125 lines
4.7 KiB
Matlab
125 lines
4.7 KiB
Matlab
function pdraw = prior_draw(M_,bayestopt_,options_,estim_params_,init,rdraw)
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% pdraw = prior_draw(M_,bayestopt_,options_,estim_params_,init,rdraw)
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% Draws from the prior distributions for use with Sensitivity Toolbox for DYNARE
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%
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% INPUTS
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% - M_ [structure] describing the model
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% - bayestopt_ [structure] describing the priors
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% - options_ [structure] describing the options
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% - estim_params_ [structure] characterizing parameters to be estimated
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% - init [integer] scalar equal to 1 (first call) or 0.
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% - rdraw
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%
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% OUTPUTS
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% o pdraw [double] draw from the joint prior density.
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%
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% ALGORITHM
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% ...
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%
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% SPECIAL REQUIREMENTS
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% MATLAB Statistics Toolbox
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%
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% Written by Marco Ratto
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% Joint Research Centre, The European Commission,
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% marco.ratto@ec.europa.eu
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% Copyright © 2012-2015 European Commission
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% Copyright © 2012-2017 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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persistent npar pshape p6 p7 p3 p4 lbcum ubcum
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if init
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pshape = bayestopt_.pshape;
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p6 = bayestopt_.p6;
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p7 = bayestopt_.p7;
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p3 = bayestopt_.p3;
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p4 = bayestopt_.p4;
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npar = length(p6);
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pdraw = zeros(npar,1);
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lbcum = zeros(npar,1);
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ubcum = ones(npar,1);
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[~,~,~,lb,ub] = set_prior(estim_params_,M_,options_); %Prepare bounds
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if ~isempty(bayestopt_) && any(bayestopt_.pshape > 0)
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% Set prior bounds
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bounds = prior_bounds(bayestopt_, options_.prior_trunc);
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bounds.lb = max(bounds.lb,lb);
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bounds.ub = min(bounds.ub,ub);
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else % estimated parameters but no declared priors
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% No priors are declared so Dynare will estimate the model by
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% maximum likelihood with inequality constraints for the parameters.
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bounds.lb = lb;
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bounds.ub = ub;
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end
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% set bounds for cumulative probabilities
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for i = 1:npar
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switch pshape(i)
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case 1% Beta distribution (TODO: generalized beta distribution)
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lbcum(i) = betainc((bounds.lb(i)-p3(i))./(p4(i)-p3(i)),p6(i),p7(i));
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ubcum(i) = betainc((bounds.ub(i)-p3(i))./(p4(i)-p3(i)),p6(i),p7(i));
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case 2% Gamma prior.
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lbcum(i) = gamcdf(bounds.lb(i)-p3(i),p6(i),p7(i));
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ubcum(i) = gamcdf(bounds.ub(i)-p3(i),p6(i),p7(i));
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case 3% Gaussian prior.
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lbcum(i) = 0.5 * erfc(-(bounds.lb(i)-p6(i))/p7(i) ./ sqrt(2));
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ubcum(i) = 0.5 * erfc(-(bounds.ub(i)-p6(i))/p7(i) ./ sqrt(2));
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case 4% INV-GAMMA1 distribution
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% TO BE CHECKED
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lbcum(i) = gamcdf(1/(bounds.ub(i)-p3(i))^2,p7(i)/2,2/p6(i));
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ubcum(i) = gamcdf(1/(bounds.lb(i)-p3(i))^2,p7(i)/2,2/p6(i));
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case 5% Uniform prior.
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p4(i) = min(p4(i),bounds.ub(i));
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p3(i) = max(p3(i),bounds.lb(i));
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case 6% INV-GAMMA2 distribution
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% TO BE CHECKED
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lbcum(i) = gamcdf(1/(bounds.ub(i)-p3(i)),p7(i)/2,2/p6(i));
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ubcum(i) = gamcdf(1/(bounds.lb(i)-p3(i)),p7(i)/2,2/p6(i));
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case 8
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lbcum(i) = wblcdf(bounds.lb(i)-p3(i),p6(i),p7(i));
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ubcum(i) = wblcdf(bounds.ub(i)-p3(i),p6(i),p7(i));
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otherwise
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% Nothing to do here.
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end
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end
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return
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end
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pdraw=NaN(size(rdraw,1),npar);
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for i = 1:npar
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rdraw(:,i) = rdraw(:,i).*(ubcum(i)-lbcum(i))+lbcum(i);
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switch pshape(i)
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case 5% Uniform prior.
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pdraw(:,i) = rdraw(:,i)*(p4(i)-p3(i)) + p3(i);
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case 3% Gaussian prior.
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pdraw(:,i) = norminv(rdraw(:,i),p6(i),p7(i));
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case 2% Gamma prior.
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pdraw(:,i) = gaminv(rdraw(:,i),p6(i),p7(i))+p3(i);
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case 1% Beta distribution (TODO: generalized beta distribution)
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pdraw(:,i) = betainv(rdraw(:,i),p6(i),p7(i))*(p4(i)-p3(i))+p3(i);
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case 4% INV-GAMMA1 distribution
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% TO BE CHECKED
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pdraw(:,i) = sqrt(1./gaminv(rdraw(:,i),p7(i)/2,2/p6(i)))+p3(i);
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case 6% INV-GAMMA2 distribution
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% TO BE CHECKED
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pdraw(:,i) = 1./gaminv(rdraw(:,i),p7(i)/2,2/p6(i))+p3(i);
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case 8
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pdraw(:,i) = wblinv(rdraw(:,i),p6(i),p7(i))+p3(i);
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otherwise
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% Nothing to do here.
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end
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end
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