Commit ef22c716 authored by Frédéric Karamé's avatar Frédéric Karamé

Initial particles are drawn in the prior distribution + bug fixes.

parent 43615ce4
...@@ -43,7 +43,7 @@ persistent start_param sample_size number_of_observed_variables number_of_struct ...@@ -43,7 +43,7 @@ persistent start_param sample_size number_of_observed_variables number_of_struct
% Set seed for randn(). % Set seed for randn().
set_dynare_seed('default') ; set_dynare_seed('default') ;
pruning = DynareOptions.particle.pruning; pruning = DynareOptions.particle.pruning;
second_resample = 0 ; second_resample = DynareOptions.particle.resampling.status.systematic ;
variance_update = 1 ; variance_update = 1 ;
% initialization of state particles % initialization of state particles
...@@ -75,25 +75,31 @@ if pruning ...@@ -75,25 +75,31 @@ if pruning
end end
% parameters for the Liu & West filter % parameters for the Liu & West filter
h_square = (3*liu_west_delta-1)/(2*liu_west_delta) ; small_a = (3*liu_west_delta-1)/(2*liu_west_delta) ;
h_square = 1-h_square*h_square ; b_square = 1-small_a*small_a ;
small_a = sqrt(1-h_square) ;
% Initialization of parameter particles % Initialization of parameter particles
xparam = zeros(number_of_parameters,number_of_particles) ; xparam = zeros(number_of_parameters,number_of_particles) ;
stderr = sqrt(bsxfun(@power,bounds.ub-bounds.lb,2)/12)/100 ; %stderr = sqrt(bsxfun(@power,bounds.ub-bounds.lb,2)/12)/100 ;
stderr = sqrt(bsxfun(@power,bounds.ub-bounds.lb,2)/12)/50 ; %stderr = sqrt(bsxfun(@power,bounds.ub-bounds.lb,2)/12)/50 ;
%stderr = sqrt(bsxfun(@power,bounds.ub-bounds.lb,2)/12)/20 ; %stderr = sqrt(bsxfun(@power,bounds.ub-bounds.lb,2)/12)/20 ;
i = 1 ; bounds = prior_bounds(BayesInfo,DynareOptions.prior_trunc); %reset bounds as lb and ub must only be operational during mode-finding
while i<=number_of_particles prior_draw(BayesInfo,DynareOptions.prior_trunc);
%candidate = start_param + .001*liu_west_chol_sigma_bar*randn(number_of_parameters,1) ; for i=1:number_of_particles
candidate = start_param + bsxfun(@times,stderr,randn(number_of_parameters,1)) ; info = 1;
if all(candidate(:) >= bounds.lb) && all(candidate(:) <= bounds.ub) while info==1
xparam(:,i) = candidate(:) ; %candidate = start_param + .001*liu_west_chol_sigma_bar*randn(number_of_parameters,1) ;
i = i+1 ; %candidate = start_param + bsxfun(@times,stderr,randn(number_of_parameters,1)) ;
candidate = prior_draw()';
if all(candidate(:) >= bounds.lb) && all(candidate(:) <= bounds.ub)
[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
solve_model_for_online_filter(1,candidate(:),DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
if info==0
xparam(:,i) = candidate(:) ;
end
end
end end
end end
%xparam = bsxfun(@plus,bounds(:,1),bsxfun(@times,(bounds(:,2)-bounds(:,1)),rand(number_of_parameters,number_of_particles))) ; %xparam = bsxfun(@plus,bounds(:,1),bsxfun(@times,(bounds(:,2)-bounds(:,1)),rand(number_of_parameters,number_of_particles))) ;
% Initialization of the weights of particles. % Initialization of the weights of particles.
...@@ -119,81 +125,87 @@ for t=1:sample_size ...@@ -119,81 +125,87 @@ for t=1:sample_size
temp = bsxfun(@minus,xparam,m_bar) ; temp = bsxfun(@minus,xparam,m_bar) ;
sigma_bar = (bsxfun(@times,weights,temp))*(temp') ; sigma_bar = (bsxfun(@times,weights,temp))*(temp') ;
if variance_update==1 if variance_update==1
chol_sigma_bar = chol(h_square*sigma_bar)' ; chol_sigma_bar = chol(b_square*sigma_bar)' ;
end end
% Prediction (without shocks) % Prediction (without shocks)
fore_xparam = bsxfun(@plus,(1-small_a).*m_bar,small_a.*xparam) ;
tau_tilde = zeros(1,number_of_particles) ; tau_tilde = zeros(1,number_of_particles) ;
for i=1:number_of_particles for i=1:number_of_particles
% model resolution % model resolution
[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ... [ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
solve_model_for_online_filter(t,xparam(:,i),DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ; solve_model_for_online_filter(t,fore_xparam(:,i),DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
steadystate = ReducedForm.steadystate; if info==0
state_variables_steady_state = ReducedForm.state_variables_steady_state;
% Set local state space model (second-order approximation).
