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Add methods for computing moments. 

- prior mean
 - prior mode
 - prior median
 - prior variance
remove-particles-submodule
Stéphane Adjemian (Ryûk) 2023-05-16 13:53:49 +02:00
parent 301a45ef59
commit e05e9c5690
Signed by: stepan
GPG Key ID: 295C1FE89E17EB3C
1 changed files with 380 additions and 32 deletions
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412
matlab/@dprior/dprior.m
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@ -1,4 +1,4 @@
classdef dprior
classdef dprior < handle
properties
p1 = []; % Prior mean.
@ -8,6 +8,7 @@ classdef dprior
p5 = []; % Prior mode.
p6 = []; % Prior first hyperparameter.
p7 = []; % Prior second hyperparameter.
p11 = []; % Prior median
lb = []; % Truncated prior lower bound.
ub = []; % Truncated prior upper bound.
iduniform = []; % Index for the uniform priors.
@ -48,27 +49,28 @@ classdef dprior
if isfield(BayesInfo, 'p5'), o.p5 = BayesInfo.p5; end
if isfield(BayesInfo, 'p6'), o.p6 = BayesInfo.p6; end
if isfield(BayesInfo, 'p7'), o.p7 = BayesInfo.p7; end
bounds = prior_bounds(BayesInfo, PriorTrunc);
o.lb = bounds.lb;
o.ub = bounds.ub;
if nargin>2 && Uniform
prior_shape = repmat(5, length(o.p6), 1);
else
prior_shape = BayesInfo.pshape;
end
o.idbeta = find(prior_shape==1);
if ~isempty(o.idbeta)
o.isbeta = true;
end
o.idgamma = find(prior_shape==2);
if ~isempty(o.idgamma)
o.isgamma = true;
end
o.idgaussian = find(prior_shape==3);
if ~isempty(o.idgaussian)
o.isgaussian = true;
end
o.idinvgamma1 = find(prior_shape==4);
if isfield(BayesInfo, 'p11'), o.p11 = BayesInfo.p11; end
bounds = prior_bounds(BayesInfo, PriorTrunc);
o.lb = bounds.lb;
o.ub = bounds.ub;
if nargin>2 && Uniform
prior_shape = repmat(5, length(o.p6), 1);
else
prior_shape = BayesInfo.pshape;
end
o.idbeta = find(prior_shape==1);
if ~isempty(o.idbeta)
o.isbeta = true;
end
o.idgamma = find(prior_shape==2);
if ~isempty(o.idgamma)
o.isgamma = true;
end
o.idgaussian = find(prior_shape==3);
if ~isempty(o.idgaussian)
o.isgaussian = true;
end
o.idinvgamma1 = find(prior_shape==4);
if ~isempty(o.idinvgamma1)
o.isinvgamma1 = true;
end
@ -90,14 +92,24 @@ classdef dprior
switch S(1).type
case '.'
if ismember(S(1).subs, {'p1','p2','p3','p4','p5','p6','p7','lb','ub'})
r = builtin('subsref', o, S(1));
p = builtin('subsref', o, S(1));
elseif ismember(S(1).subs, {'draw'})
p = feval(S(1).subs, o);
elseif ismember(S(1).subs, {'draws', 'density', 'densities', 'moments'})
p = feval(S(1).subs, o , S(2).subs{:});
elseif ismember(S(1).subs, {'mean', 'median', 'variance', 'mode'})
if (length(S)==2 && isempty(S(2).subs)) || length(S)==1
p = feval(S(1).subs, o);
else
p = feval(S(1).subs, o , S(2).subs{:});
end
else
error('dprior::subsref: unknown method.')
error('dprior::subsref: unknown method (%s).', S(1).subs)
end
otherwise
error('dprior::subsref: case not implemented.')
error('dprior::subsref: %s indexing not implemented.', S(1).type)
end
end
end
function p = draw(o)
% Return a random draw from the prior distribution.
@ -155,7 +167,7 @@ classdef dprior
while ~isempty(oob)
p(o.idinvgamma1(oob)) = ...
sqrt(1./gamrnd(o.p7(o.idinvgamma1(oob))/2, 2./o.p6(o.idinvgamma1(oob))))+o.p3(o.idinvgamma1(oob));
oob = find( (p(o.idinvgamma1)>o.ub(idinvgamma1)) | (p(o.idinvgamma1)<o.lb(o.idinvgamma1)));
oob = find( (p(o.idinvgamma1)>o.ub(o.idinvgamma1)) | (p(o.idinvgamma1)<o.lb(o.idinvgamma1)));
end
end
if o.isinvgamma2
@ -255,7 +267,7 @@ classdef dprior
lpd = lpd + sum(tmp);
case {3,4}
[tmp, dlpd(o.idgaussian), d2lpd(o.idgaussian)] = lpdfnorm(x(o.idgaussian), o.p6(o.idgaussian), o.p7(o.idgaussian));
lpd = lpd + sum(lpd);
lpd = lpd + sum(tmp);
end
end
if o.isgamma
@ -275,7 +287,7 @@ classdef dprior
[tmp, dlpd(o.idgamma), d2lpd(o.idgamma)] = lpdfgam(x(o.idgamma)-o.p3(o.idgamma), o.p6(o.idgamma), o.p7(o.idgamma));
lpd = lpd + sum(tmp);
if isinf(lpd)
info = o.idgamma(isinf(tmp))
info = o.idgamma(isinf(tmp));
return
end
end
@ -330,9 +342,9 @@ classdef dprior
lpd = lpd + sum(lpdfig2(x(o.idinvgamma2)-o.p3(o.idinvgamma2), o.p6(o.idinvgamma2), o.p7(o.idinvgamma2)));
if isinf(lpd), return, end
case 2
[tmp, dlpd(o.idinvgamma2)] = lpdfig2(x(o.idinvgamma2)-o.p3(o.idinvgamma2), o.p6(o.idinvgamma2), o.p7(o.idinvgamma2));
lpd = lpd + sum(tmp);
if isinf(lpd), return, end
[tmp, dlpd(o.idinvgamma2)] = lpdfig2(x(o.idinvgamma2)-o.p3(o.idinvgamma2), o.p6(o.idinvgamma2), o.p7(o.idinvgamma2));
lpd = lpd + sum(tmp);
if isinf(lpd), return, end
case 3
[tmp, dlpd(o.idinvgamma2), d2lpd(o.idinvgamma2)] = lpdfig2(x(o.idinvgamma2)-o.p3(o.idinvgamma2), o.p6(o.idinvgamma2), o.p7(o.idinvgamma2));
lpd = lpd + sum(tmp);
@ -386,6 +398,251 @@ classdef dprior
end
end % densities
function o = moments(o, name)
% Compute the prior moments.
