Add Geweke 1992 convergence diagnostics
Johannes Pfeifer
parent
20dba7e623
commit
241fd07424
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@ -1,4 +1,4 @@
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function McMCDiagnostics(options_, estim_params_, M_)
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function oo_ = McMCDiagnostics(options_, estim_params_, M_, oo_)
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% function McMCDiagnostics
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% Computes convergence tests
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%
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@ -8,7 +8,7 @@ function McMCDiagnostics(options_, estim_params_, M_)
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% M_ [structure]
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%
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% OUTPUTS
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% none
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% oo_ [structure]
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%
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% SPECIAL REQUIREMENTS
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% none
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@ -38,10 +38,6 @@ MhDirectoryName = CheckPath('metropolis',M_.dname);
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TeX = options_.TeX;
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nblck = options_.mh_nblck;
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% Brooks and Gelman tests need more than one block
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if nblck == 1
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return;
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end
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npar = estim_params_.nvx;
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npar = npar + estim_params_.nvn;
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npar = npar + estim_params_.ncx;
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@ -56,6 +52,57 @@ NumberOfMcFilesPerBlock = size(dir([MhDirectoryName ,filesep, M_.fname '_mh*_blc
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% check if all previous files are there for block 1
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check_presence_consecutive_MC_files(MhDirectoryName,M_.fname,1)
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if nblck == 1 % Brooks and Gelman tests need more than one block
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convergence_diagnostics_geweke=zeros(npar,4+2*length(options_.convergence.geweke.taper_steps));
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if any(options_.convergence.geweke.geweke_interval<0) || any(options_.convergence.geweke.geweke_interval>1) || length(any(options_.convergence.geweke.geweke_interval<0))~=2 ...
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|| (options_.convergence.geweke.geweke_interval(2)-options_.convergence.geweke.geweke_interval(1)<0)
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fprintf('\nCONVERGENCE DIAGNOSTICS: Invalid option for geweke_interval. Using the default of [0.2 0.5].\n')
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options_.convergence.geweke.geweke_interval=[0.2 0.5];
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end
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first_obs_begin_sample = max(1,ceil(options_.mh_drop*options_.mh_replic));
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last_obs_begin_sample = first_obs_begin_sample+round(options_.convergence.geweke.geweke_interval(1)*options_.mh_replic*options_.mh_drop);
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first_obs_end_sample = first_obs_begin_sample+round(options_.convergence.geweke.geweke_interval(2)*options_.mh_replic*options_.mh_drop);
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param_name=[];
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for jj=1:npar
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param_name = strvcat(param_name,get_the_name(jj,options_.TeX,M_,estim_params_,options_));
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end
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fprintf('\nGeweke (1992) Convergence Tests, based on means of draws %d to %d vs %d to %d.\n',first_obs_begin_sample,last_obs_begin_sample,first_obs_end_sample,options_.mh_replic);
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fprintf('p-values are for Chi2-test for equality of means.\n');
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Geweke_header={'Parameter', 'Post. Mean', 'Post. Std', 'p-val No Taper'};
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print_string=['%',num2str(size(param_name,2)+3),'s \t %12.3f \t %12.3f \t %12.3f'];
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print_string_header=['%',num2str(size(param_name,2)+3),'s \t %12s \t %12s \t %12s'];
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for ii=1:length(options_.convergence.geweke.taper_steps)
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Geweke_header=[Geweke_header, ['p-val ' num2str(options_.convergence.geweke.taper_steps(ii)),'% Taper']];
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print_string=[print_string,'\t %12.3f'];
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print_string_header=[print_string_header,'\t %12s'];
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end
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print_string=[print_string,'\n'];
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print_string_header=[print_string_header,'\n'];
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fprintf(print_string_header,Geweke_header{1,:});
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for jj=1:npar
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startline=0;
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for n = 1:NumberOfMcFilesPerBlock
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load([MhDirectoryName '/' M_.fname '_mh',int2str(n),'_blck1.mat'],'x2');
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nx2 = size(x2,1);
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param_draws(startline+(1:nx2),1) = x2(:,jj);
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startline = startline + nx2;
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end
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[results_vec, results_struct] = geweke_moments(param_draws,options_);
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convergence_diagnostics_geweke(jj,:)=results_vec;
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param_draws1 = param_draws(first_obs_begin_sample:last_obs_begin_sample,:);
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param_draws2 = param_draws(first_obs_end_sample:end,:);
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[results_vec1] = geweke_moments(param_draws1,options_);
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[results_vec2] = geweke_moments(param_draws2,options_);
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results_struct = geweke_chi2_test(results_vec1,results_vec2,results_struct,options_);
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eval(['oo_.convergence.geweke.',param_name(jj,:),'=results_struct;'])
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fprintf(print_string,param_name(jj,:),results_struct.posteriormean,results_struct.posteriorstd,results_struct.prob_chi2_test)
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end
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skipline(2);
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return;
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end
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for blck = 2:nblck
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tmp = size(dir([MhDirectoryName ,filesep, M_.fname '_mh*_blck' int2str(blck) '.mat']),1);
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if tmp~=NumberOfMcFilesPerBlock
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@ -611,8 +611,8 @@ if (any(bayestopt_.pshape >0 ) && options_.mh_replic) || ...
