Commit 857168dd authored by Frédéric Karamé's avatar Frédéric Karamé

Added routines for Dynamic Striated Metropolis Hastings.

parent 84d213ea
function [ ix2, temperedlogpost, loglik, ModelName, MetropolisFolder, npar, NumberOfParticles, bayestopt_] = ...
DSMH_initialization(TargetFun, xparam1, mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
% function [ ix2, ilogpo2, ModelName, MetropolisFolder, FirstBlock, FirstLine, npar, NumberOfParticles, bayestopt_] = ...
% DSMH_initialization(TargetFun, xparam1, mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
% Dynamic Striated Metropolis-Hastings initialization.
%
% INPUTS
% o TargetFun [char] string specifying the name of the objective
% function (tempered posterior kernel and likelihood).
% 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
%
% OUTPUTS
% o ix2 [double] (NumberOfParticles*npar) vector of starting points for different chains
% o ilogpo2 [double] (NumberOfParticles*1) vector of initial posterior values for different chains
% o iloglik2 [double] (NumberOfParticles*1) vector of initial likelihood values for different chains
% o ModelName [string] name of the mod-file
% o MetropolisFolder [string] path to the Metropolis subfolder
% o npar [scalar] number of parameters estimated
% o NumberOfParticles [scalar] Number of particles requested for the parameters distributions
% o bayestopt_ [structure] estimation options structure
%
% SPECIAL REQUIREMENTS
% None.
% Copyright (C) 2006-2017 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 <http://www.gnu.org/licenses/>.
%Initialize outputs
ix2 = [];
ilogpo2 = [];
iloglik2 = [];
ModelName = [];
MetropolisFolder = [];
npar = [];
NumberOfParticles = [];
ModelName = M_.fname;
if ~isempty(M_.bvar)
ModelName = [ModelName '_bvar'];
end
MetropolisFolder = CheckPath('dsmh',M_.dname);
BaseName = [MetropolisFolder filesep ModelName];
NumberOfParticles = options_.dsmh.number_of_particles; %Number of particles for the parameters
npar = length(xparam1);
% Here we start a new DS Metropolis-Hastings, previous draws are discarded.
disp('Estimation::dsmh: Initialization...')
% Delete old dsmh files if any...
files = dir([BaseName '_dsmh*_blck*.mat']);
%if length(files)
% delete([BaseName '_dsmh*_blck*.mat']);
% disp('Estimation::smc: Old dsmh-files successfully erased!')
%end
% Delete old log file.
file = dir([ MetropolisFolder '/dsmh.log']);
%if length(file)
% delete([ MetropolisFolder '/dsmh.log']);
% disp('Estimation::dsmh: Old dsmh.log file successfully erased!')
% disp('Estimation::dsmh: Creation of a new dsmh.log file.')
%end
fidlog = fopen([MetropolisFolder '/dsmh.log'],'w');
fprintf(fidlog,'%% DSMH log file (Dynare).\n');
fprintf(fidlog,['%% ' datestr(now,0) '.\n']);
fprintf(fidlog,' \n\n');
fprintf(fidlog,'%% Session 1.\n');
fprintf(fidlog,' \n');
prior_draw(bayestopt_,options_.prior_trunc);
% Find initial values for the NumberOfParticles chains...
set_dynare_seed('default');
fprintf(fidlog,[' Initial values of the parameters:\n']);
disp('Estimation::dsmh: Searching for initial values...');
ix2 = zeros(npar,NumberOfParticles);
temperedlogpost = zeros(NumberOfParticles,1);
loglik = zeros(NumberOfParticles,1);
%stderr = sqrt(bsxfun(@power,mh_bounds.ub-mh_bounds.lb,2)/12)/10;
for j=1:NumberOfParticles
validate = 0;
while validate == 0
candidate = prior_draw()';
% candidate = xparam1(:) + 0.001*randn(npar,1);%bsxfun(@times,stderr,randn(npar,1)) ;
if all(candidate(:) >= mh_bounds.lb) && all(candidate(:) <= mh_bounds.ub)
ix2(:,j) = candidate ;
[temperedlogpost(j),loglik(j)] = tempered_likelihood(TargetFun,candidate,0.0,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
if isfinite(loglik(j)) % if returned log-density is Inf or Nan (penalized value)
validate = 1;
end
end
end
end
fprintf(fidlog,' \n');
disp('Estimation::dsmh: Initial values found!')
