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function [x,f,abscissa,dens,binf,bsup] = draw_prior_density(indx,bayestopt_)
% Computes values of prior densities at many points (before plotting)
%
% INPUTS
% indx [integer] Parameter number.
% bayestopt_ [structure] Describes the prior beliefs.
%
% OUTPUTS
% x [double] Row vector, subset of 'abscissa' such as the density is less than 10
% f [double] Row vector, subset of 'dens' such as the density is less than 10
% abscissa [double] Row vector, abscissa
% dens [double] Row vector, density
% binf: [double] Scalar, first element of x
% bsup: [double] Scalar, last element of x
% Copyright (C) 2004-2017 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/>.
pshape = bayestopt_.pshape;
p3 = bayestopt_.p3;
p4 = bayestopt_.p4;
p6 = bayestopt_.p6;
p7 = bayestopt_.p7;
truncprior = 1e-3;
steps = 200;
switch pshape(indx)
case 1% Beta prior
density = @(x,a,b,aa,bb) betapdf((x-aa)/(bb-aa), a, b)/(bb-aa);
infbound = betainv(truncprior,p6(indx),p7(indx))*(p4(indx)-p3(indx))+p3(indx);
supbound = betainv(1-truncprior,p6(indx),p7(indx))*(p4(indx)-p3(indx))+p3(indx);
abscissa = linspace(infbound,supbound,steps);
dens = density(abscissa,p6(indx),p7(indx),p3(indx),p4(indx));
case 2% Generalized Gamma prior
density = @(x,a,b,c) gampdf(x-c,a,b);
try
infbound = gaminv(truncprior,p6(indx),p7(indx))+p3(indx);
supbound = gaminv(1-truncprior,p6(indx),p7(indx))+p3(indx);
catch
% Workaround for ticket #161, see http://savannah.gnu.org/bugs/?52569
if isoctave
error(['Due to a computational limitation in Octave, the prior cannot be plotted. You must either use plot_priors=0 or choose other values for mean and/or variance of your prior on ' bayestopt_.name{indx} ', or use another shape'])
else
rethrow(lasterror)
end
end
abscissa = linspace(infbound,supbound,steps);
dens = density(abscissa,p6(indx),p7(indx),p3(indx));
case 3% Gaussian prior
infbound = norminv(truncprior,p6(indx),p7(indx));
supbound = norminv(1-truncprior,p6(indx),p7(indx));
abscissa = linspace(infbound,supbound,steps);
dens = normpdf(abscissa,p6(indx),p7(indx));
case 4% Inverse-gamma of type 1 prior
try
infbound = 1/sqrt(gaminv(1-10*truncprior, p7(indx)/2, 2/p6(indx)))+p3(indx);
supbound = 1/sqrt(gaminv(10*truncprior, p7(indx)/2, 2/p6(indx)))+p3(indx);
catch
% Workaround for ticket #161, see http://savannah.gnu.org/bugs/?52569
if isoctave
error(['Due to a computational limitation in Octave, the prior cannot be plotted. You must either use plot_priors=0 or choose other values for mean and/or variance of your prior on ' bayestopt_.name{indx} ', or use another shape'])
else
rethrow(lasterror)
end
end
abscissa = linspace(infbound,supbound,steps);
dens = exp(lpdfig1(abscissa-p3(indx),p6(indx),p7(indx)));
case 5% Uniform prior
infbound = p6(indx);
supbound = p7(indx);
abscissa = linspace(infbound,supbound,steps);
dens = ones(1, steps) / (supbound-infbound);
case 6% Inverse-gamma of type 2 prior
try
infbound = 1/(gaminv(1-10*truncprior, p7(indx)/2, 2/p6(indx)))+p3(indx);
supbound = 1/(gaminv(10*truncprior, p7(indx)/2, 2/p6(indx)))+p3(indx);
catch
% Workaround for ticket #161, see http://savannah.gnu.org/bugs/?52569
if isoctave
error(['Due to a computational limitation in Octave, the prior cannot be plotted. You must either use plot_priors=0 or choose other values for mean and/or variance of your prior on ' bayestopt_.name{indx} ', or use another shape'])
else
rethrow(lasterror)
end
end
abscissa = linspace(infbound,supbound,steps);
dens = exp(lpdfig2(abscissa-p3(indx),p6(indx),p7(indx)));
case 8
density = @(x,a,b,c) exp(lpdfgweibull(x, a, b, c));
infbound = p3(indx)+wblinv(truncprior,p6(indx),p7(indx));
supbound = p3(indx)+wblinv(1-truncprior,p6(indx),p7(indx));
abscissa = linspace(infbound,supbound,steps);
dens = density(abscissa,p6(indx),p7(indx),p3(indx));
otherwise
error(sprintf('draw_prior_density: unknown distribution shape (index %d, type %d)', indx, pshape(indx)));
end
if pshape(indx) ~= 5
[~,k1] = max(dens);
if k1 == 1 || k1 == length(dens)
k = find(dens > 10);
dens(k) = NaN;
end
end
binf = abscissa(1);
bsup = abscissa(end);
x = abscissa;
f = dens;
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