306 lines
14 KiB
Matlab
306 lines
14 KiB
Matlab
function [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_)
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% function [xparam1,estim_params_,bayestopt_,lb,ub]=set_prior(estim_params_)
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% sets prior distributions
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%
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% INPUTS
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% o estim_params_ [structure] characterizing parameters to be estimated.
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% o M_ [structure] characterizing the model.
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% o options_ [structure]
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%
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% OUTPUTS
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% o xparam1 [double] vector of parameters to be estimated (initial values)
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% o estim_params_ [structure] characterizing parameters to be estimated
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% o bayestopt_ [structure] characterizing priors
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% o lb [double] vector of lower bounds for the estimated parameters.
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% o ub [double] vector of upper bounds for the estimated parameters.
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% o M_ [structure] characterizing the model.
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%
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% SPECIAL REQUIREMENTS
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% None
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% Copyright (C) 2003-2013 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 <http://www.gnu.org/licenses/>.
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nvx = size(estim_params_.var_exo,1);
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nvn = size(estim_params_.var_endo,1);
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ncx = size(estim_params_.corrx,1);
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ncn = size(estim_params_.corrn,1);
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np = size(estim_params_.param_vals,1);
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estim_params_.nvx = nvx; %exogenous shock variances
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estim_params_.nvn = nvn; %endogenous variances, i.e. measurement error
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estim_params_.ncx = ncx; %exogenous shock correlations
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estim_params_.ncn = ncn; % correlation between endogenous variables, i.e. measurement error.
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estim_params_.np = np; % other parameters of the model
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xparam1 = [];
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ub = []; % Upper bound imposed for optimization.
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lb = []; % Lower bound imposed for optimization.
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bayestopt_.pshape = [];
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bayestopt_.p1 = []; % prior mean
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bayestopt_.p2 = []; % prior standard deviation
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bayestopt_.p3 = []; % lower bound of the distribution, only considering whether a generalized distribution is used, not when the prior is truncated
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bayestopt_.p4 = []; % upper bound of the distribution, only considering whether a generalized distribution is used, not when the prior is truncated
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bayestopt_.p5 = zeros(nvx+nvn+ncx+ncn+np,1); % prior mode
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bayestopt_.p6 = []; % first hyper-parameter (\alpha for the BETA and GAMMA distributions, s for the INVERSE GAMMAs, expectation for the GAUSSIAN distribution, lower bound for the UNIFORM distribution).
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bayestopt_.p7 = []; % second hyper-parameter (\beta for the BETA and GAMMA distributions, \nu for the INVERSE GAMMAs, standard deviation for the GAUSSIAN distribution, upper bound for the UNIFORM distribution).
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bayestopt_.jscale = [];
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bayestopt_.name = {};
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if nvx
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xparam1 = estim_params_.var_exo(:,2);
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ub = estim_params_.var_exo(:,4);
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lb = estim_params_.var_exo(:,3);
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bayestopt_.pshape = estim_params_.var_exo(:,5);
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bayestopt_.p1 = estim_params_.var_exo(:,6);
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bayestopt_.p2 = estim_params_.var_exo(:,7);
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bayestopt_.p3 = estim_params_.var_exo(:,8); %take generalized distribution into account
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bayestopt_.p4 = estim_params_.var_exo(:,9); %take generalized distribution into account
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bayestopt_.jscale = estim_params_.var_exo(:,10);
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bayestopt_.name = cellstr(M_.exo_names(estim_params_.var_exo(:,1),:));
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end
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if nvn
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estim_params_.nvn_observable_correspondence=NaN(nvn,1); % stores number of corresponding observable
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if isequal(M_.H,0) %if no previously set measurement error, initialize H
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nvarobs = length(options_.varobs);
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M_.H = zeros(nvarobs,nvarobs);
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M_.Correlation_matrix_ME = eye(nvarobs);
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end
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for i=1:nvn
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obsi_ = strmatch(deblank(M_.endo_names(estim_params_.var_endo(i,1),:)),options_.varobs,'exact');
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if isempty(obsi_)
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error(['The variable ' deblank(M_.endo_names(estim_params_.var_endo(i,1),:)) ' has to be declared as observable since you assume a measurement error on it.'])
