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function [marginal,oo_] = marginal_density(M_, options_, estim_params_, oo_, bayestopt_)
% function marginal = marginal_density()
% Computes the marginal density
%
% INPUTS
% options_ [structure]
% estim_params_ [structure]
% M_ [structure]
% oo_ [structure]
%
% OUTPUTS
% marginal: [double] marginal density (modified harmonic mean)
% oo_ [structure]
%
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2005-2017 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/>.
npar = estim_params_.np+estim_params_.nvn+estim_params_.ncx+estim_params_.ncn+estim_params_.nvx;
nblck = options_.mh_nblck;
MetropolisFolder = CheckPath('metropolis',M_.dname);
ModelName = M_.fname;
BaseName = [MetropolisFolder filesep ModelName];
load_last_mh_history_file(MetropolisFolder, ModelName);
FirstMhFile = record.KeepedDraws.FirstMhFile;
FirstLine = record.KeepedDraws.FirstLine; ifil = FirstLine;
TotalNumberOfMhFiles = sum(record.MhDraws(:,2));
TotalNumberOfMhDraws = sum(record.MhDraws(:,1));
MAX_nruns = ceil(options_.MaxNumberOfBytes/(npar+2)/8);
TODROP = floor(options_.mh_drop*TotalNumberOfMhDraws);
fprintf('Estimation::marginal density: I''m computing the posterior mean and covariance... ');
[posterior_mean,posterior_covariance,posterior_mode,posterior_kernel_at_the_mode] = compute_mh_covariance_matrix();
MU = transpose(posterior_mean);
SIGMA = posterior_covariance;
lpost_mode = posterior_kernel_at_the_mode;
xparam1 = posterior_mean;
hh = inv(SIGMA);
fprintf(' Done!\n');
if ~isfield(oo_,'posterior_mode') || (options_.mh_replic && isequal(options_.posterior_sampler_options.posterior_sampling_method,'slice'))
oo_=fill_mh_mode(posterior_mode',NaN(npar,1),M_,options_,estim_params_,bayestopt_,oo_,'posterior');
end
% save the posterior mean and the inverse of the covariance matrix
% (usefull if the user wants to perform some computations using
% the posterior mean instead of the posterior mode ==> ).
parameter_names = bayestopt_.name;
save([M_.fname '_mean.mat'],'xparam1','hh','parameter_names','SIGMA');
fprintf('Estimation::marginal density: I''m computing the posterior log marginal density (modified harmonic mean)... ');
logdetSIGMA = log(det(SIGMA));
invSIGMA = hh;
marginal = zeros(9,2);
linee = 0;
check_coverage = 1;
increase = 1;
while check_coverage
for p = 0.1:0.1:0.9
critval = chi2inv(p,npar);
ifil = FirstLine;
tmp = 0;
for n = FirstMhFile:TotalNumberOfMhFiles
for b=1:nblck
load([ BaseName '_mh' int2str(n) '_blck' int2str(b) '.mat'],'x2','logpo2');
EndOfFile = size(x2,1);
for i = ifil:EndOfFile
deviation = ((x2(i,:)-MU)*invSIGMA*(x2(i,:)-MU)')/increase;
if deviation <= critval
lftheta = -log(p)-(npar*log(2*pi)+(npar*log(increase)+logdetSIGMA)+deviation)/2;
tmp = tmp + exp(lftheta - logpo2(i) + lpost_mode);
end
end
end
ifil = 1;
end
linee = linee + 1;
warning_old_state = warning;
warning off;
marginal(linee,:) = [p, lpost_mode-log(tmp/((TotalNumberOfMhDraws-TODROP)*nblck))];
warning(warning_old_state);
end
if abs((marginal(9,2)-marginal(1,2))/marginal(9,2)) > 0.01 || isinf(marginal(1,2))
fprintf('\n')
if increase == 1
disp('Estimation::marginal density: The support of the weighting density function is not large enough...')
disp('Estimation::marginal density: I increase the variance of this distribution.')
increase = 1.2*increase;
linee = 0;
else
disp('Estimation::marginal density: Let me try again.')