constant = ReducedForm.constant;
ghx = ReducedForm.ghx;
ghu = ReducedForm.ghu;
ghxx = ReducedForm.ghxx;
ghuu = ReducedForm.ghuu;
ghxu = ReducedForm.ghxu;
% particle likelihood contribution
yhat = bsxfun(@minus,StateVectors(:,i),state_variables_steady_state);
if pruning
yhat_ = bsxfun(@minus,StateVectors_(:,i),state_variables_steady_state);
[tmp, tmp_] = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,1),ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
else
tmp = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,1),ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
end
PredictionError = bsxfun(@minus,Y(t,:)',tmp(mf1,:));
% Replace Gaussian density with a Student density with 3 degrees of
% freedom for fat tails.
z = sum(PredictionError.*(ReducedForm.H\PredictionError),1) ;
tau_tilde(i) = weights(i).*(tpdf(z,3*ones(size(z)))+1e-99) ;
%tau_tilde(i) = weights(i).*exp(-.5*(const_lik+log(det(ReducedForm.H))+sum(PredictionError.*(ReducedForm.H\PredictionError),1))) ;
end
% particles selection
tau_tilde = tau_tilde/sum(tau_tilde) ;
indx = resample(0,tau_tilde',DynareOptions.particle);
StateVectors = StateVectors(:,indx) ;
if pruning
StateVectors_ = StateVectors_(:,indx) ;
end
xparam = bsxfun(@plus,(1-small_a).*m_bar,small_a.*xparam(:,indx)) ;
w_stage1 = weights(indx)./tau_tilde(indx) ;
% draw in the new distributions
wtilde = zeros(1,number_of_particles) ;
i = 1 ;
while i<=number_of_particles
candidate = xparam(:,i) + chol_sigma_bar*randn(number_of_parameters,1) ;
if all(candidate >= bounds.lb) && all(candidate <= bounds.ub)
xparam(:,i) = candidate ;
% model resolution for new parameters particles
[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
solve_model_for_online_filter(t,xparam(:,i),DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
steadystate = ReducedForm.steadystate; steadystate = ReducedForm.steadystate;
state_variables_steady_state = ReducedForm.state_variables_steady_state; state_variables_steady_state = ReducedForm.state_variables_steady_state;
% Set local state space model (second order approximation). % Set local state space model (second-order approximation).
constant = ReducedForm.constant; constant = ReducedForm.constant;
ghx = ReducedForm.ghx; ghx = ReducedForm.ghx;
ghu = ReducedForm.ghu; ghu = ReducedForm.ghu;
ghxx = ReducedForm.ghxx; ghxx = ReducedForm.ghxx;
ghuu = ReducedForm.ghuu; ghuu = ReducedForm.ghuu;
ghxu = ReducedForm.ghxu; ghxu = ReducedForm.ghxu;
% Get covariance matrices and structural shocks % particle likelihood contribution
epsilon = chol(ReducedForm.Q)'*randn(number_of_structural_innovations,1) ;
% compute particles likelihood contribution
yhat = bsxfun(@minus,StateVectors(:,i),state_variables_steady_state); yhat = bsxfun(@minus,StateVectors(:,i),state_variables_steady_state);
if pruning if pruning
yhat_ = bsxfun(@minus,StateVectors_(:,i),state_variables_steady_state); yhat_ = bsxfun(@minus,StateVectors_(:,i),state_variables_steady_state);
[tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2); [tmp, tmp_] = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,1),ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
StateVectors_(:,i) = tmp_(mf0,:) ;
else else
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2); tmp = local_state_space_iteration_2(yhat,zeros(number_of_structural_innovations,1),ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
end end
StateVectors(:,i) = tmp(mf0,:) ;
PredictionError = bsxfun(@minus,Y(t,:)',tmp(mf1,:)); PredictionError = bsxfun(@minus,Y(t,:)',tmp(mf1,:));
wtilde(i) = w_stage1(i)*exp(-.5*(const_lik+log(det(ReducedForm.H))+sum(PredictionError.*(ReducedForm.H\PredictionError),1))); % Replace Gaussian density with a Student density with 3 degrees of
i = i+1 ; % freedom for fat tails.