skipline()
function DSMH_sampler(TargetFun,xparam1,mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
% function DSMH_sampler(TargetFun,ProposalFun,xparam1,sampler_options,mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
% Dynamic Striated Metropolis-Hastings algorithm.
%
% INPUTS
% o TargetFun [char] string specifying the name of the objective
% function (posterior kernel).
% o ProposalFun [char] string specifying the name of the proposal
% density
% o xparam1 [double] (p*1) vector of parameters to be estimated (initial values).
% o sampler_options structure
% .invhess [double] (p*p) matrix, posterior covariance matrix (at the mode).
% 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 (C) 2006-2017 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 <http://www.gnu.org/licenses/>.
lambda = exp(bsxfun(@minus,options_.dsmh.H,1:1:options_.dsmh.H)/(options_.dsmh.H-1)*log(options_.dsmh.lambda1));
c = 55 ;
% Step 0: Initialization of the sampler
[ param, tlogpost_iminus1, loglik, ~, ~, npar, nparticles, bayestopt_] = ...
DSMH_initialization(TargetFun, xparam1, mh_bounds, dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_);
ESS = zeros(options_.dsmh.H,1) ;
zhat = 1 ;
% The DSMH starts here
for i=1:options_.dsmh.H
disp('');
disp('Tempered iteration');
disp(i) ;
% Step 1: sort the densities and compute IS weigths
[tlogpost_iminus1,loglik,param] = sort_matrices(tlogpost_iminus1,loglik,param) ;
[tlogpost_i,weights,zhat,ESS,mu,Omegachol] = compute_IS_weights_and_moments(param,tlogpost_iminus1,loglik,lambda,i,zhat,ESS) ;
% Step 2: tune c_i
c = tune_c(TargetFun,param,tlogpost_i,lambda,i,c,Omegachol,weights,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
% Step 3: Metropolis step
[param,tlogpost_iminus1,loglik] = mutation_DSMH(TargetFun,param,tlogpost_i,tlogpost_iminus1,loglik,lambda,i,c,Omegachol,weights,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
end
weights = exp(loglik*(lambda(end)-lambda(end-1)));
weights = weights/sum(weights);
indx_resmpl = DSMH_resampling(weights,rand(1,1),nparticles);
distrib_param = param(:,indx_resmpl);
%% Plot parameters densities
TeX = options_.TeX;
[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.
for plt = 1:nbplt,
if TeX
NAMES = [];
TeXNAMES = [];
end
hh = dyn_figure(options_.nodisplay,'Name','Parameters Densities');
for k=1:min(nstar,npar-(plt-1)*nstar)
subplot(nr,nc,k)
kk = (plt-1)*nstar+k;
[name,texname] = get_the_name(kk,TeX,M_,estim_params_,options_);
if TeX
if isempty(NAMES)
NAMES = name;
TeXNAMES = texname;
else
NAMES = char(NAMES,name);
TeXNAMES = char(TeXNAMES,texname);
end
end
optimal_bandwidth = mh_optimal_bandwidth(distrib_param(kk,:)',nparticles,bandwidth,kernel_function);
[density(:,1),density(:,2)] = kernel_density_estimate(distrib_param(kk,:)',number_of_grid_points,...