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end
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estim_params_.nvn_observable_correspondence(i,1)=obsi_;
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end
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xparam1 = [xparam1; estim_params_.var_endo(:,2)];
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ub = [ub; estim_params_.var_endo(:,4)];
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lb = [lb; estim_params_.var_endo(:,3)];
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bayestopt_.pshape = [ bayestopt_.pshape; estim_params_.var_endo(:,5)];
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bayestopt_.p1 = [ bayestopt_.p1; estim_params_.var_endo(:,6)];
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bayestopt_.p2 = [ bayestopt_.p2; estim_params_.var_endo(:,7)];
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bayestopt_.p3 = [ bayestopt_.p3; estim_params_.var_endo(:,8)]; %take generalized distribution into account
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bayestopt_.p4 = [ bayestopt_.p4; estim_params_.var_endo(:,9)]; %take generalized distribution into account
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bayestopt_.jscale = [ bayestopt_.jscale; estim_params_.var_endo(:,10)];
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bayestopt_.name = [ bayestopt_.name; transpose(options_.varobs(estim_params_.nvn_observable_correspondence))];
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end
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if ncx
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xparam1 = [xparam1; estim_params_.corrx(:,3)];
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ub = [ub; max(min(estim_params_.corrx(:,5),1),-1)];
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lb = [lb; min(max(estim_params_.corrx(:,4),-1),1)];
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bayestopt_.pshape = [ bayestopt_.pshape; estim_params_.corrx(:,6)];
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bayestopt_.p1 = [ bayestopt_.p1; estim_params_.corrx(:,7)];
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bayestopt_.p2 = [ bayestopt_.p2; estim_params_.corrx(:,8)];
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bayestopt_.p3 = [ bayestopt_.p3; estim_params_.corrx(:,9)]; %take generalized distribution into account
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bayestopt_.p4 = [ bayestopt_.p4; estim_params_.corrx(:,10)]; %take generalized distribution into account
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bayestopt_.jscale = [ bayestopt_.jscale; estim_params_.corrx(:,11)];
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bayestopt_.name = [bayestopt_.name; cellstr([repmat('corr ',ncx,1)...
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deblank(M_.exo_names(estim_params_.corrx(:,1),:)) ...
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repmat(', ',ncx,1) , deblank(M_.exo_names(estim_params_.corrx(:,2),:))])];
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end
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if ncn
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estim_params_.corrn_observable_correspondence=NaN(ncn,2);
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if isequal(M_.H,0)
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nvarobs = length(options_.varobs);
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M_.H = zeros(nvarobs,nvarobs);
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M_.Correlation_matrix_ME = eye(nvarobs);
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end
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xparam1 = [xparam1; estim_params_.corrn(:,3)];
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ub = [ub; max(min(estim_params_.corrn(:,5),1),-1)];
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lb = [lb; min(max(estim_params_.corrn(:,4),-1),1)];
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bayestopt_.pshape = [ bayestopt_.pshape; estim_params_.corrn(:,6)];
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bayestopt_.p1 = [ bayestopt_.p1; estim_params_.corrn(:,7)];
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bayestopt_.p2 = [ bayestopt_.p2; estim_params_.corrn(:,8)];
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bayestopt_.p3 = [ bayestopt_.p3; estim_params_.corrn(:,9)]; %take generalized distribution into account
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bayestopt_.p4 = [ bayestopt_.p4; estim_params_.corrn(:,10)]; %take generalized distribution into account
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bayestopt_.jscale = [ bayestopt_.jscale; estim_params_.corrn(:,11)];
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bayestopt_.name = [bayestopt_.name; cellstr([repmat('corr ',ncn,1) ...
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deblank(M_.endo_names(estim_params_.corrn(:,1),:)) ...
