Added routines for Dynamic Striated Metropolis Hastings.
Frédéric Karamé
parent
84d213ea3e
commit
857168ddf8
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function [ ix2, temperedlogpost, loglik, ModelName, MetropolisFolder, npar, NumberOfParticles, bayestopt_] = ...
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DSMH_initialization(TargetFun, xparam1, mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
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% function [ ix2, ilogpo2, ModelName, MetropolisFolder, FirstBlock, FirstLine, npar, NumberOfParticles, bayestopt_] = ...
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% DSMH_initialization(TargetFun, xparam1, mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
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% Dynamic Striated Metropolis-Hastings initialization.
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%
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% INPUTS
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% o TargetFun [char] string specifying the name of the objective
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% function (tempered posterior kernel and likelihood).
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% o xparam1 [double] (p*1) vector of parameters to be estimated (initial values).
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% o mh_bounds [double] (p*2) matrix defining lower and upper bounds for the parameters.
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% o dataset_ data structure
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% o dataset_info dataset info structure
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% o options_ options structure
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% o M_ model structure
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% o estim_params_ estimated parameters structure
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% o bayestopt_ estimation options structure
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% o oo_ outputs structure
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%
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% OUTPUTS
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% o ix2 [double] (NumberOfParticles*npar) vector of starting points for different chains
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% o ilogpo2 [double] (NumberOfParticles*1) vector of initial posterior values for different chains
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% o iloglik2 [double] (NumberOfParticles*1) vector of initial likelihood values for different chains
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% o ModelName [string] name of the mod-file
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% o MetropolisFolder [string] path to the Metropolis subfolder
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% o npar [scalar] number of parameters estimated
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% o NumberOfParticles [scalar] Number of particles requested for the parameters distributions
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% o bayestopt_ [structure] estimation options structure
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%
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% SPECIAL REQUIREMENTS
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% None.
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% Copyright (C) 2006-2017 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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%Initialize outputs
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ix2 = [];
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ilogpo2 = [];
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iloglik2 = [];
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ModelName = [];
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MetropolisFolder = [];
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npar = [];
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NumberOfParticles = [];
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ModelName = M_.fname;
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if ~isempty(M_.bvar)
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ModelName = [ModelName '_bvar'];
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end
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MetropolisFolder = CheckPath('dsmh',M_.dname);
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BaseName = [MetropolisFolder filesep ModelName];
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NumberOfParticles = options_.dsmh.number_of_particles; %Number of particles for the parameters
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npar = length(xparam1);
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% Here we start a new DS Metropolis-Hastings, previous draws are discarded.
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disp('Estimation::dsmh: Initialization...')
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% Delete old dsmh files if any...
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files = dir([BaseName '_dsmh*_blck*.mat']);
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%if length(files)
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% delete([BaseName '_dsmh*_blck*.mat']);
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% disp('Estimation::smc: Old dsmh-files successfully erased!')
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%end
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% Delete old log file.
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file = dir([ MetropolisFolder '/dsmh.log']);
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%if length(file)
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% delete([ MetropolisFolder '/dsmh.log']);
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% disp('Estimation::dsmh: Old dsmh.log file successfully erased!')
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% disp('Estimation::dsmh: Creation of a new dsmh.log file.')
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%end
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fidlog = fopen([MetropolisFolder '/dsmh.log'],'w');
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fprintf(fidlog,'%% DSMH log file (Dynare).\n');
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fprintf(fidlog,['%% ' datestr(now,0) '.\n']);
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fprintf(fidlog,' \n\n');
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fprintf(fidlog,'%% Session 1.\n');
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fprintf(fidlog,' \n');
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prior_draw(bayestopt_,options_.prior_trunc);
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% Find initial values for the NumberOfParticles chains...
