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dynare/matlab/Herbst_Schorfheide_sampler.m

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Matlab
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function Herbst_Schorfheide_sampler(TargetFun,xparam1,mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
% function Herbst_Schorfheide_sampler(TargetFun,xparam1,mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
% SMC sampler from JAE 2014 .
%
% INPUTS
% o TargetFun [char] string specifying the name of the objective
% function (posterior kernel).
% o xparam1 [double] (p*1) vector of parameters to be estimated (initial values).
% o mh_bounds [double] (p*2) matrix defining lower and upper bounds for the parameters.
% o dataset_ data structure
% o dataset_info dataset info structure
% o options_ options structure
% o M_ model structure
% o estim_params_ estimated parameters structure
% o bayestopt_ estimation options structure
% o oo_ outputs structure
%
% SPECIAL REQUIREMENTS
% None.
%
% PARALLEL CONTEXT
% The most computationally intensive part of this function may be executed
% in parallel. The code suitable to be executed in
% parallel on multi core or cluster machine (in general a 'for' cycle)
% has been removed from this function and been placed in the posterior_sampler_core.m funtion.
%
% The DYNARE parallel packages comprise a i) set of pairs of Matlab functions that can be executed in
% parallel and called name_function.m and name_function_core.m and ii) a second set of functions used
% to manage the parallel computations.
%
% This function was the first function to be parallelized. Later, other
% functions have been parallelized using the same methodology.
% Then the comments write here can be used for all the other pairs of
% parallel functions and also for management functions.
% Copyright © 2006-2023 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 <https://www.gnu.org/licenses/>.
% Create the tempering schedule
phi = bsxfun(@power,(bsxfun(@minus,1:1:options_.posterior_sampler_options.HSsmc.nphi,1)/(options_.posterior_sampler_options.HSsmc.nphi-1)),options_.posterior_sampler_options.HSsmc.lambda) ;
% tuning for MH algorithms matrices
zhat = 0 ; % normalization constant
csim = zeros(options_.posterior_sampler_options.HSsmc.nphi,1) ; % scale parameter
ESSsim = zeros(options_.posterior_sampler_options.HSsmc.nphi,1) ; % ESS
acptsim = zeros(options_.posterior_sampler_options.HSsmc.nphi,1) ; % average acceptance rate
% Step 0: Initialization of the sampler
[ param, tlogpost_i, loglik, bayestopt_] = ...
SMC_samplers_initialization(TargetFun, xparam1, mh_bounds, dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_,options_.posterior_sampler_options.HSsmc.nparticles);
weights = ones(options_.posterior_sampler_options.HSsmc.nparticles,1)/options_.posterior_sampler_options.HSsmc.nparticles ;
% The Herbst and Schorfheide sampler starts here
for i=2:options_.posterior_sampler_options.HSsmc.nphi
% (a) Correction
% incremental weights
incwt = exp((phi(i)-phi(i-1))*loglik) ;
% update weights
weights = bsxfun(@times,weights,incwt) ;
sum_weights = sum(weights) ;
zhat = zhat + log(sum_weights) ;
% normalize weights
weights = weights/sum_weights ;
% (b) Selection
ESSsim(i) = 1/sum(weights.^2) ;
if (ESSsim(i) < options_.posterior_sampler_options.HSsmc.nparticles/2)
indx_resmpl = smc_resampling(weights,rand(1,1),options_.posterior_sampler_options.HSsmc.nparticles) ;
param = param(:,indx_resmpl) ;
loglik = loglik(indx_resmpl) ;
tlogpost_i = tlogpost_i(indx_resmpl) ;
weights = ones(options_.posterior_sampler_options.HSsmc.nparticles,1)/options_.posterior_sampler_options.HSsmc.nparticles ;
