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function [x,f,abscissa,dens,binf,bsup] = draw_prior_density ( indx,bayestopt_) ;
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% Computes values of prior densities at many points (before plotting)
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%
% INPUTS
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% indx [integer] Parameter number.
% bayestopt_ [structure] Describes the prior beliefs.
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%
% OUTPUTS
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% 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
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% Copyright (C) 2004-2011 Dynare Team
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%
% 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/>.
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pshape = bayestopt_ . pshape ;
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p3 = bayestopt_ . p3 ;
p4 = bayestopt_ . p4 ;
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p6 = bayestopt_ . p6 ;
p7 = bayestopt_ . p7 ;
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truncprior = 1e-3 ;
steps = 200 ;
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switch pshape ( indx )
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case 1 % Beta prior
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density = @ ( x , a , b , aa , bb ) betapdf ( ( x - aa ) / ( bb - aa ) , a , b ) / ( bb - aa ) ;
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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 ) ;
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abscissa = linspace ( infbound , supbound , steps ) ;
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dens = density ( abscissa , p6 ( indx ) , p7 ( indx ) , p3 ( indx ) , p4 ( indx ) ) ;
case 2 % Generalized Gamma prior
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density = @ ( x , a , b , c ) gampdf ( x - c , a , b ) ;
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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
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if isoctave
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error ( [ ' Due to a bug in Octave, you must choose other values for mean and/or variance of your prior on ' bayestopt_ . name { indx } ' , or use another shape' ] )
else
rethrow ( lasterror )
end
end
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abscissa = linspace ( infbound , supbound , steps ) ;
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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 ) ) ;
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abscissa = linspace ( infbound , supbound , steps ) ;
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dens = normpdf ( abscissa , p6 ( indx ) , p7 ( indx ) ) ;
case 4 % Inverse-gamma of type 1 prior
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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
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if isoctave
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error ( [ ' Due to a bug in Octave, you must choose other values for mean and/or variance of your prior on ' bayestopt_ . name { indx } ' , or use another shape' ] )
else
rethrow ( lasterror )
end
end
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abscissa = linspace ( infbound , supbound , steps ) ;
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dens = exp ( lpdfig1 ( abscissa - p3 ( indx ) , p6 ( indx ) , p7 ( indx ) ) ) ;
case 5 % Uniform prior
infbound = p6 ( indx ) ;
supbound = p7 ( indx ) ;
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abscissa = linspace ( infbound , supbound , steps ) ;
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dens = ones ( 1 , steps ) / ( supbound - infbound ) ;
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case 6 % Inverse-gamma of type 2 prior
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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
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if isoctave
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error ( [ ' Due to a bug in Octave, you must choose other values for mean and/or variance of your prior on ' bayestopt_ . name { indx } ' , or use another shape' ] )
else
rethrow ( lasterror )
end
end
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abscissa = linspace ( infbound , supbound , steps ) ;
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dens = exp ( lpdfig2 ( abscissa - p3 ( indx ) , p6 ( indx ) , p7 ( indx ) ) ) ;
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case 8
density = @ ( x , a , b , c ) exp ( lpdfgweibull ( x , a , b , c ) ) ;
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infbound = p3 ( indx ) + wblinv ( truncprior , p6 ( indx ) , p7 ( indx ) ) ;
supbound = p3 ( indx ) + wblinv ( 1 - truncprior , p6 ( indx ) , p7 ( indx ) ) ;
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abscissa = linspace ( infbound , supbound , steps ) ;
dens = density ( abscissa , p6 ( indx ) , p7 ( indx ) , p3 ( indx ) ) ;
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otherwise
error ( sprintf ( ' draw_prior_density: unknown distribution shape (index %d, type %d)' , indx , pshape ( indx ) ) ) ;
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end
if pshape ( indx ) ~= 5
[ junk , k1 ] = max ( dens ) ;
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if k1 == 1 || k1 == length ( dens )
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k = find ( dens > 10 ) ;
dens ( k ) = NaN ;
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end
end
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binf = abscissa ( 1 ) ;
bsup = abscissa ( end ) ;
x = abscissa ;
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f = dens ;