From 8d401a22f5138773f7092456c9553ebbb11dd3a9 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: Tue, 20 Oct 2015 15:12:56 +0200
Subject: [PATCH] Fix the calculation of the likelihood on the APF.
---
src/auxiliary_particle_filter.m | 93 ++++++++++++++++-----------------
1 file changed, 44 insertions(+), 49 deletions(-)
diff --git a/src/auxiliary_particle_filter.m b/src/auxiliary_particle_filter.m
index 78c0bdd..a48973b 100644
--- a/src/auxiliary_particle_filter.m
+++ b/src/auxiliary_particle_filter.m
@@ -1,8 +1,9 @@
function [LIK,lik] = auxiliary_particle_filter(ReducedForm,Y,start,ParticleOptions,ThreadsOptions)
-% Evaluates the likelihood of a nonlinear model with a particle filter allowing eventually resampling.
-
-% Copyright (C) 2011-2014 Dynare Team
+% Evaluates the likelihood of a nonlinear model with the auxiliary particle filter
+% allowing eventually resampling.
+%
+% Copyright (C) 2011-2015 Dynare Team
%
% This file is part of Dynare (particles module).
%
@@ -20,7 +21,7 @@ function [LIK,lik] = auxiliary_particle_filter(ReducedForm,Y,start,ParticleOptio
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
persistent init_flag mf0 mf1 number_of_particles
-persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
+persistent sample_size number_of_observed_variables number_of_structural_innovations
% Set default
if isempty(start)
@@ -40,7 +41,6 @@ if isempty(init_flag)
mf0 = ReducedForm.mf0;
mf1 = ReducedForm.mf1;
sample_size = size(Y,2);
- number_of_state_variables = length(mf0);
number_of_observed_variables = length(mf1);
number_of_structural_innovations = length(ReducedForm.Q);
number_of_particles = ParticleOptions.number_of_particles;
@@ -58,55 +58,44 @@ ghxu = ReducedForm.ghxu;
% Get covariance matrices
Q = ReducedForm.Q;
H = ReducedForm.H;
-if isempty(H)
- H = 0;
-end
% Get initial condition for the state vector.
StateVectorMean = ReducedForm.StateVectorMean;
-StateVectorVarianceSquareRoot = chol(ReducedForm.StateVectorVariance)';%reduced_rank_cholesky(ReducedForm.StateVectorVariance)';
+StateVectorVarianceSquareRoot = chol(ReducedForm.StateVectorVariance)';
state_variance_rank = size(StateVectorVarianceSquareRoot,2);
Q_lower_triangular_cholesky = chol(Q)';
-if pruning
- StateVectorMean_ = StateVectorMean;
- StateVectorVarianceSquareRoot_ = StateVectorVarianceSquareRoot;
-end
% Set seed for randn().
set_dynare_seed('default');
% Initialization of the likelihood.
-const_lik = log(2*pi)*number_of_observed_variables +log(det(H));
+const_lik = log(2*pi)*number_of_observed_variables+log(det(H));
lik = NaN(sample_size,1);
LIK = NaN;
% Initialization of the weights across particles.
weights = ones(1,number_of_particles)/number_of_particles ;
StateVectors = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
+%StateVectors = bsxfun(@plus,zeros(state_variance_rank,number_of_particles),StateVectorMean);
if pruning
StateVectors_ = StateVectors;
end
-epsilon = Q_lower_triangular_cholesky*randn(number_of_structural_innovations,number_of_particles);
-yhat = zeros(2,number_of_particles) ;
-if pruning
- yhat_ = zeros(2,number_of_particles) ;
- [tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,ThreadsOptions.local_state_space_iteration_2);
- StateVectors_ = tmp_(mf0,:);
-else
- tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
-end
-StateVectors = tmp(mf0,:) ;
-
-if ParticleOptions.proposal_approximation.cubature
- [nodes,nodes_weights] = spherical_radial_sigma_points(number_of_structural_innovations) ;
- nodes_weights = ones(size(nodes,1),1)*nodes_weights ;
-elseif ParticleOptions.proposal_approximation.unscented
- [nodes,nodes_weights,nodes_weights_c] = unscented_sigma_points(number_of_structural_innovations,ParticleOptions);
-else
- error('Estimation: This approximation for the proposal is not implemented or unknown!')