increase = 1.2*increase;
linee = 0;
if increase > 20
check_coverage = 0;
clear invSIGMA detSIGMA increase;
disp('Estimation::marginal density: There''s probably a problem with the modified harmonic mean estimator.')
end
end
else
check_coverage = 0;
clear invSIGMA detSIGMA increase;
fprintf('Done!\n')
end
end
oo_.MarginalDensity.ModifiedHarmonicMean = mean(marginal(:,2));
return
function oo_=fill_mh_mode(xparam1,stdh,M_,options_,estim_params_,bayestopt_,oo_, field_name)
%function oo_=fill_mh_mode(xparam1,stdh,M_,options_,estim_params_,bayestopt_,oo_, field_name)
%
% INPUTS
% o xparam1 [double] (p*1) vector of estimate parameters.
% o stdh [double] (p*1) vector of estimate parameters.
% o M_ Matlab's structure describing the Model (initialized by dynare, see @ref{M_}).
% o estim_params_ Matlab's structure describing the estimated_parameters (initialized by dynare, see @ref{estim_params_}).
% o options_ Matlab's structure describing the options (initialized by dynare, see @ref{options_}).
% o bayestopt_ Matlab's structure describing the priors (initialized by dynare, see @ref{bayesopt_}).
% o oo_ Matlab's structure gathering the results (initialized by dynare, see @ref{oo_}).
%
% OUTPUTS
% o oo_ Matlab's structure gathering the results
%
% SPECIAL REQUIREMENTS
% None.
nvx = estim_params_.nvx; % Variance of the structural innovations (number of parameters).
nvn = estim_params_.nvn; % Variance of the measurement innovations (number of parameters).
ncx = estim_params_.ncx; % Covariance of the structural innovations (number of parameters).
ncn = estim_params_.ncn; % Covariance of the measurement innovations (number of parameters).
np = estim_params_.np ; % Number of deep parameters.
nx = nvx+nvn+ncx+ncn+np; % Total number of parameters to be estimated.
if np
ip = nvx+nvn+ncx+ncn+1;
for i=1:np
name = bayestopt_.name{ip};
eval(['oo_.' field_name '_mode.parameters.' name ' = xparam1(ip);']);
eval(['oo_.' field_name '_std_at_mode.parameters.' name ' = stdh(ip);']);
ip = ip+1;
end
end
if nvx
ip = 1;
for i=1:nvx
k = estim_params_.var_exo(i,1);
name = deblank(M_.exo_names(k,:));
eval(['oo_.' field_name '_mode.shocks_std.' name ' = xparam1(ip);']);
eval(['oo_.' field_name '_std_at_mode.shocks_std.' name ' = stdh(ip);']);
ip = ip+1;
end
end
if nvn
ip = nvx+1;
for i=1:nvn
name = options_.varobs{estim_params_.nvn_observable_correspondence(i,1)};
eval(['oo_.' field_name '_mode.measurement_errors_std.' name ' = xparam1(ip);']);
eval(['oo_.' field_name '_std_at_mode.measurement_errors_std.' name ' = stdh(ip);']);
ip = ip+1;
end
end
if ncx
ip = nvx+nvn+1;
for i=1:ncx
k1 = estim_params_.corrx(i,1);
k2 = estim_params_.corrx(i,2);
NAME = [deblank(M_.exo_names(k1,:)) '_' deblank(M_.exo_names(k2,:))];
eval(['oo_.' field_name '_mode.shocks_corr.' NAME ' = xparam1(ip);']);
eval(['oo_.' field_name '_std_at_mode.shocks_corr.' NAME ' = stdh(ip);']);
ip = ip+1;
end
end
if ncn
ip = nvx+nvn+ncx+1;
for i=1:ncn
k1 = estim_params_.corrn(i,1);
k2 = estim_params_.corrn(i,2);
NAME = [deblank(M_.endo_names(k1,:)) '_' deblank(M_.endo_names(k2,:))];
eval(['oo_.' field_name '_mode.measurement_errors_corr.' NAME ' = xparam1(ip);']);
eval(['oo_.' field_name '_std_at_mode.measurement_errors_corr.' NAME ' = stdh(ip);']);
ip = ip+1;
end
end
return
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