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CutSample(M_, options_, estim_params_);
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return
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else
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if ~options_.nodiagnostic && options_.mh_replic > 2000 && options_.mh_nblck > 1
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McMCDiagnostics(options_, estim_params_, M_);
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if ~options_.nodiagnostic && options_.mh_replic > 2000
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oo_= McMCDiagnostics(options_, estim_params_, M_,oo_);
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end
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%% Here i discard first half of the draws:
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CutSample(M_, options_, estim_params_);
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@ -0,0 +1,74 @@
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function results_struct = geweke_chi2_test(results1,results2,results_struct,options)
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% results_struct = geweke_chi2_test(results1,results2,results_struct,options)
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% PURPOSE: computes Geweke's chi-squared test for two sets of MCMC sample draws
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%
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% INPUTS
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% results1 [1 by (4+n_taper*2) vector] vector with post. mean,
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% std, NSE_iid, RNE_iid, and tapered NSE and RNE
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% for chain part 1
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% results2 [1 by (4+n_taper*2) vector] vector with post. mean,
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% std, NSE_iid, RNE_iid, and tapered NSE and RNE
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% for chain part 2
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% results_struct [structure] results structure generated by geweke_moments
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% Dynareoptions [structure]
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%
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% OUTPUTS
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% results_struct [structure] containing the following fields:
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% pooled_mean Pooled mean of the chain parts, weighted
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% with precision
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% rpooled_nse Pooled NSE of the chain parts, weighted
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% with precision
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% prob_chi2_test p-value of Chi2-test for equality of
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% means in both chain parts
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% -----------------------------------------------------------------
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%
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% SPECIAL REQUIREMENTS
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% None.
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% Copyright (C) 2013 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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%
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% ------------------------------------------------
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% REFERENCES: Geweke (1992), `Evaluating the accuracy of sampling-based
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% approaches to the calculation of posterior moments', in J.O. Berger,
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% J.M. Bernardo, A.P. Dawid, and A.F.M. Smith (eds.) Proceedings of
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% the Fourth Valencia International Meeting on Bayesian Statistics,
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% pp. 169-194, Oxford University Press
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% Geweke (1999): `Using simulation methods for Bayesian econometric models:
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% Inference, development and communication', Econometric Reviews, 18(1),
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% 1-73
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% written by: Johannes Pfeifer,
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% based on code by James P. LeSage, who in turn
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% drew on MATLAB programs written by Siddartha Chib
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for k=1:length(options.convergence.geweke.taper_steps)+1;
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NSE=[results1(:,3+(k-1)*2) results2(:,3+(k-1)*2)];
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means=[results1(:,1) results2(:,1)];
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diff_Means=means(:,1)-means(:,2);
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sum_of_weights=sum(1./(NSE.^2),2);
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pooled_mean=sum(means./(NSE.^2),2)./sum_of_weights;
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pooled_NSE=1./sqrt(sum_of_weights);
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test_stat=diff_Means.^2./sum(NSE.^2,2);
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p = 1-chi2cdf(test_stat,1);
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results_struct.pooled_mean(:,k) = pooled_mean;
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results_struct.pooled_nse(:,k) = pooled_NSE;
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results_struct.prob_chi2_test(:,k) = p;
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end;
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@ -0,0 +1,109 @@
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function [results_vec, results_struct] = geweke_moments(draws,Dynareoptions)
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%[results_vec, results_struct] = geweke_moments(draws,Dynareoptions)
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% PURPOSE: computes Gewke's convergence diagnostics NSE and RNE
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% (numerical std error and relative numerical efficiencies)
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% INPUTS
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% draws [ndraws by 1 vector]
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% Dynareoptions [structure]
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%
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% OUTPUTS
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% results_vec
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% results_struct [structure] containing the following fields:
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% posteriormean= posterior parameter mean
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% posteriorstd = posterior standard deviation
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% nse_iid = nse assuming no serial correlation for variable i
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% rne_iid = rne assuming no serial correlation for variable i
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% nse_x = nse using x% autocovariance tapered estimate
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% rne_x = rne using x% autocovariance taper
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% -----------------------------------------------------------------
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%
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% SPECIAL REQUIREMENTS
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% None.