-end
-nodes = Q_lower_triangular_cholesky*nodes ;
+% Uncomment for building the mean average predictions based on a sparse
+% grids of structural shocks. Otherwise, all shocks are set to 0 in the
+% prediction.
+%if ParticleOptions.proposal_approximation.cubature
+% [nodes,nodes_weights] = spherical_radial_sigma_points(number_of_structural_innovations) ;
+% nodes_weights = ones(size(nodes,1),1)*nodes_weights ;
+%elseif ParticleOptions.proposal_approximation.unscented
+% [nodes,nodes_weights,nodes_weights_c] = unscented_sigma_points(number_of_structural_innovations,ParticleOptions);
+%else
+% error('Estimation: This approximation for the proposal is not implemented or unknown!')
+%end
+%nodes = Q_lower_triangular_cholesky*nodes ;
+
+nodes = zeros(1,number_of_structural_innovations) ;
+nodes_weights = 1 ;
for t=1:sample_size
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
@@ -125,21 +114,19 @@ for t=1:sample_size
tmp = tmp + nodes_weights(i)*local_state_space_iteration_2(yhat,nodes(i,:)*ones(1,number_of_particles),ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
end
end
- %PredictedObservedMean = weights*(tmp(mf1,:)');
PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
- %dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean');
- %PredictedObservedVariance = bsxfun(@times,weights,dPredictedObservedMean)*dPredictedObservedMean' +H;
- wtilde = exp(-.5*(const_lik+sum(PredictionError.*(H\PredictionError),1))) ;
- tau_tilde = weights.*wtilde ;
- sum_tau_tilde = sum(tau_tilde) ;
- lik(t) = log(sum_tau_tilde) ;
- tau_tilde = tau_tilde/sum_tau_tilde;
+ %tau_tilde = weights.*(exp(-.5*(const_lik+sum(PredictionError.*(H\PredictionError),1))) + 1e-99) ;
+ % Replace Gaussian density with a Student density with 3 degrees of
+ % freedom for fat tails.
+ z = sum(PredictionError.*(H\PredictionError),1) ;
+ tau_tilde = weights.*(tpdf(z,3*ones(size(z)))+1e-99) ;
+ tau_tilde = tau_tilde/sum(tau_tilde) ;
indx = resample(0,tau_tilde',ParticleOptions);
if pruning
yhat_ = yhat_(:,indx) ;
end
yhat = yhat(:,indx) ;
- factor = weights(indx)./tau_tilde(indx) ;
+ weights_stage_1 = weights(indx)./tau_tilde(indx) ;
epsilon = Q_lower_triangular_cholesky*randn(number_of_structural_innovations,number_of_particles);
if pruning
[tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,ThreadsOptions.local_state_space_iteration_2);
@@ -148,13 +135,21 @@ for t=1:sample_size
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
end
StateVectors = tmp(mf0,:);
- %PredictedObservedMean = mean(tmp(mf1,:),2);
PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
- %dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean);
- %PredictedObservedVariance = (dPredictedObservedMean*dPredictedObservedMean')/number_of_particles + H;
- lnw = exp(-.5*(const_lik+sum(PredictionError.*(H\PredictionError),1)));
- wtilde = lnw.*factor ;
- weights = wtilde/sum(wtilde);
+ weights_stage_2 = weights_stage_1.*(exp(-.5*(const_lik+sum(PredictionError.*(H\PredictionError),1))) + 1e-99) ;
+ lik(t) = log(mean(weights_stage_2)) ;
+ weights = weights_stage_2/sum(weights_stage_2);
+ if (ParticleOptions.resampling.status.generic && neff(weights)<ParticleOptions.resampling.threshold*sample_size) || ParticleOptions.resampling.status.systematic
+ if pruning
+ temp = resample([StateVectors' StateVectors_'],weights',ParticleOptions);
+ StateVectors = temp(:,1:number_of_state_variables)';
+ StateVectors_ = temp(:,number_of_state_variables+1:2*number_of_state_variables)';
+ else
+ StateVectors = resample(StateVectors',weights',ParticleOptions)';
+ end
+ weights = ones(1,number_of_particles)/number_of_particles;
+ end
end
+%plot(lik) ;
LIK = -sum(lik(start:end));
\ No newline at end of file
--
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