292 lines
10 KiB
Matlab
292 lines
10 KiB
Matlab
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function o = moments(o, name)
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% Compute the prior moments.
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%
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% INPUTS
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% - o [dprior]
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%
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% OUTPUTS
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% - o [dprior]
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% Copyright © 2023 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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switch name
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case 'mean'
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m = o.p1;
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case 'median'
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m = o.p11;
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case 'std'
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m = o.p2;
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case 'mode'
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m = o.p5;
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otherwise
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error('%s is not an implemented moemnt.', name)
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end
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id = isnan(m);
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if any(id)
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% For some parameters the prior mean is not defined.
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% We compute the first order moment from the
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% hyperparameters, if the hyperparameters are not
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% available an error is thrown.
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if o.isuniform
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jd = intersect(o.iduniform, find(id));
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if ~isempty(jd)
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if any(isnan(o.p3(jd))) || any(isnan(o.p4(jd)))
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error('dprior::mean: Some hyperparameters are missing (uniform distribution).')
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end
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switch name
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case 'mean'
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m(jd) = o.p3(jd) + .5*(o.p4(jd)-o.p3(jd));
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case 'median'
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m(jd) = o.p3(jd) + .5*(o.p4(jd)-o.p3(jd));
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case 'std'
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m(jd) = (o.p4(jd)-o.p3(jd))/sqrt(12);
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case 'mode' % Actually we have a continuum of modes with the uniform distribution.
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m(jd) = o.p3(jd) + .5*(o.p4(jd)-o.p3(jd));
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end
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end
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end
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if o.isgaussian
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jd = intersect(o.idgaussian, find(id));
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if ~isempty(jd)
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if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd)))
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error('dprior::mean: Some hyperparameters are missing (gaussian distribution).')
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end
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switch name
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case 'mean'
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m(jd) = o.p6(jd);
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case 'median'
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m(jd) = o.p6(jd);
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case 'std'
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m(jd) = o.p7(jd);
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case 'mode' % Actually we have a continuum of modes with the uniform distribution.
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m(jd) = o.p6(jd);
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end
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end
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end
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if o.isgamma
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jd = intersect(o.idgamma, find(id));
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if ~isempty(jd)
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if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd))) || any(isnan(o.p3(jd)))
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error('dprior::mean: Some hyperparameters are missing (gamma distribution).')
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end
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% α → o.p6, β → o.p7
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switch name
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case 'mean'
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m(jd) = o.p3(jd) + o.p6(jd).*o.p7(jd);
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case 'median'
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m(jd) = o.p3(jd) + gaminv(.5, o.p6(jd), o.p7(jda));
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case 'std'
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m(jd) = sqrt(o.p6(jd)).*o.p7(jd);
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case 'mode'
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m(jd) = 0;
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hd = o.p6(jd)>1;
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m(jd(hd)) = (o.p6(jd(hd))-1).*o.p7(jd(hd));
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end
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end
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end
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if o.isbeta
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jd = intersect(o.idbeta, find(id));
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if ~isempty(jd)
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if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd))) || any(isnan(o.p3(jd))) || any(isnan(o.p4(jd)))
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error('dprior::mean: Some hyperparameters are missing (beta distribution).')
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end
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% α → o.p6, β → o.p7
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switch name
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case 'mean'
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m(jd) = o.p3(jd) + (o.p6(jd)./(o.p6(jd)+o.p7(jd))).*(o.p4(jd)-o.p3(jd));
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case 'median'
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m(jd) = o.p3(jd) + betainv(.5, o.p6(jd), o.p7(jd)).*(o.p4(jd)-o.p3(jd));
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case 'std'
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m(jd) = (o.p4(jd)-o.p3(jd)).*sqrt(o.p6(jd).*o.p7(jd)./((o.p6(jd)+o.p7(jd)).^2.*(o.p6(jd)+o.p7(jd)+1)));
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case 'mode'
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h0 = true(jd, 1);
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h1 = o.p6(jd)<=1 & o.p7(jd)>1; h0 = h0 & ~h1;
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h2 = o.p7(jd)<=1 & o.p6(jd)>1; h0 = h0 & ~h2;
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h3 = o.p6(jd)<1 & o.p7(jd)<1; h0 = h0 & ~h3;
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h4 = ismembertol(o.p6(jd), 1) & ismembertol(o.p7(jd),1); h0 = h0 & ~h4;
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m(jd(h1)) = o.p3(jd(h1)); % Standard β has a mode at 0
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m(jd(h2)) = o.p4(jd(h2)); % Standard β has a mode at 1
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m(jd(h3)) = o.p3(jd(h3)); % Standard β is bimodal, we pick the lowest mode (0)
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m(jd(h4)) = o.p3(jd(h4)) + .5*(o.p4(jd(h4))-o.p3(jd(h4))); % Standard β is the uniform distribution (continuum of modes), we pick the mean as the mode
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m(jd(h0)) = o.p3(jd(h0))+(o.p4(jd(h0))-o.p3(jd(h0))).*((o.p6(jd(h0))-1)./(o.p6(jd(h0))+o.p7(jd(h0))-2)); % β distribution is concave and has a unique interior mode.
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end
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end
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end
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if o.isinvgamma1
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jd = intersect(o.idinvgamma1, find(id));
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if ~isempty(jd)
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if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd))) || any(isnan(o.p3(jd)))
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error('dprior::mean: Some hyperparameters are missing (inverse gamma type 1 distribution).')