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set_dynare_seed('default');
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fprintf(fidlog,[' Initial values of the parameters:\n']);
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disp('Estimation::dsmh: Searching for initial values...');
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ix2 = zeros(npar,NumberOfParticles);
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temperedlogpost = zeros(NumberOfParticles,1);
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loglik = zeros(NumberOfParticles,1);
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%stderr = sqrt(bsxfun(@power,mh_bounds.ub-mh_bounds.lb,2)/12)/10;
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for j=1:NumberOfParticles
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validate = 0;
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while validate == 0
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candidate = prior_draw()';
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% candidate = xparam1(:) + 0.001*randn(npar,1);%bsxfun(@times,stderr,randn(npar,1)) ;
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if all(candidate(:) >= mh_bounds.lb) && all(candidate(:) <= mh_bounds.ub)
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ix2(:,j) = candidate ;
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[temperedlogpost(j),loglik(j)] = tempered_likelihood(TargetFun,candidate,0.0,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
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if isfinite(loglik(j)) % if returned log-density is Inf or Nan (penalized value)
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validate = 1;
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end
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end
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end
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end
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fprintf(fidlog,' \n');
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disp('Estimation::dsmh: Initial values found!')
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skipline()
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@ -0,0 +1,303 @@
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function DSMH_sampler(TargetFun,xparam1,mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
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% function DSMH_sampler(TargetFun,ProposalFun,xparam1,sampler_options,mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
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% Dynamic Striated Metropolis-Hastings algorithm.
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%
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% INPUTS
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% o TargetFun [char] string specifying the name of the objective
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% function (posterior kernel).
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% o ProposalFun [char] string specifying the name of the proposal
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% density
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% o xparam1 [double] (p*1) vector of parameters to be estimated (initial values).
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% o sampler_options structure
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% .invhess [double] (p*p) matrix, posterior covariance matrix (at the mode).
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% o mh_bounds [double] (p*2) matrix defining lower and upper bounds for the parameters.
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% o dataset_ data structure
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% o dataset_info dataset info structure
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% o options_ options structure
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% o M_ model structure
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% o estim_params_ estimated parameters structure
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% o bayestopt_ estimation options structure
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% o oo_ outputs structure
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%
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% SPECIAL REQUIREMENTS
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% None.
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%
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% PARALLEL CONTEXT
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% The most computationally intensive part of this function may be executed
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% in parallel. The code suitable to be executed in
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% parallel on multi core or cluster machine (in general a 'for' cycle)
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% has been removed from this function and been placed in the posterior_sampler_core.m funtion.
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%
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% The DYNARE parallel packages comprise a i) set of pairs of Matlab functions that can be executed in
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% parallel and called name_function.m and name_function_core.m and ii) a second set of functions used
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% to manage the parallel computations.
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%
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% This function was the first function to be parallelized. Later, other
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% functions have been parallelized using the same methodology.
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% Then the comments write here can be used for all the other pairs of
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% parallel functions and also for management functions.
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% Copyright (C) 2006-2017 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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lambda = exp(bsxfun(@minus,options_.dsmh.H,1:1:options_.dsmh.H)/(options_.dsmh.H-1)*log(options_.dsmh.lambda1));
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c = 55 ;
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% Step 0: Initialization of the sampler
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[ param, tlogpost_iminus1, loglik, ~, ~, npar, nparticles, bayestopt_] = ...
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DSMH_initialization(TargetFun, xparam1, mh_bounds, dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_);
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ESS = zeros(options_.dsmh.H,1) ;
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zhat = 1 ;
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% The DSMH starts here
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for i=1:options_.dsmh.H
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disp('');
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disp('Tempered iteration');
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disp(i) ;
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% Step 1: sort the densities and compute IS weigths
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[tlogpost_iminus1,loglik,param] = sort_matrices(tlogpost_iminus1,loglik,param) ;
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[tlogpost_i,weights,zhat,ESS,mu,Omegachol] = compute_IS_weights_and_moments(param,tlogpost_iminus1,loglik,lambda,i,zhat,ESS) ;
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% Step 2: tune c_i
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c = tune_c(TargetFun,param,tlogpost_i,lambda,i,c,Omegachol,weights,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
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% Step 3: Metropolis step
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[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_);
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end
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weights = exp(loglik*(lambda(end)-lambda(end-1)));
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weights = weights/sum(weights);
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indx_resmpl = DSMH_resampling(weights,rand(1,1),nparticles);
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distrib_param = param(:,indx_resmpl);
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%% Plot parameters densities
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TeX = options_.TeX;
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[nbplt,nr,nc,lr,lc,nstar] = pltorg(npar);
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if TeX
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fidTeX = fopen([M_.fname '_param_density.tex'],'w');
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fprintf(fidTeX,'%% TeX eps-loader file generated by DSMH.m (Dynare).\n');
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fprintf(fidTeX,['%% ' datestr(now,0) '\n']);
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fprintf(fidTeX,' \n');
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end
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number_of_grid_points = 2^9; % 2^9 = 512 !... Must be a power of two.
