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function pdraw = prior_draw_gsa(init,rdraw)
% Draws from the prior distributions
% Adapted by M. Ratto from prior_draw (of DYNARE, copyright M. Juillard),
% 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,
% (http://eemc.jrc.ec.europa.eu/),
% marco.ratto@jrc.it
%
% Reference:
% M. Ratto, Global Sensitivity Analysis for Macroeconomic models, MIMEO, 2006.
% Copyright (C) 2012 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 M_ options_ estim_params_ bayestopt_
global bayestopt_
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);
% set bounds for cumulative probabilities
for i = 1:npar
switch pshape(i)
case 5% Uniform prior.
p4(i) = min(p4(i),bayestopt_.ub(i));
p3(i) = max(p3(i),bayestopt_.lb(i));
case 3% Gaussian prior.
lbcum(i) = 0.5 * erfc(-(bayestopt_.lb(i)-p6(i))/p7(i) ./ sqrt(2));;
ubcum(i) = 0.5 * erfc(-(bayestopt_.ub(i)-p6(i))/p7(i) ./ sqrt(2));;
case 2% Gamma prior.
lbcum(i) = gamcdf(bayestopt_.lb(i)-p3(i),p6(i),p7(i));
ubcum(i) = gamcdf(bayestopt_.ub(i)-p3(i),p6(i),p7(i));
case 1% Beta distribution (TODO: generalized beta distribution)
lbcum(i) = betainc((bayestopt_.lb(i)-p3(i))./(p4(i)-p3(i)),p6(i),p7(i));
ubcum(i) = betainc((bayestopt_.ub(i)-p3(i))./(p4(i)-p3(i)),p6(i),p7(i));
case 4% INV-GAMMA1 distribution
% TO BE CHECKED
lbcum(i) = gamcdf(1/(bayestopt_.ub(i)-p3(i))^2,p7(i)/2,2/p6(i));
ubcum(i) = gamcdf(1/(bayestopt_.lb(i)-p3(i))^2,p7(i)/2,2/p6(i));
case 6% INV-GAMMA2 distribution
% TO BE CHECKED
lbcum(i) = gamcdf(1/(bayestopt_.ub(i)-p3(i)),p7(i)/2,2/p6(i));
ubcum(i) = gamcdf(1/(bayestopt_.lb(i)-p3(i)),p7(i)/2,2/p6(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);
otherwise
% Nothing to do here.
end
end
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