dynare/matlab/set_prior.m

function [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_)
% function [xparam1,estim_params_,bayestopt_,lb,ub]=set_prior(estim_params_)
% sets prior distributions
%
% INPUTS
%    o estim_params_    [structure] characterizing parameters to be estimated.
%    o M_               [structure] characterizing the model. 
%    o options_         [structure] 
%    
% OUTPUTS
%    o xparam1          [double]    vector of parameters to be estimated (initial values)
%    o estim_params_    [structure] characterizing parameters to be estimated
%    o bayestopt_       [structure] characterizing priors
%    o lb               [double]    vector of lower bounds for the estimated parameters. 
%    o ub               [double]    vector of upper bounds for the estimated parameters.
%    o M_               [structure] characterizing the model.
%    
% SPECIAL REQUIREMENTS
%    None

% Copyright (C) 2003-2009 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/>.
  
    nvx = size(estim_params_.var_exo,1);
    nvn = size(estim_params_.var_endo,1);
    ncx = size(estim_params_.corrx,1);
    ncn = size(estim_params_.corrn,1);
    np = size(estim_params_.param_vals,1);
    
    estim_params_.nvx = nvx;
    estim_params_.nvn = nvn;
    estim_params_.ncx = ncx;
    estim_params_.ncn = ncn;
    estim_params_.np = np;
  
    xparam1 = [];
    ub = [];
    lb = [];
    bayestopt_.pshape = [];
    bayestopt_.p1 = []; % prior mean
    bayestopt_.p2 = []; % prior standard deviation
    bayestopt_.p3 = []; % lower bound
    bayestopt_.p4 = []; % upper bound
    bayestopt_.p5 = []; % prior mode
    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).
    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).
    
    bayestopt_.jscale = [];
    bayestopt_.name = [];
    if nvx
        xparam1 = estim_params_.var_exo(:,2);
        ub = estim_params_.var_exo(:,4); 
        lb = estim_params_.var_exo(:,3); 
        bayestopt_.pshape =  estim_params_.var_exo(:,5);
        bayestopt_.p1 =  estim_params_.var_exo(:,6);
        bayestopt_.p2 =  estim_params_.var_exo(:,7);
        bayestopt_.p3 =  estim_params_.var_exo(:,8);
        bayestopt_.p4 =  estim_params_.var_exo(:,9);
        bayestopt_.jscale =  estim_params_.var_exo(:,10);
        bayestopt_.name = cellstr(M_.exo_names(estim_params_.var_exo(:,1),:));
    end
    if nvn
        if M_.H == 0
            nvarobs = size(options_.varobs,1);
            M_.H = zeros(nvarobs,nvarobs);
        end
        for i=1:nvn
            estim_params_.var_endo(i,1) = strmatch(deblank(M_.endo_names(estim_params_.var_endo(i,1),:)),deblank(options_.varobs),'exact');
        end
        xparam1 = [xparam1; estim_params_.var_endo(:,2)];
        ub = [ub; estim_params_.var_endo(:,4)]; 
        lb = [lb; estim_params_.var_endo(:,3)]; 
        bayestopt_.pshape = [ bayestopt_.pshape; estim_params_.var_endo(:,5)];
        bayestopt_.p1 = [ bayestopt_.p1; estim_params_.var_endo(:,6)];
        bayestopt_.p2 = [ bayestopt_.p2; estim_params_.var_endo(:,7)];
        bayestopt_.p3 = [ bayestopt_.p3; estim_params_.var_endo(:,8)];
        bayestopt_.p4 = [ bayestopt_.p4; estim_params_.var_endo(:,9)];
        bayestopt_.jscale = [ bayestopt_.jscale; estim_params_.var_endo(:,10)];
        bayestopt_.name = cellstr(strvcat(char(bayestopt_.name), M_.endo_names(estim_params_.var_endo(:,1),:)));
    end
    if ncx
        xparam1 = [xparam1; estim_params_.corrx(:,3)];
        ub = [ub; max(min(estim_params_.corrx(:,5),1),-1)];
        lb = [lb; max(min(estim_params_.corrx(:,4),1),-1)];
        bayestopt_.pshape = [ bayestopt_.pshape; estim_params_.corrx(:,6)];
        bayestopt_.p1 = [ bayestopt_.p1; estim_params_.corrx(:,7)];
        bayestopt_.p2 = [ bayestopt_.p2; estim_params_.corrx(:,8)];
        bayestopt_.p3 = [ bayestopt_.p3; estim_params_.corrx(:,9)];
        bayestopt_.p4 = [ bayestopt_.p4; estim_params_.corrx(:,10)];
        bayestopt_.jscale = [ bayestopt_.jscale; estim_params_.corrx(:,11)];
        bayestopt_.name = cellstr(strvcat(char(bayestopt_.name), char(strcat(cellstr(M_.exo_names(estim_params_.corrx(:,1),:)), ...
						  ',' , cellstr(M_.exo_names(estim_params_.corrx(:,2),:))))));
    end
    if ncn
        if M_.H == 0
            nvarobs = size(options_.varobs,1);
            M_.H = zeros(nvarobs,nvarobs);
        end
        xparam1 = [xparam1; estim_params_.corrn(:,3)];
        ub = [ub; max(min(estim_params_.corrn(:,5),1),-1)];
        lb = [lb; max(min(estim_params_.corrn(:,4),1),-1)];
        bayestopt_.pshape = [ bayestopt_.pshape; estim_params_.corrn(:,6)];
        bayestopt_.p1 = [ bayestopt_.p1; estim_params_.corrn(:,7)];
        bayestopt_.p2 = [ bayestopt_.p2; estim_params_.corrn(:,8)];
        bayestopt_.p3 = [ bayestopt_.p3; estim_params_.corrn(:,9)];
        bayestopt_.p4 = [ bayestopt_.p4; estim_params_.corrn(:,10)];
        bayestopt_.jscale = [ bayestopt_.jscale; estim_params_.corrn(:,11)];
        bayestopt_.name = cellstr(strvcat(char(bayestopt_.name), char(strcat(cellstr(M_.endo_names(estim_params_.corrn(:,1),:)),...
						  ',' ,  cellstr(M_.endo_names(estim_params_.corrn(:,2),:))))));
    end
    if np
        xparam1 = [xparam1; estim_params_.param_vals(:,2)];
        ub = [ub; estim_params_.param_vals(:,4)];
        lb = [lb; estim_params_.param_vals(:,3)];
        bayestopt_.pshape = [ bayestopt_.pshape; estim_params_.param_vals(:,5)];
        bayestopt_.p1 = [ bayestopt_.p1; estim_params_.param_vals(:,6)];
        bayestopt_.p2 = [ bayestopt_.p2; estim_params_.param_vals(:,7)];
        bayestopt_.p3 = [ bayestopt_.p3; estim_params_.param_vals(:,8)];
        bayestopt_.p4 = [ bayestopt_.p4; estim_params_.param_vals(:,9)];
        bayestopt_.jscale = [ bayestopt_.jscale; estim_params_.param_vals(:,10)];
        bayestopt_.name = cellstr(strvcat(char(bayestopt_.name),M_.param_names(estim_params_.param_vals(:,1),:)));
    end

