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function pdraw = prior_draw_gsa(init,rdraw)
% Draws from the prior distributions for use with Sensitivity Toolbox for DYNARE
%
% INPUTS
% o init [integer] scalar equal to 1 (first call) or 0.
% o rdraw
%
% OUTPUTS
% o pdraw [double] draw from the joint prior density.
%
% ALGORITHM
% ...
%
% SPECIAL REQUIREMENTS
% MATLAB Statistics Toolbox
%
% Written by Marco Ratto
% Joint Research Centre, The European Commission,
% marco.ratto@ec.europa.eu
% Copyright (C) 2012-2015 European Commission
% Copyright (C) 2012-2017 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/>.
global bayestopt_ options_ estim_params_ M_
persistent npar pshape p6 p7 p3 p4 lbcum ubcum
if init
pshape = bayestopt_.pshape;
p6 = bayestopt_.p6;
p7 = bayestopt_.p7;
p3 = bayestopt_.p3;
p4 = bayestopt_.p4;
npar = length(p6);
pdraw = zeros(npar,1);
lbcum = zeros(npar,1);
ubcum = ones(npar,1);
[junk1,junk2,junk3,lb,ub,junk4] = set_prior(estim_params_,M_,options_); %Prepare bounds
if ~isempty(bayestopt_) && any(bayestopt_.pshape > 0)
% Set prior bounds
bounds = prior_bounds(bayestopt_, options_.prior_trunc);
bounds.lb = max(bounds.lb,lb);
bounds.ub = min(bounds.ub,ub);
else % estimated parameters but no declared priors
% No priors are declared so Dynare will estimate the model by
% maximum likelihood with inequality constraints for the parameters.
bounds.lb = lb;
bounds.ub = ub;
end
% set bounds for cumulative probabilities
for i = 1:npar
switch pshape(i)
case 5% Uniform prior.
p4(i) = min(p4(i),bounds.ub(i));
p3(i) = max(p3(i),bounds.lb(i));
case 3% Gaussian prior.
lbcum(i) = 0.5 * erfc(-(bounds.lb(i)-p6(i))/p7(i) ./ sqrt(2));
ubcum(i) = 0.5 * erfc(-(bounds.ub(i)-p6(i))/p7(i) ./ sqrt(2));
case 2% Gamma prior.
lbcum(i) = gamcdf(bounds.lb(i)-p3(i),p6(i),p7(i));
ubcum(i) = gamcdf(bounds.ub(i)-p3(i),p6(i),p7(i));
case 1% Beta distribution (TODO: generalized beta distribution)
lbcum(i) = betainc((bounds.lb(i)-p3(i))./(p4(i)-p3(i)),p6(i),p7(i));
ubcum(i) = betainc((bounds.ub(i)-p3(i))./(p4(i)-p3(i)),p6(i),p7(i));
case 4% INV-GAMMA1 distribution
% TO BE CHECKED
lbcum(i) = gamcdf(1/(bounds.ub(i)-p3(i))^2,p7(i)/2,2/p6(i));
ubcum(i) = gamcdf(1/(bounds.lb(i)-p3(i))^2,p7(i)/2,2/p6(i));
case 6% INV-GAMMA2 distribution
% TO BE CHECKED
lbcum(i) = gamcdf(1/(bounds.ub(i)-p3(i)),p7(i)/2,2/p6(i));
ubcum(i) = gamcdf(1/(bounds.lb(i)-p3(i)),p7(i)/2,2/p6(i));
case 8
lbcum(i) = weibcdf(bounds.lb(i)-p3(i),p6(i),p7(i));
ubcum(i) = weibcdf(bounds.ub(i)-p3(i),p6(i),p7(i));
otherwise
% Nothing to do here.
end
end
return
end
for i = 1:npar
rdraw(:,i) = rdraw(:,i).*(ubcum(i)-lbcum(i))+lbcum(i);
switch pshape(i)
case 5% Uniform prior.
pdraw(:,i) = rdraw(:,i)*(p4(i)-p3(i)) + p3(i);
case 3% Gaussian prior.
pdraw(:,i) = norminv(rdraw(:,i),p6(i),p7(i));
case 2% Gamma prior.
pdraw(:,i) = gaminv(rdraw(:,i),p6(i),p7(i))+p3(i);
case 1% Beta distribution (TODO: generalized beta distribution)
pdraw(:,i) = betainv(rdraw(:,i),p6(i),p7(i))*(p4(i)-p3(i))+p3(i);
case 4% INV-GAMMA1 distribution
% TO BE CHECKED
pdraw(:,i) = sqrt(1./gaminv(rdraw(:,i),p7(i)/2,2/p6(i)))+p3(i);
case 6% INV-GAMMA2 distribution
% TO BE CHECKED
pdraw(:,i) = 1./gaminv(rdraw(:,i),p7(i)/2,2/p6(i))+p3(i);
case 8
pdraw(:,i) = wblinv(rdraw(:,i),p6(i),p7(i))+p3(i);
otherwise
% Nothing to do here.
end
end
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