Commit 418382b3 authored by Stéphane Adjemian's avatar Stéphane Adjemian

Fixed bug (trac#225). Added texinfo header and unitary test.

parent 9c3551bc
function err = ig1fun(nu,mu2,sigma2)
err = 2*mu2*gamma(nu/2).^2-(sigma2+mu2)*(nu-2).*gamma((nu-1)/2).^2;
\ No newline at end of file
function [s,nu] = inverse_gamma_specification(mu,sigma,type)
function [s,nu] = inverse_gamma_specification(mu,sigma,type,use_fzero_flag)
% Computes the inverse Gamma hyperparameters from the prior mean and standard deviation.
% function [s,nu] = inverse_gamma_specification(mu,sigma,type)
% Specification of the inverse Gamma function parameters
% X ~ IG(s,nu)
%
% INPUTS
% mu: expectation
% sigma: standard deviation
% type=1: inverse Gamma 1
% type=2: inverse Gamma 2
% OUTPUTS
% s: shape parameter
% nu: scale parameter
%
% SPECIAL REQUIREMENTS
% none
%@info:
%! @deftypefn {Function File} {[@var{s}, @var{nu} ]=} colon (@var{mu}, @var{sigma}, @var{type}, @var{use_fzero_flag})
%! @anchor{distributions/inverse_gamma_specification}
%! @sp 1
%! Computes the inverse Gamma (type 1 or 2) hyperparameters from the prior mean (@var{mu}) and standard deviation (@var{sigma}).
%! @sp 2
%! @strong{Inputs}
%! @sp 1
%! @table @ @var
%! @item mu
%! Double scalar, prior mean.
%! @item sigma
%! Positive double scalar, prior standard deviation.
%! @item type
%! Integer scalar equal to one or two, type of the Inverse-Gamma distribution.
%! @item use_fzero_flag
%! Integer scalar equal to 0 (default) or 1. Use (matlab/octave's implementation of) fzero to solve for @var{nu} if equal to 1, use
%! dynare's implementation of the secant method otherwise.
%! @end table
%! @sp 1
%! @strong{Outputs}
%! @sp 1
%! @table @ @var
%! @item s
%! Positive double scalar (greater than two), first hypermarameter of the Inverse-Gamma prior.
%! @item nu
%! Positive double scala, second hypermarameter of the Inverse-Gamma prior.
%! @end table
%! @sp 2
%! @strong{This function is called by:}
%! @sp 1
%! @ref{set_prior}
%! @sp 2
%! @strong{This function calls:}
%!
%! @end deftypefn
%@eod:
% Copyright (C) 2003-2010 Dynare Team
% Copyright (C) 2003-2011 Dynare Team
%
% This file is part of Dynare.
%
......@@ -34,6 +56,12 @@ function [s,nu] = inverse_gamma_specification(mu,sigma,type)
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
check_solution_flag = 1;
if nargin==3
use_fzero_flag = 0;
end
sigma2 = sigma^2;
mu2 = mu^2;
......@@ -41,12 +69,28 @@ if type == 2; % Inverse Gamma 2
nu = 2*(2+mu2/sigma2);
s = 2*mu*(1+mu2/sigma2);
elseif type == 1; % Inverse Gamma 1
if sigma2 < Inf;
if sigma2 < Inf
nu = sqrt(2*(2+mu2/sigma2));
if use_fzero_flag
nu = fzero(@(nu)ig1fun(nu,mu2,sigma2),nu);
else
nu2 = 2*nu;
nu1 = 2;
err = 2*mu2*gamma(nu/2)^2-(sigma2+mu2)*(nu-2)*gamma((nu-1)/2)^2;
while abs(nu2-nu1) > 1e-12
err = ig1fun(nu,mu2,sigma2);
err1 = ig1fun(nu1,mu2,sigma2);
err2 = ig1fun(nu2,mu2,sigma2);
if sign(err2) % Too short interval.
while nu2/nu<1000 % Shift the interval contaioning the root.
nu1 = nu2;
nu2 = nu2*1.01;
err2 = ig1fun(nu2,mu2,sigma2);
if err2<0
break
end
end
end
% Sove for nu using the secant method.
while abs(nu2-nu1) > 1e-14
if err > 0
nu1 = nu;
if nu < nu2
......@@ -59,18 +103,36 @@ elseif type == 1; % Inverse Gamma 1
nu2 = nu;
end
nu = (nu1+nu2)/2;
err = 2*mu2*gamma(nu/2)^2-(sigma2+mu2)*(nu-2)*gamma((nu-1)/2)^2;
err = ig1fun(nu,mu2,sigma2);
end
end
s = (sigma2+mu2)*(nu-2);
else;
if check_solution_flag
if abs(mu-sqrt(s/2)*gamma((nu-1)/2)/gamma(nu/2))>1e-9
error('inverse_gamma_specification:: Failed in solving for the hyperparameters!');
end
if abs(sigma-sqrt(s/(nu-2)-mu^2))>1e-9
error('inverse_gamma_specification:: Failed in solving for the hyperparameters!');
end
end
else
nu = 2;
s = 2*mu2/pi;
end;
else;
end
else
s = -1;
nu = -1;
end;
end
% 01/18/2004 MJ replaced fsolve with secant
% suppressed chck
% changed order of output parameters
\ No newline at end of file
%@test:1
%$ %addpath ../matlab/distributions
%$
%$ % Define two dates
%$ [s0,nu0] = inverse_gamma_specification(.75,.1,1,0);
%$ [s1,nu1] = inverse_gamma_specification(.75,.1,1,1);
%$
%$ % Check the results.
%$ t(1) = dyn_assert(s0,s1,1e-6);
%$ t(2) = dyn_assert(nu0,nu1,1e-6);
%$ T = all(t);
%@eof:1
\ No newline at end of file
......@@ -222,7 +222,7 @@ 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) ;
inverse_gamma_specification(bayestopt_.p1(k(i))-bayestopt_.p3(k(i)),bayestopt_.p2(k(i)),1,0) ;
bayestopt_.p5(k(i)) = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) ], 4) ;
end
......@@ -244,7 +244,7 @@ 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);
inverse_gamma_specification(bayestopt_.p1(k(i))-bayestopt_.p3(k(i)),bayestopt_.p2(k(i)),2,0);
bayestopt_.p5(k(i)) = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) ], 6) ;
end
......
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