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repmat(', ',ncn,1) , deblank(M_.endo_names(estim_params_.corrn(:,2),:))])];
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for i=1:ncn
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k1 = estim_params_.corrn(i,1);
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k2 = estim_params_.corrn(i,2);
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obsi1 = strmatch(deblank(M_.endo_names(k1,:)),options_.varobs,'exact'); %find correspondence to varobs to construct H in set_all_paramters
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obsi2 = strmatch(deblank(M_.endo_names(k2,:)),options_.varobs,'exact');
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estim_params_.corrn_observable_correspondence(i,:)=[obsi1,obsi2]; %save correspondence
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end
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end
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if np
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xparam1 = [xparam1; estim_params_.param_vals(:,2)];
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ub = [ub; estim_params_.param_vals(:,4)];
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lb = [lb; estim_params_.param_vals(:,3)];
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bayestopt_.pshape = [ bayestopt_.pshape; estim_params_.param_vals(:,5)];
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bayestopt_.p1 = [ bayestopt_.p1; estim_params_.param_vals(:,6)];
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bayestopt_.p2 = [ bayestopt_.p2; estim_params_.param_vals(:,7)];
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bayestopt_.p3 = [ bayestopt_.p3; estim_params_.param_vals(:,8)]; %take generalized distribution into account
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bayestopt_.p4 = [ bayestopt_.p4; estim_params_.param_vals(:,9)]; %take generalized distribution into account
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bayestopt_.jscale = [ bayestopt_.jscale; estim_params_.param_vals(:,10)];
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bayestopt_.name = [bayestopt_.name; cellstr(M_.param_names(estim_params_.param_vals(:,1),:))];
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end
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bayestopt_.p6 = NaN(size(bayestopt_.p1)) ;
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bayestopt_.p7 = bayestopt_.p6 ;
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%% check for point priors and disallow them as they do not work with MCMC
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if any(bayestopt_.p2 ==0)
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error(sprintf(['Error in prior for %s: you cannot use a point prior in estimation. Either increase the prior standard deviation',...
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' or fix the parameter completely.'], bayestopt_.name{bayestopt_.p2 ==0}))
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end
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% generalized location parameters by default for beta distribution
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k = find(bayestopt_.pshape == 1);
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k1 = find(isnan(bayestopt_.p3(k)));
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bayestopt_.p3(k(k1)) = zeros(length(k1),1);
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k1 = find(isnan(bayestopt_.p4(k)));
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bayestopt_.p4(k(k1)) = ones(length(k1),1);
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for i=1:length(k)
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if (bayestopt_.p1(k(i))<bayestopt_.p3(k(i))) || (bayestopt_.p1(k(i))>bayestopt_.p4(k(i)))
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error(['The prior mean of ' bayestopt_.name{k(i)} ' has to be between the lower (' num2str(bayestopt_.p3(k(i))) ') and upper (' num2str(bayestopt_.p4(k(i))) ') bounds of the beta prior density!']);
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end
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mu = (bayestopt_.p1(k(i))-bayestopt_.p3(k(i)))/(bayestopt_.p4(k(i))-bayestopt_.p3(k(i)));
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stdd = bayestopt_.p2(k(i))/(bayestopt_.p4(k(i))-bayestopt_.p3(k(i)));
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if stdd^2 > (1-mu)*mu
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error(sprintf(['Error in prior for %s: in a beta distribution with ' ...
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'mean %f, the standard error can''t be larger than' ...
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' %f.'], bayestopt_.name{k(i)},mu,sqrt((1-mu)*mu)))
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end
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bayestopt_.p6(k(i)) = (1-mu)*mu^2/stdd^2 - mu ;
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bayestopt_.p7(k(i)) = bayestopt_.p6(k(i))*(1/mu-1) ;
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m = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) , bayestopt_.p4(k(i)) ],1);
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if length(m)==1
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bayestopt_.p5(k(i)) = m;
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else
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disp(['Prior distribution for parameter ' bayestopt_.name{k(i)} ' has two modes!'])
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bayestopt_.p5(k(i)) = m(1);
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end
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end
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% generalized location parameter by default for gamma distribution
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k = find(bayestopt_.pshape == 2);
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k1 = find(isnan(bayestopt_.p3(k)));
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k2 = find(isnan(bayestopt_.p4(k)));
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bayestopt_.p3(k(k1)) = zeros(length(k1),1);
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bayestopt_.p4(k(k2)) = Inf(length(k2),1);
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for i=1:length(k)
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if isinf(bayestopt_.p2(k(i)))
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error(['Infinite prior standard deviation for parameter ' bayestopt_.name{k(i)} ' is not allowed (Gamma prior)!'])
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end
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mu = bayestopt_.p1(k(i))-bayestopt_.p3(k(i));
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bayestopt_.p7(k(i)) = bayestopt_.p2(k(i))^2/mu ;
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bayestopt_.p6(k(i)) = mu/bayestopt_.p7(k(i)) ;
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bayestopt_.p5(k(i)) = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) ], 2) ;
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end
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% truncation parameters by default for normal distribution
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k = find(bayestopt_.pshape == 3);
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k1 = find(isnan(bayestopt_.p3(k)));
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bayestopt_.p3(k(k1)) = -Inf*ones(length(k1),1);
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k1 = find(isnan(bayestopt_.p4(k)));
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bayestopt_.p4(k(k1)) = Inf*ones(length(k1),1);
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for i=1:length(k)
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bayestopt_.p6(k(i)) = bayestopt_.p1(k(i)) ;
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bayestopt_.p7(k(i)) = bayestopt_.p2(k(i)) ;
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bayestopt_.p5(k(i)) = bayestopt_.p1(k(i)) ;
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end
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% inverse gamma distribution (type 1)
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k = find(bayestopt_.pshape == 4);
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k1 = find(isnan(bayestopt_.p3(k)));
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k2 = find(isnan(bayestopt_.p4(k)));
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bayestopt_.p3(k(k1)) = zeros(length(k1),1);
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bayestopt_.p4(k(k2)) = Inf(length(k2),1);
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for i=1:length(k)
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[bayestopt_.p6(k(i)),bayestopt_.p7(k(i))] = ...