    bayestopt_.ub = ub;
    bayestopt_.lb = lb;
    
    bayestopt_.p6 = NaN(size(bayestopt_.p1)) ;
    bayestopt_.p7 = bayestopt_.p6 ;
  
    % generalized location parameters by default for beta distribution
    k = find(bayestopt_.pshape == 1);
    k1 = find(isnan(bayestopt_.p3(k)));
    bayestopt_.p3(k(k1)) = zeros(length(k1),1);
    k1 = find(isnan(bayestopt_.p4(k)));
    bayestopt_.p4(k(k1)) = ones(length(k1),1);
    for i=1:length(k)
        mu = (bayestopt_.p1(k(i))-bayestopt_.p3(k(i)))/(bayestopt_.p4(k(i))-bayestopt_.p3(k(i)));
        stdd = bayestopt_.p2(k(i))/(bayestopt_.p4(k(i))-bayestopt_.p3(k(i)));
        bayestopt_.p6(k(i)) = (1-mu)*mu^2/stdd^2 - mu ;
        bayestopt_.p7(k(i)) = bayestopt_.p6(k(i))*(1/mu-1) ;
        m = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) , bayestopt_.p4(k(i)) ],1);
        if length(m)==1
            bayestopt_.p5(k(i)) = m;
        else
            disp(['Prior distribution for parameter ' int2str(k(i))  ' has two modes!'])
            bayestopt_.p5(k(i)) = bayestopt_.p1(k(i)) ; 
        end
    end
    
    % generalized location parameter by default for gamma distribution
    k =  find(bayestopt_.pshape == 2);
    k1 = find(isnan(bayestopt_.p3(k)));
    k2 = find(isnan(bayestopt_.p4(k)));
    bayestopt_.p3(k(k1)) = zeros(length(k1),1);
    bayestopt_.p4(k(k2)) = Inf(length(k2),1);
    for i=1:length(k)
        mu = bayestopt_.p1(k(i))-bayestopt_.p3(k(i));
        bayestopt_.p7(k(i)) = bayestopt_.p2(k(i))^2/mu ;
        bayestopt_.p6(k(i)) = mu/bayestopt_.p7(k(i)) ;  
        bayestopt_.p5(k(i)) = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) ], 2) ;
    end
    