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bandwidth = 0; % Rule of thumb optimal bandwidth parameter.
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kernel_function = 'gaussian'; % Gaussian kernel for Fast Fourier Transform approximation.
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for plt = 1:nbplt,
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if TeX
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NAMES = [];
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TeXNAMES = [];
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end
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hh = dyn_figure(options_.nodisplay,'Name','Parameters Densities');
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for k=1:min(nstar,npar-(plt-1)*nstar)
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subplot(nr,nc,k)
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kk = (plt-1)*nstar+k;
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[name,texname] = get_the_name(kk,TeX,M_,estim_params_,options_);
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if TeX
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if isempty(NAMES)
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NAMES = name;
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TeXNAMES = texname;
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else
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NAMES = char(NAMES,name);
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TeXNAMES = char(TeXNAMES,texname);
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end
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end
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optimal_bandwidth = mh_optimal_bandwidth(distrib_param(kk,:)',nparticles,bandwidth,kernel_function);
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[density(:,1),density(:,2)] = kernel_density_estimate(distrib_param(kk,:)',number_of_grid_points,...
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nparticles,optimal_bandwidth,kernel_function);
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plot(density(:,1),density(:,2));
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hold on
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title(name,'interpreter','none')
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hold off
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axis tight
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drawnow
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end
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dyn_saveas(hh,[ M_.fname '_param_density' int2str(plt) ],options_.nodisplay,options_.graph_format);
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if TeX
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% TeX eps loader file
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fprintf(fidTeX,'\\begin{figure}[H]\n');
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for jj = 1:min(nstar,length(x)-(plt-1)*nstar)
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fprintf(fidTeX,'\\psfrag{%s}[1][][0.5][0]{%s}\n',deblank(NAMES(jj,:)),deblank(TeXNAMES(jj,:)));
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end
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fprintf(fidTeX,'\\centering \n');
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fprintf(fidTeX,'\\includegraphics[scale=0.5]{%s_ParametersDensities%s}\n',M_.fname,int2str(plt));
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fprintf(fidTeX,'\\caption{ParametersDensities.}');
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fprintf(fidTeX,'\\label{Fig:ParametersDensities:%s}\n',int2str(plt));
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fprintf(fidTeX,'\\end{figure}\n');
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fprintf(fidTeX,' \n');
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end
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end
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function indx = DSMH_resampling(weights,noise,number)
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indx = zeros(number,1);
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cumweights = cumsum(weights);
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randvec = (transpose(1:number)-1+noise(:))/number;
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j = 1;
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for i=1:number
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while (randvec(i)>cumweights(j))
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j = j+1;
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end
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indx(i) = j;
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end
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function [tlogpost_iminus1,loglik,param] = sort_matrices(tlogpost_iminus1,loglik,param)
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[~,indx_ord] = sortrows(tlogpost_iminus1);
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tlogpost_iminus1 = tlogpost_iminus1(indx_ord);
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param = param(:,indx_ord);
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loglik = loglik(indx_ord);
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function [tlogpost_i,weights,zhat,ESS,mu,Omegachol] = compute_IS_weights_and_moments(param,tlogpost_iminus1,loglik,lambda,i,zhat,ESS)
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if i==1
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tlogpost_i = tlogpost_iminus1 + loglik*lambda(i);
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else
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tlogpost_i = tlogpost_iminus1 + loglik*(lambda(i)-lambda(i-1));
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end
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weights = exp(tlogpost_i-tlogpost_iminus1);
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zhat = (mean(weights))*zhat ;
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weights = weights/sum(weights);
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ESS(i) = 1/sum(weights.^2);
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% estimates of mean and variance
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mu = param*weights;
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z = bsxfun(@minus,param,mu);
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Omega = z*diag(weights)*z';
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Omegachol = chol(Omega)';
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function c = tune_c(TargetFun,param,tlogpost_i,lambda,i,c,Omegachol,weights,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_)
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disp('tuning c_i...');
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disp('Initial value =');