z = sum(PredictionError.*(ReducedForm.H\PredictionError),1) ;
tau_tilde(i) = weights(i).*(tpdf(z,3*ones(size(z)))+1e-99) ;
%tau_tilde(i) = weights(i).*exp(-.5*(const_lik+log(det(ReducedForm.H))+sum(PredictionError.*(ReducedForm.H\PredictionError),1))) ;
end
end
% particles selection
tau_tilde = tau_tilde/sum(tau_tilde) ;
indx = resample(0,tau_tilde',DynareOptions.particle);
StateVectors = StateVectors(:,indx) ;
xparam = fore_xparam(:,indx);
if pruning
StateVectors_ = StateVectors_(:,indx) ;
end
w_stage1 = weights(indx)./tau_tilde(indx) ;
% draw in the new distributions
wtilde = zeros(1,number_of_particles) ;
for i=1:number_of_particles
info=1 ;
while info==1
candidate = xparam(:,i) + chol_sigma_bar*randn(number_of_parameters,1) ;
if all(candidate >= bounds.lb) && all(candidate <= bounds.ub)
% model resolution for new parameters particles
[ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = ...
solve_model_for_online_filter(t,candidate,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults) ;
if info==0
xparam(:,i) = candidate ;
steadystate = ReducedForm.steadystate;
state_variables_steady_state = ReducedForm.state_variables_steady_state;
% Set local state space model (second order approximation).
constant = ReducedForm.constant;
ghx = ReducedForm.ghx;
ghu = ReducedForm.ghu;
ghxx = ReducedForm.ghxx;
ghuu = ReducedForm.ghuu;
ghxu = ReducedForm.ghxu;
% Get covariance matrices and structural shocks
epsilon = chol(ReducedForm.Q)'*randn(number_of_structural_innovations,1) ;
% compute particles likelihood contribution
yhat = bsxfun(@minus,StateVectors(:,i),state_variables_steady_state);
if pruning
yhat_ = bsxfun(@minus,StateVectors_(:,i),state_variables_steady_state);
[tmp, tmp_] = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,yhat_,steadystate,DynareOptions.threads.local_state_space_iteration_2);
StateVectors_(:,i) = tmp_(mf0,:) ;
else
tmp = local_state_space_iteration_2(yhat,epsilon,ghx,ghu,constant,ghxx,ghuu,ghxu,DynareOptions.threads.local_state_space_iteration_2);
end
StateVectors(:,i) = tmp(mf0,:) ;
PredictionError = bsxfun(@minus,Y(t,:)',tmp(mf1,:));
wtilde(i) = w_stage1(i)*exp(-.5*(const_lik+log(det(ReducedForm.H))+sum(PredictionError.*(ReducedForm.H\PredictionError),1)));
end
end
end end
end end
% normalization % normalization
...@@ -266,6 +278,10 @@ median_param = median_xparam(:,sample_size) ; ...@@ -266,6 +278,10 @@ median_param = median_xparam(:,sample_size) ;
TeX = DynareOptions.TeX; TeX = DynareOptions.TeX;
[nbplt,nr,nc,lr,lc,nstar] = pltorg(number_of_parameters); [nbplt,nr,nc,lr,lc,nstar] = pltorg(number_of_parameters);
nr = ceil(sqrt(number_of_parameters)) ;
nc = floor(sqrt(number_of_parameters));
nbplt = 1 ;
if TeX if TeX
fidTeX = fopen([Model.fname '_param_traj.tex'],'w'); fidTeX = fopen([Model.fname '_param_traj.tex'],'w');
...@@ -282,10 +298,9 @@ for plt = 1:nbplt, ...@@ -282,10 +298,9 @@ for plt = 1:nbplt,
TeXNAMES = []; TeXNAMES = [];
end end
hh = dyn_figure(DynareOptions.nodisplay,'Name','Parameters Trajectories'); hh = dyn_figure(DynareOptions.nodisplay,'Name','Parameters Trajectories');
for k=1:min(nstar,length(xparam)-(plt-1)*nstar) for k=1:length(xparam)
subplot(nr,nc,k) subplot(nr,nc,k)
kk = (plt-1)*nstar+k; [name,texname] = get_the_name(k,TeX,Model,EstimatedParameters,DynareOptions);