    % truncation parameters by default for normal distribution
    k  = find(bayestopt_.pshape == 3);
    k1 = find(isnan(bayestopt_.p3(k)));
    bayestopt_.p3(k(k1)) = -Inf*ones(length(k1),1);
    k1 = find(isnan(bayestopt_.p4(k)));
    bayestopt_.p4(k(k1)) = Inf*ones(length(k1),1);
    for i=1:length(k)
        bayestopt_.p6(k(i)) = bayestopt_.p1(k(i)) ; 
        bayestopt_.p7(k(i)) = bayestopt_.p2(k(i)) ;
        bayestopt_.p5(k(i)) = bayestopt_.p1(k(i)) ;
    end

    % inverse gamma distribution (type 1)
    k = find(bayestopt_.pshape == 4);
    k1 = find(isnan(bayestopt_.p3(k)));
    k2 = find(isnan(bayestopt_.p4(k)));
    bayestopt_.p3(k(k1)) = zeros(length(k1),1);
    bayestopt_.p4(k(k2)) = Inf(length(k2),1);
    for i=1:length(k)
        [bayestopt_.p6(k(i)),bayestopt_.p7(k(i))] = ...
            inverse_gamma_specification(bayestopt_.p1(k(i))-bayestopt_.p3(k(i)),bayestopt_.p2(k(i)),1) ;
        bayestopt_.p5(k(i)) = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) ], 4) ;
    end  
    
    % uniform distribution
    k = find(bayestopt_.pshape == 5);
    for i=1:length(k)
        [bayestopt_.p1(k(i)),bayestopt_.p2(k(i)),bayestopt_.p6(k(i)),bayestopt_.p7(k(i))] = ...
            uniform_specification(bayestopt_.p1(k(i)),bayestopt_.p2(k(i)),bayestopt_.p3(k(i)),bayestopt_.p4(k(i)));
        bayestopt_.p3(k(i)) = bayestopt_.p6(k(i)) ;
        bayestopt_.p4(k(i)) = bayestopt_.p7(k(i)) ;
        bayestopt_.p5(k(i)) = NaN ;
    end
    
    % inverse gamma distribution (type 2)
    k = find(bayestopt_.pshape == 6);
    k1 = find(isnan(bayestopt_.p3(k)));
    k2 = find(isnan(bayestopt_.p4(k)));
    bayestopt_.p3(k(k1)) = zeros(length(k1),1);
    bayestopt_.p4(k(k2)) = Inf(length(k2),1);
    for i=1:length(k)
        [bayestopt_.p6(k(i)),bayestopt_.p7(k(i))] = ...
            inverse_gamma_specification(bayestopt_.p1(k(i))-bayestopt_.p3(k(i)),bayestopt_.p2(k(i)),2);
        bayestopt_.p5(k(i)) = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) ], 6) ;
    end
    
    k = find(isnan(xparam1));
    xparam1(k) = bayestopt_.p1(k);

    % I create subfolder M_.dname/prior if needed.
    CheckPath('prior');

    % I save the prior definition if the prior has changed.
    if exist([ M_.dname '/prior/definition.mat'])
        old = load([M_.dname '/prior/definition.mat'],'bayestopt_');
        prior_has_changed = 0;
        if length(bayestopt_.p1)==length(old.bayestopt_.p1)
            if any(bayestopt_.p1-old.bayestopt_.p1)
                prior_has_changed = 1;
            end
            if any(bayestopt_.p2-old.bayestopt_.p2)
                prior_has_changed = 1;
            end
            if any(bayestopt_.p3-old.bayestopt_.p3)
                prior_has_changed = 1;
            end
            if any(bayestopt_.p4-old.bayestopt_.p4)
                prior_has_changed = 1;
            end
            if any(bayestopt_.p5-old.bayestopt_.p5)
                prior_has_changed = 1;
            end
            if any(bayestopt_.p6-old.bayestopt_.p6)
                prior_has_changed = 1;
            end
            if any(bayestopt_.p7-old.bayestopt_.p7)
                prior_has_changed = 1;
            end
        else
            prior_has_changed = 1;
        end
        if prior_has_changed
            delete([M_.dname '/prior/definition.mat']);
            save([M_.dname '/prior/definition.mat'],'bayestopt_');
        end
    else
        save([M_.dname '/prior/definition.mat'],'bayestopt_');
    end