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function [marginal,oo_] = marginal_density(M_, options_, estim_params_, oo_)
% 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) 2005-2011 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;
MhDirectoryName = CheckPath('metropolis',M_.dname);
load([ MhDirectoryName '/' M_.fname '_mh_history.mat'])
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('MH: 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');
%% 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 ==> ).
save([M_.fname '_mean.mat'],'xparam1','hh','SIGMA');
disp(' ');
disp('MH: I''m computing the posterior log marginale density (modified harmonic mean)... ');
detSIGMA = det(SIGMA);
invSIGMA = inv(SIGMA);
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([ MhDirectoryName '/' M_.fname '_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)';
if deviation <= critval
lftheta = -log(p)-(npar*log(2*pi)+log(detSIGMA)+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))
if increase == 1
disp('MH: The support of the weighting density function is not large enough...')
disp('MH: I increase the variance of this distribution.')
increase = 1.2*increase;
invSIGMA = inv(SIGMA*increase);
detSIGMA = det(SIGMA*increase);
linee = 0;
else
disp('MH: Let me try again.')
increase = 1.2*increase;
invSIGMA = inv(SIGMA*increase);
detSIGMA = det(SIGMA*increase);
linee = 0;
if increase > 20
check_coverage = 0;
clear invSIGMA detSIGMA increase;
disp('MH: There''s probably a problem with the modified harmonic mean estimator.')
end
end
else
check_coverage = 0;
clear invSIGMA detSIGMA increase;
disp('MH: Modified harmonic mean estimator, done!')
end
end
oo_.MarginalDensity.ModifiedHarmonicMean = mean(marginal(:,2));
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