower_triangular_cholesky,normfactO,ParticleOptions,ThreadsOptions)
|
||||
%
|
||||
gaussian_mixture_filter_bank(ReducedForm, obs, StateMu, StateSqrtP, StateWeights, ...
|
||||
StructuralShocksMu, StructuralShocksSqrtP, StructuralShocksWeights, ...
|
||||
ObservationShocksWeights, H, H_lower_triangular_cholesky, normfactO, ...
|
||||
ParticleOptions, ThreadsOptions, DynareOptions, Model)
|
||||
|
||||
% Computes the proposal with a gaussian approximation for importance
|
||||
% sampling
|
||||
% This proposal is a gaussian distribution calculated à la Kalman
|
||||
|
|
@ -23,7 +23,8 @@ function [StateMuPrior,StateSqrtPPrior,StateWeightsPrior,StateMuPost,StateSqrtPP
|
|||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
% Copyright (C) 2009-2017 Dynare Team
|
||||
|
||||
% Copyright (C) 2009-2019 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
|
|
@ -40,86 +41,73 @@ function [StateMuPrior,StateSqrtPPrior,StateWeightsPrior,StateMuPost,StateSqrtPP
|
|||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
|
||||
|
||||
persistent init_flag2 mf0 mf1 %nodes3 weights3 weights_c3
|
||||
persistent number_of_state_variables number_of_observed_variables
|
||||
persistent number_of_structural_innovations
|
||||
|
||||
% Set local state space model (first-order approximation).
|
||||
ghx = ReducedForm.ghx;
|
||||
ghu = ReducedForm.ghu;
|
||||
% Set local state space model (second-order approximation).
|
||||
ghxx = ReducedForm.ghxx;
|
||||
ghuu = ReducedForm.ghuu;
|
||||
ghxu = ReducedForm.ghxu;
|
||||
|
||||
if any(any(isnan(ghx))) || any(any(isnan(ghu))) || any(any(isnan(ghxx))) || any(any(isnan(ghuu))) || any(any(isnan(ghxu))) || ...
|
||||
any(any(isinf(ghx))) || any(any(isinf(ghu))) || any(any(isinf(ghxx))) || any(any(isinf(ghuu))) || any(any(isinf(ghxu))) ...
|
||||
any(any(abs(ghx)>1e4)) || any(any(abs(ghu)>1e4)) || any(any(abs(ghxx)>1e4)) || any(any(abs(ghuu)>1e4)) || any(any(abs(ghxu)>1e4))
|
||||
ghx
|
||||
ghu
|
||||
ghxx
|
||||
ghuu
|
||||
ghxu
|
||||
if ReducedForm.use_k_order_solver
|
||||
dr = ReducedForm.dr;
|
||||
else
|
||||
% Set local state space model (first-order approximation).
|
||||
ghx = ReducedForm.ghx;
|
||||
ghu = ReducedForm.ghu;
|
||||
% Set local state space model (second-order approximation).
|
||||
ghxx = ReducedForm.ghxx;
|
||||
ghuu = ReducedForm.ghuu;
|
||||
ghxu = ReducedForm.ghxu;
|
||||
end
|
||||
|
||||
constant = ReducedForm.constant;
|
||||
state_variables_steady_state = ReducedForm.state_variables_steady_state;
|
||||
|
||||
% Set persistent variables.
|
||||
if isempty(init_flag2)
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
init_flag2 = 1;
|
||||
end
|
||||
mf0 = ReducedForm.mf0;
|
||||
mf1 = ReducedForm.mf1;
|
||||
number_of_state_variables = length(mf0);
|
||||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
|
||||
numb = number_of_state_variables+number_of_structural_innovations ;
|
||||
numb = number_of_state_variables+number_of_structural_innovations;
|
||||
|
||||
if ParticleOptions.proposal_approximation.cubature
|
||||
[nodes3,weights3] = spherical_radial_sigma_points(numb);
|
||||
[nodes3, weights3] = spherical_radial_sigma_points(numb);
|
||||
weights_c3 = weights3;
|
||||
elseif ParticleOptions.proposal_approximation.unscented
|
||||
[nodes3,weights3,weights_c3] = unscented_sigma_points(numb,ParticleOptions);
|
||||
[nodes3, weights3, weights_c3] = unscented_sigma_points(numb, ParticleOptions);
|
||||
else
|
||||
error('Estimation: This approximation for the proposal is not implemented or unknown!')
|
||||
error('This approximation for the proposal is unknown!')
