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function bvar = dsgevar_posterior_density(deep,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
% This function characterizes the posterior distribution of a bvar with
% a dsge prior (as in Del Negro and Schorfheide 2003) for a given value
% of the deep parameters (structural parameters + the size of the
% shocks + dsge_prior_weight).
%
% INPUTS
% deep: [double] a vector with the deep parameters.
%
% OUTPUTS
% bvar: a matlab structure with prior and posterior densities.
%
% ALGORITHM
% ...
% SPECIAL REQUIREMENTS
% none
%
% Copyright (C) 1996-2011 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/>.
gend = options_.nobs;
dsge_prior_weight = M_.params(strmatch('dsge_prior_weight',M_.param_names));
DSGE_PRIOR_WEIGHT = floor(gend*(1+dsge_prior_weight));
bvar.NumberOfLags = options_.varlag;
bvar.NumberOfVariables = size(options_.varobs,1);
bvar.Constant = 'no';
bvar.NumberOfEstimatedParameters = bvar.NumberOfLags*bvar.NumberOfVariables;
if ~options_.noconstant
bvar.Constant = 'yes';
bvar.NumberOfEstimatedParameters = bvar.NumberOfEstimatedParameters + ...
bvar.NumberOfVariables;
end
[fval,cost_flag,info,PHI,SIGMAu,iXX,prior] = DsgeVarLikelihood(deep',DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults);
% Conditionnal posterior density of the lagged matrices (given Sigma) ->
% Matric-variate normal distribution.
bvar.LaggedMatricesConditionalOnSigma.posterior.density = 'matric-variate normal';
bvar.LaggedMatricesConditionalOnSigma.posterior.arg1 = PHI;
bvar.LaggedMatricesConditionalOnSigma.posterior.arg2 = 'Sigma';
bvar.LaggedMatricesConditionalOnSigma.posterior.arg3 = iXX;
% Marginal posterior density of the covariance matrix -> Inverted Wishart.
bvar.Sigma.posterior.density = 'inverse wishart';
bvar.Sigma.posterior.arg1 = SIGMAu*DSGE_PRIOR_WEIGHT;
bvar.Sigma.posterior.arg2 = DSGE_PRIOR_WEIGHT-bvar.NumberOfEstimatedParameters;
% Marginal posterior density of the lagged matrices -> Generalized
% Student distribution (See appendix B.5 in Zellner (1971)).
bvar.LaggedMatrices.posterior.density = 'matric-variate student';
bvar.LaggedMatrices.posterior.arg1 = inv(iXX);%P
bvar.LaggedMatrices.posterior.arg2 = SIGMAu*DSGE_PRIOR_WEIGHT;%Q
bvar.LaggedMatrices.posterior.arg3 = PHI;%M (posterior mean)
bvar.LaggedMatrices.posterior.arg4 = DSGE_PRIOR_WEIGHT;%(sample size)
% Conditionnal posterior density of the lagged matrices (given Sigma) ->
% Matric-variate normal distribution.
bvar.LaggedMatricesConditionalOnSigma.prior.density = 'matric-variate normal';
bvar.LaggedMatricesConditionalOnSigma.prior.arg1 = prior.PHIstar;
bvar.LaggedMatricesConditionalOnSigma.prior.arg2 = 'Sigma';
bvar.LaggedMatricesConditionalOnSigma.prior.arg3 = prior.iGXX;
% Marginal posterior density of the covariance matrix -> Inverted Wishart.
bvar.Sigma.prior.density = 'inverse wishart';
bvar.Sigma.prior.arg1 = prior.SIGMAstar*prior.ArtificialSampleSize;
bvar.Sigma.prior.arg2 = prior.DF;
% Marginal posterior density of the lagged matrices -> Generalized
% Student distribution (See appendix B.5 in Zellner (1971)).
bvar.LaggedMatrices.prior.density = 'matric-variate student';
bvar.LaggedMatrices.prior.arg1 = inv(prior.iGXX);%P
bvar.LaggedMatrices.prior.arg2 = prior.SIGMAstar*prior.ArtificialSampleSize;%Q
bvar.LaggedMatrices.prior.arg3 = prior.PHIstar;%M (posterior mean)
bvar.LaggedMatrices.prior.arg4 = prior.ArtificialSampleSize;%(sample size)
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