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inverse_gamma_specification(bayestopt_.p1(k(i))-bayestopt_.p3(k(i)),bayestopt_.p2(k(i)),1,0) ;
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bayestopt_.p5(k(i)) = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) ], 4) ;
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end
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% uniform distribution
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k = find(bayestopt_.pshape == 5);
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for i=1:length(k)
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[bayestopt_.p1(k(i)),bayestopt_.p2(k(i)),bayestopt_.p6(k(i)),bayestopt_.p7(k(i))] = ...
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uniform_specification(bayestopt_.p1(k(i)),bayestopt_.p2(k(i)),bayestopt_.p3(k(i)),bayestopt_.p4(k(i)));
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bayestopt_.p3(k(i)) = bayestopt_.p6(k(i)) ;
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bayestopt_.p4(k(i)) = bayestopt_.p7(k(i)) ;
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bayestopt_.p5(k(i)) = NaN ;
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end
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% inverse gamma distribution (type 2)
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k = find(bayestopt_.pshape == 6);
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k1 = find(isnan(bayestopt_.p3(k)));
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k2 = find(isnan(bayestopt_.p4(k)));
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bayestopt_.p3(k(k1)) = zeros(length(k1),1);
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bayestopt_.p4(k(k2)) = Inf(length(k2),1);
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for i=1:length(k)
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[bayestopt_.p6(k(i)),bayestopt_.p7(k(i))] = ...
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inverse_gamma_specification(bayestopt_.p1(k(i))-bayestopt_.p3(k(i)),bayestopt_.p2(k(i)),2,0);
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bayestopt_.p5(k(i)) = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) ], 6) ;
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end
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k = find(isnan(xparam1));
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if ~isempty(k)
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xparam1(k) = bayestopt_.p1(k);
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end
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if options_.initialize_estimated_parameters_with_the_prior_mode
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xparam1 = bayestopt_.p5;
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k = find(isnan(xparam1));% Because the uniform density do not have a mode!
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if ~isempty(k)
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xparam1(k) = bayestopt_.p1(k);
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end
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end
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% I create subfolder M_.dname/prior if needed.
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CheckPath('prior',M_.dname);
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% I save the prior definition if the prior has changed.
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if exist([ M_.dname '/prior/definition.mat'])
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old = load([M_.dname '/prior/definition.mat'],'bayestopt_');
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prior_has_changed = 0;
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if length(bayestopt_.p1)==length(old.bayestopt_.p1)
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if any(bayestopt_.p1-old.bayestopt_.p1)
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prior_has_changed = 1;
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elseif any(bayestopt_.p2-old.bayestopt_.p2)
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prior_has_changed = 1;
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elseif any(bayestopt_.p3-old.bayestopt_.p3)
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prior_has_changed = 1;
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elseif any(bayestopt_.p4-old.bayestopt_.p4)
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prior_has_changed = 1;
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elseif any(bayestopt_.p5-old.bayestopt_.p5(:))
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prior_has_changed = 1;
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elseif any(bayestopt_.p6-old.bayestopt_.p6)
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prior_has_changed = 1;
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elseif any(bayestopt_.p7-old.bayestopt_.p7)
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prior_has_changed = 1;
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end
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else
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prior_has_changed = 1;
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end
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if prior_has_changed
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delete([M_.dname '/prior/definition.mat']);
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save([M_.dname '/prior/definition.mat'],'bayestopt_');
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end
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else
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save([M_.dname '/prior/definition.mat'],'bayestopt_');
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end
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% initialize persistent variables in priordens()
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priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7, ...
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bayestopt_.p3,bayestopt_.p4,1);
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% Put bayestopt_ in matlab's workspace
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assignin('base','bayestopt_',bayestopt_); |