|
||||
end
|
||||
|
||||
epsilon = bsxfun(@plus,StructuralShocksSqrtP*nodes3(:,number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations)',StructuralShocksMu) ;
|
||||
StateVectors = bsxfun(@plus,StateSqrtP*nodes3(:,1:number_of_state_variables)',StateMu);
|
||||
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
|
||||
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
|
||||
epsilon = bsxfun(@plus, StructuralShocksSqrtP*nodes3(:,number_of_state_variables+1:number_of_state_variables+number_of_structural_innovations)', StructuralShocksMu);
|
||||
StateVectors = bsxfun(@plus, StateSqrtP*nodes3(:,1:number_of_state_variables)', StateMu);
|
||||
yhat = bsxfun(@minus, StateVectors, state_variables_steady_state);
|
||||
if ReducedForm.use_k_order_solver
|
||||
tmp = local_state_space_iteration_k(yhat, epsilon, dr, Model, DynareOptions);
|
||||
else
|
||||
tmp = local_state_space_iteration_2(yhat, epsilon, ghx, ghu, constant, ghxx, ghuu, ghxu, ThreadsOptions.local_state_space_iteration_2);
|
||||
end
|
||||
PredictedStateMean = tmp(mf0,:)*weights3;
|
||||
PredictedObservedMean = tmp(mf1,:)*weights3;
|
||||
|
||||
if ParticleOptions.proposal_approximation.cubature
|
||||
PredictedStateMean = sum(PredictedStateMean,2);
|
||||
PredictedObservedMean = sum(PredictedObservedMean,2);
|
||||
dState = (bsxfun(@minus,tmp(mf0,:),PredictedStateMean)').*sqrt(weights3);
|
||||
dObserved = (bsxfun(@minus,tmp(mf1,:),PredictedObservedMean)').*sqrt(weights3);
|
||||
PredictedStateMean = sum(PredictedStateMean, 2);
|
||||
PredictedObservedMean = sum(PredictedObservedMean, 2);
|
||||
dState = (bsxfun(@minus, tmp(mf0,:), PredictedStateMean)').*sqrt(weights3);
|
||||
dObserved = (bsxfun(@minus, tmp(mf1,:), PredictedObservedMean)').*sqrt(weights3);
|
||||
PredictedStateVariance = dState'*dState;
|
||||
big_mat = [dObserved dState ; [H_lower_triangular_cholesky zeros(number_of_observed_variables,number_of_state_variables)] ];
|
||||
[mat1,mat] = qr2(big_mat,0);
|
||||
big_mat = [dObserved, dState ; H_lower_triangular_cholesky, zeros(number_of_observed_variables, number_of_state_variables)];
|
||||
[~, mat] = qr2(big_mat, 0);
|
||||
mat = mat';
|
||||
clear('mat1');
|
||||
PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables,1:number_of_observed_variables);
|
||||
CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),1:number_of_observed_variables);
|
||||
StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables),number_of_observed_variables+(1:number_of_state_variables));
|
||||
PredictedObservedVarianceSquareRoot = mat(1:number_of_observed_variables, 1:number_of_observed_variables);
|
||||
CovarianceObservedStateSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables), 1:number_of_observed_variables);
|
||||
StateVectorVarianceSquareRoot = mat(number_of_observed_variables+(1:number_of_state_variables), number_of_observed_variables+(1:number_of_state_variables));
|
||||
iPredictedObservedVarianceSquareRoot = inv(PredictedObservedVarianceSquareRoot);
|
||||
iPredictedObservedVariance = iPredictedObservedVarianceSquareRoot'*iPredictedObservedVarianceSquareRoot;
|
||||
sqrdet = 1/sqrt(det(iPredictedObservedVariance));
|
||||
PredictionError = obs - PredictedObservedMean;
|
||||
StateVectorMean = PredictedStateMean + CovarianceObservedStateSquareRoot*iPredictedObservedVarianceSquareRoot*PredictionError;
|
||||
else
|
||||
dState = bsxfun(@minus,tmp(mf0,:),PredictedStateMean);
|
||||
dObserved = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
|
||||
dState = bsxfun(@minus, tmp(mf0,:), PredictedStateMean);
|
||||
dObserved = bsxfun(@minus, tmp(mf1,:), PredictedObservedMean);
|
||||
PredictedStateVariance = dState*diag(weights_c3)*dState';
|
||||
PredictedObservedVariance = dObserved*diag(weights_c3)*dObserved' + H;
|
||||
PredictedStateAndObservedCovariance = dState*diag(weights_c3)*dObserved';
|
||||
sqrdet = sqrt(det(PredictedObservedVariance)) ;
|
||||
sqrdet = sqrt(det(PredictedObservedVariance));
|
||||
iPredictedObservedVariance = inv(PredictedObservedVariance);
|
||||
PredictionError = obs - PredictedObservedMean;
|
||||
KalmanFilterGain = PredictedStateAndObservedCovariance*iPredictedObservedVariance;
|
||||
|
|
@ -130,9 +118,9 @@ else
|
|||
end
|
||||
|
||||
data_lik_GM_g = exp(-0.5*PredictionError'*iPredictedObservedVariance*PredictionError)/abs(normfactO*sqrdet) + 1e-99;
|
||||
StateMuPrior = PredictedStateMean ;
|
||||
StateMuPrior = PredictedStateMean;
|
||||
StateSqrtPPrior = reduced_rank_cholesky(PredictedStateVariance)';
|
||||
StateWeightsPrior = StateWeights*StructuralShocksWeights;
|
||||
StateMuPost = StateVectorMean;
|
||||
StateSqrtPPost = StateVectorVarianceSquareRoot;
|
||||
StateWeightsPost = StateWeightsPrior*ObservationShocksWeights*data_lik_GM_g ;
|
||||
StateWeightsPost = StateWeightsPrior*ObservationShocksWeights*data_lik_GM_g;
|
||||
Loading…
Reference in New Issue