end
% (c) Mutation
options_.posterior_sampler_options.HSsmc.c = options_.posterior_sampler_options.HSsmc.c*modified_logit(0.95,0.1,16.0,options_.posterior_sampler_options.HSsmc.acpt-options_.posterior_sampler_options.HSsmc.trgt) ;
% Calculate estimates of mean and variance
mu = param*weights ;
z = bsxfun(@minus,param,mu) ;
R = z*(bsxfun(@times,z',weights)) ;
Rchol = chol(R)' ;
% Mutation
if options_.posterior_sampler_options.HSsmc.option_mutation==1
[param,tlogpost_i,loglik,options_.posterior_sampler_options.HSsmc.acpt] = mutation_RW(TargetFun,param,tlogpost_i,loglik,phi,i,options_.posterior_sampler_options.HSsmc.c*Rchol,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_) ;
elseif options_.posterior_sampler_options.HSsmc.option_mutation==2
inv_R = inv(options_.posterior_sampler_options.HSsmc.c^2*R) ;
Rdiagchol = sqrt(diag(R)) ;
[param,tlogpost_i,loglik,options_.posterior_sampler_options.HSsmc.acpt] = mutation_Mixture(TargetFun,param,tlogpost_i,loglik,phi,i,options_.posterior_sampler_options.HSsmc.c*Rchol,options_.posterior_sampler_options.HSsmc.c*Rdiagchol,inv_R,mu,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_) ;
end
acptsim(i) = options_.posterior_sampler_options.HSsmc.acpt ;
csim(i) = options_.posterior_sampler_options.HSsmc.c ;
% print information
fprintf(' Iteration = %5.0f / %5.0f \n', i, options_.posterior_sampler_options.HSsmc.nphi);
fprintf(' phi = %5.4f \n', phi(i));
fprintf(' Neff = %5.4f \n', ESSsim(i));
fprintf(' %accept. = %5.4f \n', acptsim(i));
end
indx_resmpl = smc_resampling(weights,rand(1,1),options_.posterior_sampler_options.HSsmc.nparticles);
distrib_param = param(:,indx_resmpl);
fprintf(' Log_lik = %5.4f \n', zhat);
mean_xparam = mean(distrib_param,2);
npar = length(xparam1) ;
%mat_var_cov = bsxfun(@minus,distrib_param,mean_xparam) ;
%mat_var_cov = (mat_var_cov*mat_var_cov')/(options_.posterior_sampler_options.HSsmc.nparticles-1) ;
%std_xparam = sqrt(diag(mat_var_cov)) ;
lb95_xparam = zeros(npar,1) ;
ub95_xparam = zeros(npar,1) ;
for i=1:npar
temp = sortrows(distrib_param(i,:)') ;
lb95_xparam(i) = temp(0.025*options_.posterior_sampler_options.HSsmc.nparticles) ;
ub95_xparam(i) = temp(0.975*options_.posterior_sampler_options.HSsmc.nparticles) ;
end
TeX = options_.TeX;
str = sprintf(' Param. \t Lower Bound (95%%) \t Mean \t Upper Bound (95%%)');
for l=1:npar
[name,~] = get_the_name(l,TeX,M_,estim_params_,options_.varobs);
str = sprintf('%s\n %s \t\t %5.4f \t\t %7.5f \t\t %5.4f', str, name, lb95_xparam(l), mean_xparam(l), ub95_xparam(l));
end
disp([str])
disp('')
%% Plot parameters densities
[nbplt,nr,nc,lr,lc,nstar] = pltorg(npar);
if TeX
fidTeX = fopen([M_.fname '_param_density.tex'],'w');
fprintf(fidTeX,'%% TeX eps-loader file generated by DSMH.m (Dynare).\n');
fprintf(fidTeX,['%% ' datestr(now,0) '\n']);
fprintf(fidTeX,' \n');
end
number_of_grid_points = 2^9; % 2^9 = 512 !... Must be a power of two.
bandwidth = 0; % Rule of thumb optimal bandwidth parameter.
kernel_function = 'gaussian'; % Gaussian kernel for Fast Fourier Transform approximation.
plt = 1 ;
%for plt = 1:nbplt,
if TeX
NAMES = [];
TeXNAMES = [];
end
hh_fig = dyn_figure(options_.nodisplay,'Name','Parameters Densities');
for k=1:npar %min(nstar,npar-(plt-1)*nstar)
subplot(ceil(sqrt(npar)),floor(sqrt(npar)),k)
%kk = (plt-1)*nstar+k;
[name,texname] = get_the_name(k,TeX,M_,estim_params_,options_.varobs);
optimal_bandwidth = mh_optimal_bandwidth(distrib_param(k,:)',options_.posterior_sampler_options.HSsmc.nparticles,bandwidth,kernel_function);
[density(:,1),density(:,2)] = kernel_density_estimate(distrib_param(k,:)',number_of_grid_points,...