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% Copyright (C) 2013 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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% REFERENCES: Geweke (1992), `Evaluating the accuracy of sampling-based
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% approaches to the calculation of posterior moments', in J.O. Berger,
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% J.M. Bernardo, A.P. Dawid, and A.F.M. Smith (eds.) Proceedings of
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% the Fourth Valencia International Meeting on Bayesian Statistics,
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% pp. 169-194, Oxford University Press
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% Geweke (1999): `Using simulation methods for Bayesian econometric models:
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% Inference, development and communication', Econometric Reviews, 18(1),
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% 1-73
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% -----------------------------------------------------------------
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% written by: Johannes Pfeifer,
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% based on code by James P. LeSage, who in turn
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% drew on MATLAB programs written by Siddartha Chib
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ndraw = size(draws,1);
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n_groups=100;
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taper_steps=Dynareoptions.convergence.geweke.taper_steps;
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results_vec=zeros(1,4+2*length(taper_steps));
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ns = floor(ndraw/n_groups); %step_size
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n_draws_used = ns*n_groups; %effective number of draws used after rounding down
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window_means= zeros(n_groups,1);
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window_uncentered_variances= zeros(n_groups,1);
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for ig=1:n_groups;
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window_means(ig,1)=sum(draws((ig-1)*ns+1:ig*ns,1))/ns;
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window_uncentered_variances(ig,1)=sum(draws((ig-1)*ns+1:ig*ns,1).^2)/ns;
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end; %for ig
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total_mean=mean(window_means);
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total_variance=mean(window_uncentered_variances)-total_mean^2;
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% save posterior means and std deviations to results_struct structure
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results_vec(1,1)=total_mean;
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results_vec(1,2)=sqrt(total_variance);
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results_struct.posteriormean = total_mean;
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results_struct.posteriorstd = results_vec(1,2);
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% numerical standard error assuming no serial correlation
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NSE=std(draws(1:n_draws_used,1),1)/sqrt(n_draws_used);
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% save to results_struct structure
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results_vec(1,3)=NSE;
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results_vec(1,4)=total_variance/(n_draws_used*NSE^2);
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results_struct.nse_iid = NSE;
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results_struct.rne_iid = results_vec(1,4);
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%get autocovariance of grouped means
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centered_window_means=window_means-total_mean;
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autocov_grouped_means=zeros(n_groups,1);
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for lag=0:n_groups-1;
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autocov_grouped_means(lag+1)=centered_window_means(lag+1:n_groups,1)'*centered_window_means(1:n_groups-lag,1)/100;
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end;
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% numerical standard error with tapered autocovariance functions
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for taper_index=1:length(taper_steps)
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taper=taper_steps(taper_index);
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taper_lags=(1:taper-1)';
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taper_lag_weight=1-taper_lags/taper;
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tapered_sum_of_covariances=autocov_grouped_means(1)+sum(2*taper_lag_weight.*autocov_grouped_means(1+taper_lags));
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NSE_taper=sqrt(tapered_sum_of_covariances/n_groups);
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% save results_struct in structure
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results_vec(1,4+taper_index*2-1)=NSE_taper;
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results_vec(1,4+taper_index*2)=total_variance/(n_draws_used*NSE_taper^2);
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eval(['results_struct.nse_taper_',num2str(taper),'= NSE_taper;']);
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eval(['results_struct.rne_taper_',num2str(taper),'= total_variance/(n_draws_used*NSE_taper^2);']);
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end; % end of for mm loop
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@ -577,6 +577,10 @@ options_.osr.verbose=2;
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% use GPU
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options_.gpu = 0;
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%Geweke convergence diagnostics
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options_.convergence.geweke.taper_steps=[4 8 15];
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options_.convergence.geweke.geweke_interval=[0.2 0.5];
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% initialize persistent variables in priordens()
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priordens([],[],[],[],[],[],1);
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% initialize persistent variables in dyn_first_order_solver()
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