Commit 8d401a22 authored by Frédéric Karamé's avatar Frédéric Karamé
Browse files

Fix the calculation of the likelihood on the APF.

parent 5922f881
function [LIK,lik] = auxiliary_particle_filter(ReducedForm,Y,start,ParticleOptions,ThreadsOptions) 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. % Evaluates the likelihood of a nonlinear model with the auxiliary particle filter
% allowing eventually resampling.
% Copyright (C) 2011-2014 Dynare Team %
% Copyright (C) 2011-2015 Dynare Team
% %
% This file is part of Dynare (particles module). % This file is part of Dynare (particles module).
% %
...@@ -20,7 +21,7 @@ function [LIK,lik] = auxiliary_particle_filter(ReducedForm,Y,start,ParticleOptio ...@@ -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/>. % along with Dynare. If not, see <http://www.gnu.org/licenses/>.
persistent init_flag mf0 mf1 number_of_particles 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 % Set default
if isempty(start) if isempty(start)
...@@ -40,7 +41,6 @@ if isempty(init_flag) ...@@ -40,7 +41,6 @@ if isempty(init_flag)
mf0 = ReducedForm.mf0; mf0 = ReducedForm.mf0;
mf1 = ReducedForm.mf1; mf1 = ReducedForm.mf1;
sample_size = size(Y,2); sample_size = size(Y,2);
number_of_state_variables = length(mf0);
number_of_observed_variables = length(mf1); number_of_observed_variables = length(mf1);
number_of_structural_innovations = length(ReducedForm.Q); number_of_structural_innovations = length(ReducedForm.Q);
number_of_particles = ParticleOptions.number_of_particles; number_of_particles = ParticleOptions.number_of_particles;
...@@ -58,55 +58,44 @@ ghxu = ReducedForm.ghxu; ...@@ -58,55 +58,44 @@ ghxu = ReducedForm.ghxu;
% Get covariance matrices % Get covariance matrices
Q = ReducedForm.Q; Q = ReducedForm.Q;
H = ReducedForm.H; H = ReducedForm.H;
if isempty(H)
H = 0;
end
% Get initial condition for the state vector. % Get initial condition for the state vector.
StateVectorMean = ReducedForm.StateVectorMean; StateVectorMean = ReducedForm.StateVectorMean;
StateVectorVarianceSquareRoot = chol(ReducedForm.StateVectorVariance)';%reduced_rank_cholesky(ReducedForm.StateVectorVariance)'; StateVectorVarianceSquareRoot = chol(ReducedForm.StateVectorVariance)';
state_variance_rank = size(StateVectorVarianceSquareRoot,2); state_variance_rank = size(StateVectorVarianceSquareRoot,2);
Q_lower_triangular_cholesky = chol(Q)'; Q_lower_triangular_cholesky = chol(Q)';
if pruning
StateVectorMean_ = StateVectorMean;
StateVectorVarianceSquareRoot_ = StateVectorVarianceSquareRoot;
end
% Set seed for randn(). % Set seed for randn().
set_dynare_seed('default'); set_dynare_seed('default');
% Initialization of the likelihood. % 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(sample_size,1);
LIK = NaN; LIK = NaN;
% Initialization of the weights across particles. % Initialization of the weights across particles.
weights = ones(1,number_of_particles)/number_of_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,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean);
%StateVectors = bsxfun(@plus,zeros(state_variance_rank,number_of_particles),StateVectorMean);
if pruning if pruning
StateVectors_ = StateVectors; StateVectors_ = StateVectors;
end end
epsilon = Q_lower_triangular_cholesky*randn(number_of_structural_innovations,number_of_particles); % Uncomment for building the mean average predictions based on a sparse
yhat = zeros(2,number_of_particles) ; % grids of structural shocks. Otherwise, all shocks are set to 0 in the
if pruning % prediction.
yhat_ = zeros(2,number_of_particles) ; %if ParticleOptions.proposal_approximation.cubature
[tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,ThreadsOptions.local_state_space_iteration_2); % [nodes,nodes_weights] = spherical_radial_sigma_points(number_of_structural_innovations) ;
StateVectors_ = tmp_(mf0,:); % nodes_weights = ones(size(nodes,1),1)*nodes_weights ;
else %elseif ParticleOptions.proposal_approximation.unscented
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2); % [nodes,nodes_weights,nodes_weights_c] = unscented_sigma_points(number_of_structural_innovations,ParticleOptions);
end %else
StateVectors = tmp(mf0,:) ; % error('Estimation: This approximation for the proposal is not implemented or unknown!')
