Fix the calculation of the likelihood on the APF.

src/auxiliary_particle_filter.m

 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