dynare/matlab/marginal_density.m

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) 2005-2007 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');
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);

MU = zeros(1,npar);
SIGMA = zeros(npar,npar);
lpost_mode = -Inf;

fprintf('MH: I''m computing the posterior mean... ');
for n = FirstMhFile:TotalNumberOfMhFiles
  for b = 1:nblck
    load([ MhDirectoryName '/' M_.fname '_mh' int2str(n) '_blck' int2str(b) '.mat'],'x2','logpo2'); 
    MU = MU + sum(x2(ifil:end,:));
    lpost_mode = max(lpost_mode,max(logpo2));
  end
  ifil = 1;
end
MU = MU/((TotalNumberOfMhDraws-TODROP)*nblck);
xparam1 = MU';
MU1 = repmat(MU,MAX_nruns,1);
%% lpost_mode is the value of the log posterior kernel at the mode.	
fprintf(' Done!\n');
fprintf('MH: I''m computing the posterior covariance matrix... ');
ifil = FirstLine;
for n = FirstMhFile:TotalNumberOfMhFiles
  for b = 1:nblck
    load([MhDirectoryName '/' M_.fname '_mh' int2str(n) '_blck' int2str(b) '.mat'],'x2');
    x = x2(ifil:end,:)-MU1(1:size(x2(ifil:end,:),1),:);
    SIGMA = SIGMA + x'*x;
  end
  ifil = 1;
end
SIGMA =  SIGMA/((TotalNumberOfMhDraws-TODROP)*nblck);%<=== Variance of the parameters (ok!)
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');
%% end%Save.
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));