%end
if ParticleOptions.proposal_approximation.cubature %nodes = Q_lower_triangular_cholesky*nodes ;
[nodes,nodes_weights] = spherical_radial_sigma_points(number_of_structural_innovations) ;
nodes_weights = ones(size(nodes,1),1)*nodes_weights ; nodes = zeros(1,number_of_structural_innovations) ;
elseif ParticleOptions.proposal_approximation.unscented nodes_weights = 1 ;
[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 ;
for t=1:sample_size for t=1:sample_size
yhat = bsxfun(@minus,StateVectors,state_variables_steady_state); yhat = bsxfun(@minus,StateVectors,state_variables_steady_state);
...@@ -125,21 +114,19 @@ for t=1:sample_size ...@@ -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); 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
end end
%PredictedObservedMean = weights*(tmp(mf1,:)');
PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:)); PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
%dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean'); %tau_tilde = weights.*(exp(-.5*(const_lik+sum(PredictionError.*(H\PredictionError),1))) + 1e-99) ;
%PredictedObservedVariance = bsxfun(@times,weights,dPredictedObservedMean)*dPredictedObservedMean' +H; % Replace Gaussian density with a Student density with 3 degrees of
wtilde = exp(-.5*(const_lik+sum(PredictionError.*(H\PredictionError),1))) ; % freedom for fat tails.
tau_tilde = weights.*wtilde ; z = sum(PredictionError.*(H\PredictionError),1) ;
sum_tau_tilde = sum(tau_tilde) ; tau_tilde = weights.*(tpdf(z,3*ones(size(z)))+1e-99) ;
lik(t) = log(sum_tau_tilde) ; tau_tilde = tau_tilde/sum(tau_tilde) ;
tau_tilde = tau_tilde/sum_tau_tilde;
indx = resample(0,tau_tilde',ParticleOptions); indx = resample(0,tau_tilde',ParticleOptions);
if pruning if pruning
yhat_ = yhat_(:,indx) ; yhat_ = yhat_(:,indx) ;
end end
yhat = yhat(:,indx) ; 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); epsilon = Q_lower_triangular_cholesky*randn(number_of_structural_innovations,number_of_particles);
if pruning 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); [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 ...@@ -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); tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,ThreadsOptions.local_state_space_iteration_2);
end end
StateVectors = tmp(mf0,:); StateVectors = tmp(mf0,:);
%PredictedObservedMean = mean(tmp(mf1,:),2);
PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:)); PredictionError = bsxfun(@minus,Y(:,t),tmp(mf1,:));
%dPredictedObservedMean = bsxfun(@minus,tmp(mf1,:),PredictedObservedMean); weights_stage_2 = weights_stage_1.*(exp(-.5*(const_lik+sum(PredictionError.*(H\PredictionError),1))) + 1e-99) ;
%PredictedObservedVariance = (dPredictedObservedMean*dPredictedObservedMean')/number_of_particles + H; lik(t) = log(mean(weights_stage_2)) ;
lnw = exp(-.5*(const_lik+sum(PredictionError.*(H\PredictionError),1))); weights = weights_stage_2/sum(weights_stage_2);
wtilde = lnw.*factor ; if (ParticleOptions.resampling.status.generic && neff(weights)<ParticleOptions.resampling.threshold*sample_size) || ParticleOptions.resampling.status.systematic
weights = wtilde/sum(wtilde); 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 end
%plot(lik) ;
LIK = -sum(lik(start:end)); LIK = -sum(lik(start:end));
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