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end
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% s → o.p6, ν → o.p7
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switch name
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case 'mean'
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m(jd) = o.p3(jd) + sqrt(.5*o.p6(jd)) .*(gamma(.5*(o.p7(jd)-1))./gamma(.5*o.p7(jd)));
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case 'median'
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m(jd) = o.p3(jd) + 1.0/sqrt(gaminv(.5, o.p7(jd)/2.0, 2.0/o.p6(jd)));
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case 'std'
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m(jd) = sqrt( o.p6(jd)./(o.p7(jd)-2)-(.5*o.p6(jd)).*(gamma(.5*(o.p7(jd)-1))./gamma(.5*o.p7(jd))).^2);
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case 'mode'
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m(jd) = sqrt((o.p7(jd)-1)./o.p6(jd));
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end
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end
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end
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if o.isinvgamma2
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jd = intersect(o.idinvgamma2, find(id));
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if ~isempty(jd)
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if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd))) || any(isnan(o.p3(jd)))
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error('dprior::mean: Some hyperparameters are missing (inverse gamma type 2 distribution).')
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end
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% s → o.p6, ν → o.p7
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switch name
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case 'mean'
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m(jd) = o.p3(jd) + o.p6(jd)./(o.p7(jd)-2);
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case 'median'
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m(jd) = o.p3(jd) + 1.0/gaminv(.5, o.p7(jd)/2.0, 2.0/o.p6(jd));
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case 'std'
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m(jd) = sqrt(2./(o.p7(jd)-4)).*o.p6(jd)./(o.p7(jd)-2);
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case 'mode'
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m(jd) = o.p6(jd)./(o.p7(jd)+2);
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end
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end
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end
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if o.isweibull
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jd = intersect(o.idweibull, find(id));
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if ~isempty(jd)
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if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd))) || any(isnan(o.p3(jd)))
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error('dprior::mean: Some hyperparameters are missing (weibull distribution).')
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end
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% k → o.p6 (shape parameter), λ → o.p7 (scale parameter)
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% See https://en.wikipedia.org/wiki/Weibull_distribution
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switch name
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case 'mean'
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m(jd) = o.p3(jd) + o.p7(jd).*gamma(1+1./o.p6(jd));
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case 'median'
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m(jd) = o.p3(jd) + o.p7(jd).*log(2).^(1./o.p6(jd));
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case 'std'
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m(jd) = o.p7(jd).*sqrt(gamma(1+2./o.p6(jd))-gamma(1+1./o.p6(jd)).^2);
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case 'mode'
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m(jd) = 0;
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hd = o.p6(jd)>1;
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m(jd(hd)) = o.p3(jd(hd)) + o.p7(jd(hd)).*((o.p6(jd(hd))-1)./o.p6(jd(hd))).^(1./o.p6(jd(hd)));
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end
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end
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end
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switch name
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case 'mean'
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o.p1 = m;
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case 'median'
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o.p11 = m;
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case 'std'
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o.p2 = m;
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case 'mode'
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o.p5 = m;
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end
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end
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return % --*-- Unit tests --*--
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%@test:5
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% Fill global structures with required fields...
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prior_trunc = 1e-10;
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p0 = repmat([1; 2; 3; 4; 5; 6; 8], 2, 1); % Prior shape
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p1 = .4*ones(14,1); % Prior mean
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p2 = .2*ones(14,1); % Prior std.
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p3 = NaN(14,1);
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p4 = NaN(14,1);
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p5 = NaN(14,1);
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p6 = NaN(14,1);
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p7 = NaN(14,1);
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for i=1:14
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switch p0(i)
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case 1
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% Beta distribution
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p3(i) = 0;
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p4(i) = 1;
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[p6(i), p7(i)] = beta_specification(p1(i), p2(i)^2, p3(i), p4(i));
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p5(i) = compute_prior_mode([p6(i) p7(i)], 1);
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case 2
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% Gamma distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = gamma_specification(p1(i), p2(i)^2, p3(i), p4(i));
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p5(i) = compute_prior_mode([p6(i) p7(i)], 2);
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case 3
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% Normal distribution
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p3(i) = -Inf;
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p4(i) = Inf;
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p6(i) = p1(i);
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p7(i) = p2(i);
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p5(i) = p1(i);
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case 4
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% Inverse Gamma (type I) distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = inverse_gamma_specification(p1(i), p2(i)^2, p3(i), 1, false);
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p5(i) = compute_prior_mode([p6(i) p7(i)], 4);
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case 5
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% Uniform distribution
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[p1(i), p2(i), p6(i), p7(i)] = uniform_specification(p1(i), p2(i), p3(i), p4(i));
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p3(i) = p6(i);
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p4(i) = p7(i);
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p5(i) = compute_prior_mode([p6(i) p7(i)], 5);
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case 6
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% Inverse Gamma (type II) distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = inverse_gamma_specification(p1(i), p2(i)^2, p3(i), 2, false);
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p5(i) = compute_prior_mode([p6(i) p7(i)], 6);
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case 8
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% Weibull distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = weibull_specification(p1(i), p2(i)^2, p3(i));
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p5(i) = compute_prior_mode([p6(i) p7(i)], 8);
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otherwise
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error('This density is not implemented!')
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end
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end
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BayesInfo.pshape = p0;
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BayesInfo.p1 = p1;
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BayesInfo.p2 = p2;
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BayesInfo.p3 = p3;
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BayesInfo.p4 = p4;
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BayesInfo.p5 = p5;
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BayesInfo.p6 = p6;
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BayesInfo.p7 = p7;
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% Call the tested routine
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try
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Prior = dprior(BayesInfo, prior_trunc, false);
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = all(Prior.mean()==.4);
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t(3) = all(ismembertol(Prior.mean(true),.4));
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t(4) = all(ismembertol(Prior.variance(),.04));
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t(5) = all(ismembertol(Prior.variance(true),.04));
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end
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T = all(t);
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%@eof:5
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