nparticles,optimal_bandwidth,kernel_function);
plot(density(:,1),density(:,2));
hold on
title(name,'interpreter','none')
hold off
axis tight
drawnow
end
dyn_saveas(hh,[ M_.fname '_param_density' int2str(plt) ],options_.nodisplay,options_.graph_format);
if TeX
% TeX eps loader file
fprintf(fidTeX,'\\begin{figure}[H]\n');
for jj = 1:min(nstar,length(x)-(plt-1)*nstar)
fprintf(fidTeX,'\\psfrag{%s}[1][][0.5][0]{%s}\n',deblank(NAMES(jj,:)),deblank(TeXNAMES(jj,:)));
end
fprintf(fidTeX,'\\centering \n');
fprintf(fidTeX,'\\includegraphics[scale=0.5]{%s_ParametersDensities%s}\n',M_.fname,int2str(plt));
fprintf(fidTeX,'\\caption{ParametersDensities.}');
fprintf(fidTeX,'\\label{Fig:ParametersDensities:%s}\n',int2str(plt));
fprintf(fidTeX,'\\end{figure}\n');
fprintf(fidTeX,' \n');
end
end
function indx = DSMH_resampling(weights,noise,number)
indx = zeros(number,1);
cumweights = cumsum(weights);
randvec = (transpose(1:number)-1+noise(:))/number;
j = 1;
for i=1:number
while (randvec(i)>cumweights(j))
j = j+1;
end
indx(i) = j;
end
function [tlogpost_iminus1,loglik,param] = sort_matrices(tlogpost_iminus1,loglik,param)
[~,indx_ord] = sortrows(tlogpost_iminus1);
tlogpost_iminus1 = tlogpost_iminus1(indx_ord);
param = param(:,indx_ord);
loglik = loglik(indx_ord);
function [tlogpost_i,weights,zhat,ESS,mu,Omegachol] = compute_IS_weights_and_moments(param,tlogpost_iminus1,loglik,lambda,i,zhat,ESS)
if i==1
tlogpost_i = tlogpost_iminus1 + loglik*lambda(i);
else
tlogpost_i = tlogpost_iminus1 + loglik*(lambda(i)-lambda(i-1));
end
weights = exp(tlogpost_i-tlogpost_iminus1);
zhat = (mean(weights))*zhat ;
weights = weights/sum(weights);
ESS(i) = 1/sum(weights.^2);
% estimates of mean and variance
mu = param*weights;
z = bsxfun(@minus,param,mu);
Omega = z*diag(weights)*z';
Omegachol = chol(Omega)';
function c = tune_c(TargetFun,param,tlogpost_i,lambda,i,c,Omegachol,weights,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_)
disp('tuning c_i...');
disp('Initial value =');
disp(c) ;
npar = size(param,1);
lower_prob = (.5*(options_.dsmh.alpha0+options_.dsmh.alpha1))^5;
upper_prob = (.5*(options_.dsmh.alpha0+options_.dsmh.alpha1))^(1/5);
stop=0 ;
while stop==0
acpt = 0.0;
indx_resmpl = DSMH_resampling(weights,rand(1,1),options_.dsmh.G);
param0 = param(:,indx_resmpl);
tlogpost0 = tlogpost_i(indx_resmpl);
for j=1:options_.dsmh.G
for l=1:options_.dsmh.K
validate = 0;
while validate == 0
candidate = param0(:,j) + sqrt(c)*Omegachol*randn(npar,1);
if all(candidate >= mh_bounds.lb) && all(candidate <= mh_bounds.ub)
[tlogpostx,loglikx] = tempered_likelihood(TargetFun,candidate,lambda(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-tlogpost0(j)) % accept
acpt = acpt + 1/(options_.dsmh.G*options_.dsmh.K);
param0(:,j)= candidate;
tlogpost0(j) = tlogpostx;
end
end
end
end
end
end
disp('Acceptation rate =') ;
disp(acpt) ;
if options_.dsmh.alpha0<=acpt && acpt<=options_.dsmh.alpha1
disp('done!');
stop=1;
else