options_.posterior_sampler_options.HSsmc.nparticles,optimal_bandwidth,kernel_function);
plot(density(:,1),density(:,2));
hold on
if TeX
title(texname,'interpreter','latex')
else
title(name,'interpreter','none')
end
hold off
axis tight
drawnow
end
dyn_saveas(hh_fig,[ M_.fname '_param_density' int2str(plt) ],options_.nodisplay,options_.graph_format);
if TeX && any(strcmp('eps',cellstr(options_.graph_format)))
% TeX eps loader file
fprintf(fidTeX,'\\begin{figure}[H]\n');
fprintf(fidTeX,'\\centering \n');
fprintf(fidTeX,'\\includegraphics[width=%2.2f\\textwidth]{%_param_density%s}\n',min(k/floor(sqrt(npar)),1),M_.fname,int2str(plt));
fprintf(fidTeX,'\\caption{Parameter densities based on the Herbst/Schorfheide sampler.}');
fprintf(fidTeX,'\\label{Fig:ParametersDensities:%s}\n',int2str(plt));
fprintf(fidTeX,'\\end{figure}\n');
fprintf(fidTeX,' \n');
end
%end
function [param,tlogpost_i,loglik,acpt] = mutation_RW(TargetFun,param,tlogpost_i,loglik,phi,i,cRchol,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_)
acpt = 0.0 ;
tlogpost_i = tlogpost_i + (phi(i)-phi(i-1))*loglik ;
for j=1:options_.posterior_sampler_options.HSsmc.nparticles
validate= 0;
while validate==0
candidate = param(:,j) + cRchol*randn(size(param,1),1) ;
if all(candidate(:) >= mh_bounds.lb) && all(candidate(:) <= mh_bounds.ub)
[tlogpostx,loglikx] = tempered_likelihood(TargetFun,candidate,phi(i),dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
if isfinite(loglikx) % if returned log-density is not Inf or Nan (penalized value)
validate = 1;
if rand(1,1)<exp(tlogpostx-tlogpost_i(j)) % accept
acpt = acpt + 1 ;
param(:,j) = candidate;
loglik(j) = loglikx;
tlogpost_i(j) = tlogpostx;
end
end
end
end
end
acpt = acpt/options_.posterior_sampler_options.HSsmc.nparticles;
function [param,tlogpost_i,loglik,acpt] = mutation_Mixture(TargetFun,param,tlogpost_i,loglik,phi,i,cRchol,cRdiagchol,invR,mu,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_)
acpt = 0.0 ;
tlogpost_i = tlogpost_i + (phi(i)-phi(i-1))*loglik ;
for j=1:options_.posterior_sampler_options.HSsmc.nparticles
qx = 0 ;
q0 = 0 ;
alpind = rand(1,1) ;
validate= 0;
while validate==0
if alpind<options_.posterior_sampler_options.HSsmc.alp % RW, no need to modify qx and q0
candidate = param(:,j) + cRchol*randn(size(param,1),1);
elseif alpind<options_.posterior_sampler_options.HSsmc.alp + (1-options_.posterior_sampler_options.HSsmc.alp/2) % random walk with diagonal cov no need to modify qx and q0
candidate = param(:,j) + cRdiagchol*randn(size(param,1),1);
else % Proposal densities
candidate = mu + cRchol*randn(size(param,1),1);
qx = -.5*(candidate-mu)'*invR*(candidate-mu) ; % no need of the constants in the acceptation rule
q0 = -.5*(param(:,j)-mu)'*invR*(param(:,j)-mu) ;
end
if all(candidate(:) >= mh_bounds.lb) && all(candidate(:) <= mh_bounds.ub)
[tlogpostx,loglikx] = tempered_likelihood(TargetFun,candidate,phi(i),dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
if isfinite(loglikx) % if returned log-density is not Inf or Nan (penalized value)
validate = 1;
if rand(1,1)<exp((tlogpostx-qx)-(tlogpost_i(j)-q0)) % accept
acpt = acpt + 1 ;
param(:,j) = candidate;
loglik(j) = loglikx;
tlogpost_i(j) = tlogpostx;
end
end
end
end
end
acpt = acpt/options_.posterior_sampler_options.HSsmc.nparticles;
function x = modified_logit(a,b,c,d)
tmp = exp(c*d) ;
x = a + b*tmp/(1 + tmp) ;
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