210 lines
6.1 KiB
Matlab
210 lines
6.1 KiB
Matlab
function [s,nu] = inverse_gamma_specification(mu, sigma2, lb, type, use_fzero_flag, name)
|
|
|
|
% Computes the inverse Gamma hyperparameters from the prior mean and variance.
|
|
%
|
|
% INPUTS
|
|
% - mu [double] scalar, prior mean.
|
|
% - sigma2 [double] positive scalar, prior variance.
|
|
% - type [integer] scalar equal to 1 or 2, type of the inverse gamma distribution
|
|
% - use_fzero_flag [logical] scalar, Use (matlab/octave's implementation of) fzero to solve for nu if true, use
|
|
% dynare's implementation of the secant method otherwise.
|
|
% - name [string] name of the parameter or random variable.
|
|
%
|
|
% OUTPUS
|
|
% - s [double] scalar, first hyperparameter.
|
|
% - nu [double] scalar, second hyperparameter.
|
|
%
|
|
% REMARKS
|
|
% 1. In the Inverse Gamma parameterization with alpha and beta, we have alpha=nu/2 and beta=2/s, where
|
|
% if X is IG(alpha,beta) then 1/X is Gamma(alpha,1/beta)
|
|
% 2. The call to the matlab's implementation of the secant method is here for testing purpose and should not be used. This routine fails
|
|
% more often in finding an interval for nu containing a signe change because it expands the interval on both sides and eventually
|
|
% violates the condition nu>2.
|
|
|
|
% Copyright © 2003-2023 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 <https://www.gnu.org/licenses/>.
|
|
|
|
if nargin<4
|
|
error('At least four input arguments are required!')
|
|
end
|
|
|
|
if ~isnumeric(mu) || ~isscalar(mu) || ~isreal(mu)
|
|
error('First input argument must be a real scalar!')
|
|
end
|
|
|
|
if ~isnumeric(sigma2) || ~isscalar(sigma2) || ~isreal(sigma2) || sigma2<=0
|
|
error('Second input argument must be a real positive scalar!')
|
|
end
|
|
|
|
if ~isnumeric(lb) || ~isscalar(lb) || ~isreal(lb)
|
|
error('Third input argument must be a real scalar!')
|
|
end
|
|
|
|
if ~isnumeric(type) || ~isscalar(type) || ~ismember(type, [1, 2])
|
|
error('Fourth input argument must be equal to 1 or 2!')
|
|
end
|
|
|
|
if nargin==4 || isempty(use_fzero_flag)
|
|
use_fzero_flag = false;
|
|
else
|
|
if ~isscalar(use_fzero_flag) || ~islogical(use_fzero_flag)
|
|
error('Fifth input argument must be a scalar logical!')
|
|
end
|
|
end
|
|
|
|
if nargin>5 && (~ischar(name) || size(name, 1)>1)
|
|
error('Sixth input argument must be a string!')
|
|
else
|
|
name = '';
|
|
end
|
|
|
|
if ~isempty(name)
|
|
name = sprintf(' for %s', name);
|
|
end
|
|
|
|
if mu<=lb
|
|
error('The prior mean%s (%f) must be above the lower bound (%f)of the Inverse Gamma (type %d) prior distribution!', mu, lb, name, type);
|
|
end
|
|
|
|
check_solution_flag = true;
|
|
s = [];
|
|
nu = [];
|
|
|
|
sigma = sqrt(sigma2);
|
|
mu2 = mu*mu;
|
|
|
|
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
|
|
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 = ig1fun(nu,mu2,sigma2);
|
|
err2 = ig1fun(nu2,mu2,sigma2);
|
|
if err2 > 0 % Too short interval.
|
|
while nu2 < 1e12 % Shift the interval containing the root.
|
|
nu1 = nu2;
|
|
nu2 = nu2*2;
|
|
err2 = ig1fun(nu2,mu2,sigma2);
|
|
if err2<0
|
|
break
|
|
end
|
|
end
|
|
if err2>0
|
|
error('inverse_gamma_specification:: Failed in finding an interval containing a sign change! You should check that the prior variance is not too small compared to the prior mean...');
|
|
end
|
|
end
|
|
% Solve for nu using the secant method.
|
|
while abs(nu2/nu1-1) > 1e-14
|
|
if err > 0
|
|
nu1 = nu;
|
|
if nu < nu2
|
|
nu = nu2;
|
|
else
|
|
nu = 2*nu;
|
|
nu2 = nu;
|
|
end
|
|
else
|
|
nu2 = nu;
|
|
end
|
|
nu = (nu1+nu2)/2;
|
|
err = ig1fun(nu,mu2,sigma2);
|
|
end
|
|
end
|
|
s = (sigma2+mu2)*(nu-2);
|
|
if check_solution_flag
|
|
if abs(log(mu)-log(sqrt(s/2))-gammaln((nu-1)/2)+gammaln(nu/2))>1e-7
|
|
error('inverse_gamma_specification:: Failed in solving for the hyperparameters!');
|
|
end
|
|
if abs(sigma-sqrt(s/(nu-2)-mu*mu))>1e-7
|
|
error('inverse_gamma_specification:: Failed in solving for the hyperparameters!');
|
|
end
|
|
end
|
|
else
|
|
nu = 2;
|
|
s = 2*mu2/pi;
|
|
end
|
|
else
|
|
error('inverse_gamma_specification: unkown type')
|
|
end
|
|
|
|
return % --*-- Unit tests --*--
|
|
|
|
%@test:1
|
|
try
|
|
[s, nu] = inverse_gamma_specification(.5, .05, 0, 1);
|
|
t(1) = true;
|
|
catch
|
|
t(1) = false;
|
|
end
|
|
|
|
if t(1)
|
|
t(2) = abs(0.5-sqrt(.5*s)*gamma(.5*(nu-1))/gamma(.5*nu))<1e-12;
|
|
t(3) = abs(0.05-s/(nu-2)+.5^2)<1e-12;
|
|
end
|
|
T = all(t);
|
|
%@eof:1
|
|
|
|
%@test:2
|
|
try
|
|
[s, nu] = inverse_gamma_specification(.5, .05, 0, 2);
|
|
t(1) = true;
|
|
catch
|
|
t(1) = false;
|
|
end
|
|
|
|
if t(1)
|
|
t(2) = abs(0.5-s/(nu-2))<1e-12;
|
|
t(3) = abs(0.05-2*.5^2/(nu-4))<1e-12;
|
|
end
|
|
T = all(t);
|
|
%@eof:2
|
|
|
|
%@test:3
|
|
try
|
|
[s, nu] = inverse_gamma_specification(.5, Inf, 0, 1);
|
|
t(1) = true;
|
|
catch
|
|
t(1) = false;
|
|
end
|
|
|
|
if t(1)
|
|
t(2) = abs(0.5-sqrt(.5*s)*gamma(.5*(nu-1))/gamma(.5*nu))<1e-12;
|
|
t(3) = isequal(nu, 2); %abs(0.05-2*.5^2/(nu-4))<1e-12;
|
|
end
|
|
T = all(t);
|
|
%@eof:3
|
|
|
|
%@test:4
|
|
try
|
|
[s, nu] = inverse_gamma_specification(.5, Inf, 0, 2);
|
|
t(1) = true;
|
|
catch
|
|
t(1) = false;
|
|
end
|
|
|
|
if t(1)
|
|
t(2) = abs(0.5-s/(nu-2))<1e-12;
|
|
t(3) = isequal(nu, 4);
|
|
end
|
|
T = all(t);
|
|
%@eof:4 |