if acpt<lower_prob
c = c/5;
elseif lower_prob<=acpt && acpt<=upper_prob
c = c*log(.5*(options_.dsmh.alpha0+options_.dsmh.alpha1))/log(acpt);
else
c = 5*c;
end
disp('Trying with c= ') ;
disp(c)
end
end
function [out_param,out_tlogpost_iminus1,out_loglik] = mutation_DSMH(TargetFun,param,tlogpost_i,tlogpost_iminus1,loglik,lambda,i,c,Omegachol,weights,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_)
indx_levels = (1:1:options_.dsmh.M-1)*options_.dsmh.N*options_.dsmh.G/options_.dsmh.M;
npar = size(param,1) ;
p = 1/(10*options_.dsmh.tau);
disp('Metropolis step...');
% build the dynamic grid of levels
levels = [0.0;tlogpost_iminus1(indx_levels)];
% initialize the outputs
out_param = param;
out_tlogpost_iminus1 = tlogpost_i;
out_loglik = loglik;
% resample and initialize the starting groups
indx_resmpl = DSMH_resampling(weights,rand(1,1),options_.dsmh.G);
param0 = param(:,indx_resmpl);
tlogpost_iminus10 = tlogpost_iminus1(indx_resmpl);
tlogpost_i0 = tlogpost_i(indx_resmpl);
loglik0 = loglik(indx_resmpl);
% Start the Metropolis
for l=1:options_.dsmh.N*options_.dsmh.tau
for j=1:options_.dsmh.G
u1 = rand(1,1);
u2 = rand(1,1);
if u1<p
k=1 ;
for m=1:options_.dsmh.M-1
if levels(m)<=tlogpost_iminus10(j) && tlogpost_iminus10(j)<levels(m+1)
k = m+1;
break
end
end
indx = floor( (k-1)*options_.dsmh.N*options_.dsmh.G/options_.dsmh.M+1 + u2*(options_.dsmh.N*options_.dsmh.G/options_.dsmh.M-1) );
if i==1
alp = (loglik(indx)-loglik0(j))*lambda(i);
else
alp = (loglik(indx)-loglik0(j))*(lambda(i)-lambda(i-1));
end
if u2<exp(alp)
param0(:,j) = param(:,indx);
tlogpost_i0(j) = tlogpost_i(indx);
loglik0(j) = loglik(indx);
tlogpost_iminus10(j) = tlogpost_iminus1(indx);
end
else
validate= 0;
while validate==0
candidate = param0(:,j) + sqrt(c)*Omegachol*randn(npar,1);
if all(candidate(:) >= mh_bounds.lb) && all(candidate(:) <= mh_bounds.ub)
[tlogpostx,loglikx] = tempered_likelihood(TargetFun,candidate,lambda(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 u2<exp(tlogpostx-tlogpost_i0(j)) % accept
param0(:,j) = candidate;
tlogpost_i0(j) = tlogpostx;
loglik0(j) = loglikx;
if i==1
tlogpost_iminus10(j) = tlogpostx-loglikx*lambda(i);
else
tlogpost_iminus10(j) = tlogpostx-loglikx*(lambda(i)-lambda(i-1));
end
end
end
end
end
end
end
if mod(l,options_.dsmh.tau)==0
rang = (l/options_.dsmh.tau-1)*options_.dsmh.G+1:l*options_.dsmh.G/options_.dsmh.tau;
out_param(:,rang) = param0;
out_tlogpost_iminus1(rang) = tlogpost_i0;
out_loglik(rang) = loglik0;
end
end
\ No newline at end of file
function [tlogpostkern,loglik] = tempered_likelihood(TargetFun,xparam1,lambda,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,bounds,oo_)
logpostkern = -feval(TargetFun,xparam1,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,bounds,oo_);
logprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
loglik = logpostkern-logprior ;
tlogpostkern = lambda*loglik + logprior;
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