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disp(c) ;
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npar = size(param,1);
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lower_prob = (.5*(options_.dsmh.alpha0+options_.dsmh.alpha1))^5;
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upper_prob = (.5*(options_.dsmh.alpha0+options_.dsmh.alpha1))^(1/5);
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stop=0 ;
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while stop==0
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acpt = 0.0;
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indx_resmpl = DSMH_resampling(weights,rand(1,1),options_.dsmh.G);
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param0 = param(:,indx_resmpl);
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tlogpost0 = tlogpost_i(indx_resmpl);
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for j=1:options_.dsmh.G
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for l=1:options_.dsmh.K
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validate = 0;
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while validate == 0
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candidate = param0(:,j) + sqrt(c)*Omegachol*randn(npar,1);
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if all(candidate >= mh_bounds.lb) && all(candidate <= mh_bounds.ub)
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[tlogpostx,loglikx] = tempered_likelihood(TargetFun,candidate,lambda(i),dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
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if isfinite(loglikx) % if returned log-density is not Inf or Nan (penalized value)
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validate = 1;
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if rand(1,1)<exp(tlogpostx-tlogpost0(j)) % accept
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acpt = acpt + 1/(options_.dsmh.G*options_.dsmh.K);
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param0(:,j)= candidate;
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tlogpost0(j) = tlogpostx;
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end
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end
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end
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end
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end
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end
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disp('Acceptation rate =') ;
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disp(acpt) ;
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if options_.dsmh.alpha0<=acpt && acpt<=options_.dsmh.alpha1
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disp('done!');
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stop=1;
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else
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if acpt<lower_prob
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c = c/5;
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elseif lower_prob<=acpt && acpt<=upper_prob
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c = c*log(.5*(options_.dsmh.alpha0+options_.dsmh.alpha1))/log(acpt);
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else
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c = 5*c;
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end
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disp('Trying with c= ') ;
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disp(c)
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end
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end
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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_)
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indx_levels = (1:1:options_.dsmh.M-1)*options_.dsmh.N*options_.dsmh.G/options_.dsmh.M;
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npar = size(param,1) ;
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p = 1/(10*options_.dsmh.tau);
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disp('Metropolis step...');
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% build the dynamic grid of levels
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levels = [0.0;tlogpost_iminus1(indx_levels)];
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% initialize the outputs
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out_param = param;
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out_tlogpost_iminus1 = tlogpost_i;
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out_loglik = loglik;
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% resample and initialize the starting groups
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indx_resmpl = DSMH_resampling(weights,rand(1,1),options_.dsmh.G);
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param0 = param(:,indx_resmpl);
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tlogpost_iminus10 = tlogpost_iminus1(indx_resmpl);
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tlogpost_i0 = tlogpost_i(indx_resmpl);
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loglik0 = loglik(indx_resmpl);
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% Start the Metropolis
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for l=1:options_.dsmh.N*options_.dsmh.tau
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for j=1:options_.dsmh.G
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u1 = rand(1,1);
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u2 = rand(1,1);
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if u1<p
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k=1 ;
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for m=1:options_.dsmh.M-1
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if levels(m)<=tlogpost_iminus10(j) && tlogpost_iminus10(j)<levels(m+1)
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k = m+1;
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break
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end
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end
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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) );
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if i==1
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alp = (loglik(indx)-loglik0(j))*lambda(i);
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else
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alp = (loglik(indx)-loglik0(j))*(lambda(i)-lambda(i-1));
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end
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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
|
||||
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
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;
|
||||
Loading…
Reference in New Issue