[name,texname] = get_the_name(kk,TeX,Model,EstimatedParameters,DynareOptions);
if TeX if TeX
if isempty(NAMES) if isempty(NAMES)
NAMES = name; NAMES = name;
...@@ -295,7 +310,7 @@ for plt = 1:nbplt, ...@@ -295,7 +310,7 @@ for plt = 1:nbplt,
TeXNAMES = char(TeXNAMES,texname); TeXNAMES = char(TeXNAMES,texname);
end end
end end
y = [mean_xparam(kk,:)' median_xparam(kk,:)' lb95_xparam(kk,:)' ub95_xparam(kk,:)' xparam(kk)*ones(sample_size,1)] ; y = [mean_xparam(k,:)' median_xparam(k,:)' lb95_xparam(k,:)' ub95_xparam(k,:)' xparam(k)*ones(sample_size,1)] ;
plot(z,y); plot(z,y);
hold on hold on
title(name,'interpreter','none') title(name,'interpreter','none')
...@@ -307,7 +322,7 @@ for plt = 1:nbplt, ...@@ -307,7 +322,7 @@ for plt = 1:nbplt,
if TeX if TeX
% TeX eps loader file % TeX eps loader file
fprintf(fidTeX,'\\begin{figure}[H]\n'); fprintf(fidTeX,'\\begin{figure}[H]\n');
for jj = 1:min(nstar,length(x)-(plt-1)*nstar) for jj = 1:length(x)
fprintf(fidTeX,'\\psfrag{%s}[1][][0.5][0]{%s}\n',deblank(NAMES(jj,:)),deblank(TeXNAMES(jj,:))); fprintf(fidTeX,'\\psfrag{%s}[1][][0.5][0]{%s}\n',deblank(NAMES(jj,:)),deblank(TeXNAMES(jj,:)));
end end
fprintf(fidTeX,'\\centering \n'); fprintf(fidTeX,'\\centering \n');
...@@ -329,10 +344,9 @@ for plt = 1:nbplt, ...@@ -329,10 +344,9 @@ for plt = 1:nbplt,
TeXNAMES = []; TeXNAMES = [];
end end
hh = dyn_figure(DynareOptions.nodisplay,'Name','Parameters Densities'); hh = dyn_figure(DynareOptions.nodisplay,'Name','Parameters Densities');
for k=1:min(nstar,length(xparam)-(plt-1)*nstar) for k=1:length(xparam)
subplot(nr,nc,k) subplot(nr,nc,k)
kk = (plt-1)*nstar+k; [name,texname] = get_the_name(k,TeX,Model,EstimatedParameters,DynareOptions);
[name,texname] = get_the_name(kk,TeX,Model,EstimatedParameters,DynareOptions);
if TeX if TeX
if isempty(NAMES) if isempty(NAMES)
NAMES = name; NAMES = name;
...@@ -342,8 +356,8 @@ for plt = 1:nbplt, ...@@ -342,8 +356,8 @@ for plt = 1:nbplt,
TeXNAMES = char(TeXNAMES,texname); TeXNAMES = char(TeXNAMES,texname);
end end
end end
optimal_bandwidth = mh_optimal_bandwidth(distrib_param(kk,:)',number_of_particles,bandwidth,kernel_function); optimal_bandwidth = mh_optimal_bandwidth(distrib_param(k,:)',number_of_particles,bandwidth,kernel_function);
[density(:,1),density(:,2)] = kernel_density_estimate(distrib_param(kk,:)',number_of_grid_points,... [density(:,1),density(:,2)] = kernel_density_estimate(distrib_param(k,:)',number_of_grid_points,...
number_of_particles,optimal_bandwidth,kernel_function); number_of_particles,optimal_bandwidth,kernel_function);
plot(density(:,1),density(:,2)); plot(density(:,1),density(:,2));
hold on hold on
...@@ -356,7 +370,7 @@ for plt = 1:nbplt, ...@@ -356,7 +370,7 @@ for plt = 1:nbplt,
if TeX if TeX
% TeX eps loader file % TeX eps loader file
fprintf(fidTeX,'\\begin{figure}[H]\n'); fprintf(fidTeX,'\\begin{figure}[H]\n');
for jj = 1:min(nstar,length(x)-(plt-1)*nstar) for jj = 1:length(x)
fprintf(fidTeX,'\\psfrag{%s}[1][][0.5][0]{%s}\n',deblank(NAMES(jj,:)),deblank(TeXNAMES(jj,:))); fprintf(fidTeX,'\\psfrag{%s}[1][][0.5][0]{%s}\n',deblank(NAMES(jj,:)),deblank(TeXNAMES(jj,:)));
end end
fprintf(fidTeX,'\\centering \n'); fprintf(fidTeX,'\\centering \n');
......
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