From eb72df7bc680c51a78b72c3c29f798193d8903d2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Karam=C3=A9?=
<frederic.karame@univ-lemans.fr>
Date: Fri, 16 Nov 2012 11:29:21 +0100
Subject: [PATCH] computes the proposal distribution during the importance
sampling step for gaussian-mixture filters. Fix many bugs.
---
.../particle/gaussian_mixture_filter_bank.m | 145 ++++++++++++++++++
1 file changed, 145 insertions(+)
create mode 100644 matlab/particle/gaussian_mixture_filter_bank.m
diff --git a/matlab/particle/gaussian_mixture_filter_bank.m b/matlab/particle/gaussian_mixture_filter_bank.m
new file mode 100644
index 000000000..9d7f43fc0
--- /dev/null
+++ b/matlab/particle/gaussian_mixture_filter_bank.m
@@ -0,0 +1,145 @@
+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,DynareOptions)
+%
+% Computes the proposal with a gaussian approximation for importance
+% sampling
+% This proposal is a gaussian distribution calculated à la Kalman
+%
+% 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.
+%
+% 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/>.
+
+
+
+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
+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
+
+numb = number_of_state_variables+number_of_structural_innovations ;
+
+if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature')
+ [nodes3,weights3] = nwspgr('GQN',numb,DynareOptions.particle.smolyak_accuracy) ;
+ weights_c3 = weights3 ;
+end
+if strcmpi(DynareOptions.particle.IS_approximation_method,'cubature')
+ [nodes3,weights3] = spherical_radial_sigma_points(numb) ;
+ weights_c3 = weights3 ;
+end
+if strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
+ [nodes3,weights3,weights_c3] = unscented_sigma_points(numb,DynareOptions) ;
+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);
+%ObservationShocks = bsxfun(@plus,ObservationShocksSqrtP*nodes3(:,1+number_of_state_variables+number_of_structural_innovations:number_of_state_variables+number_of_structural_innovations+number_of_observed_variables)',ObservationShocksMu) ;
+
+yhat = bsxfun(@minus,StateVectors,state_variables_steady_state) ;
+tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
+PredictedStateMean = tmp(mf0,:)*weights3;
+PredictedObservedMean = tmp(mf1,:)*weights3;
+
+if strcmpi(DynareOptions.particle.IS_approximation_method,'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);
+ 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) ;
+ 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)) ;
+ iPredictedObservedVarianceSquareRoot = inv(PredictedObservedVarianceSquareRoot);
+ iPredictedObservedVariance = iPredictedObservedVarianceSquareRoot'*iPredictedObservedVarianceSquareRoot ;
+ sqrdet = 1/sqrt(det(iPredictedObservedVariance)) ;
+ PredictionError = obs - PredictedObservedMean ;
+ StateVectorMean = PredictedStateMean + CovarianceObservedStateSquareRoot*iPredictedObservedVarianceSquareRoot*PredictionError;
+end
+if strcmpi(DynareOptions.particle.IS_approximation_method,'quadrature') || ...
+ strcmpi(DynareOptions.particle.IS_approximation_method,'unscented')
+ 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)) ;
+ iPredictedObservedVariance = inv(PredictedObservedVariance);
+ PredictionError = obs - PredictedObservedMean;
+ KalmanFilterGain = PredictedStateAndObservedCovariance*iPredictedObservedVariance;
+ StateVectorMean = PredictedStateMean + KalmanFilterGain*PredictionError;
+ StateVectorVariance = PredictedStateVariance - KalmanFilterGain*PredictedObservedVariance*KalmanFilterGain';
+ StateVectorVariance = .5*(StateVectorVariance+StateVectorVariance');
+ StateVectorVarianceSquareRoot = reduced_rank_cholesky(StateVectorVariance)';
+end
+
+data_lik_GM_g = exp(-0.5*PredictionError'*iPredictedObservedVariance*PredictionError)/abs(normfactO*sqrdet) + 1e-99;
+StateMuPrior = PredictedStateMean ;
+StateSqrtPPrior = reduced_rank_cholesky(PredictedStateVariance)' ;
+StateWeightsPrior = StateWeights*StructuralShocksWeights ;
+StateMuPost = StateVectorMean ;
+StateSqrtPPost = StateVectorVarianceSquareRoot ;
+StateWeightsPost = StateWeightsPrior*ObservationShocksWeights*data_lik_GM_g ;
--
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