%
% INPUTS
% - o [dprior]
%
% OUTPUTS
% - o [dprior]
switch name
case 'mean'
m = o.p1;
case 'median'
m = o.p11;
case 'std'
m = o.p2;
case 'mode'
m = o.p5;
otherwise
error('%s is not an implemented moemnt.', name)
end
id = isnan(m);
if any(id)
% For some parameters the prior mean is not defined.
% We compute the first order moment from the
% hyperparameters, if the hyperparameters are not
% available an error is thrown.
if o.isuniform
jd = intersect(o.iduniform, find(id));
if ~isempty(jd)
if any(isnan(o.p3(jd))) || any(isnan(o.p4(jd)))
error('dprior::mean: Some hyperparameters are missing (uniform distribution).')
end
switch name
case 'mean'
m(jd) = o.p3(jd) + .5*(o.p4(jd)-o.p3(jd));
case 'median'
m(jd) = o.p3(jd) + .5*(o.p4(jd)-o.p3(jd));
case 'std'
m(jd) = (o.p4(jd)-o.p3(jd))/sqrt(12);
case 'mode' % Actually we have a continuum of modes with the uniform distribution.
m(jd) = o.p3(jd) + .5*(o.p4(jd)-o.p3(jd));
end
end
end
if o.isgaussian
jd = intersect(o.idgaussian, find(id));
if ~isempty(jd)
if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd)))
error('dprior::mean: Some hyperparameters are missing (gaussian distribution).')
end
switch name
case 'mean'
m(jd) = o.p6(jd);
case 'median'
m(jd) = o.p6(jd);
case 'std'
m(jd) = o.p7(jd);
case 'mode' % Actually we have a continuum of modes with the uniform distribution.
m(jd) = o.p6(jd);
end
end
end
if o.isgamma
jd = intersect(o.idgamma, find(id));
if ~isempty(jd)
if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd))) || any(isnan(o.p3(jd)))
error('dprior::mean: Some hyperparameters are missing (gamma distribution).')
end
% α → o.p6, β → o.p7
switch name
case 'mean'
m(jd) = o.p3(jd) + o.p6(jd).*o.p7(jd);
case 'median'
m(jd) = o.p3(jd) + gaminv(.5, o.p6(jd), o.p7(jda));
case 'std'
m(jd) = sqrt(o.p6(jd)).*o.p7(jd);
case 'mode'
m(jd) = 0;
hd = o.p6(jd)>1;
m(jd(hd)) = (o.p6(jd(hd))-1).*o.p7(jd(hd));
end
end
end
if o.isbeta
jd = intersect(o.idbeta, find(id));
if ~isempty(jd)
if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd))) || any(isnan(o.p3(jd))) || any(isnan(o.p4(jd)))
error('dprior::mean: Some hyperparameters are missing (beta distribution).')
end
% α → o.p6, β → o.p7
switch name
case 'mean'
m(jd) = o.p3(jd) + (o.p6(jd)./(o.p6(jd)+o.p7(jd))).*(o.p4(jd)-o.p3(jd));
case 'median'
m(jd) = o.p3(jd) + betainv(.5, o.p6(jd), o.p7(jd)).*(o.p4(jd)-o.p3(jd));
case 'std'
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)));
case 'mode'
h0 = true(jd, 1);
h1 = o.p6(jd)<=1 & o.p7(jd)>1; h0 = h0 & ~h1;
h2 = o.p7(jd)<=1 & o.p6(jd)>1; h0 = h0 & ~h2;
h3 = o.p6(jd)<1 & o.p7(jd)<1; h0 = h0 & ~h3;
h4 = ismembertol(o.p6(jd), 1) & ismembertol(o.p7(jd),1); h0 = h0 & ~h4;
m(jd(h1)) = o.p3(jd(h1)); % Standard β has a mode at 0
m(jd(h2)) = o.p4(jd(h2)); % Standard β has a mode at 1
m(jd(h3)) = o.p3(jd(h3)); % Standard β is bimodal, we pick the lowest mode (0)
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
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.
end
end
end
if o.isinvgamma1
jd = intersect(o.idinvgamma1, find(id));
if ~isempty(jd)
if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd))) || any(isnan(o.p3(jd)))
error('dprior::mean: Some hyperparameters are missing (inverse gamma type 1 distribution).')
end
% s → o.p6, ν → o.p7
switch name
case 'mean'
m(jd) = o.p3(jd) + sqrt(.5*o.p6(jd)) .*(gamma(.5*(o.p7(jd)-1))./gamma(.5*o.p7(jd)));
case 'median'
m(jd) = o.p3(jd) + 1.0/sqrt(gaminv(.5, o.p7(jd)/2.0, 2.0/o.p6(jd)));
case 'std'
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);
case 'mode'
m(jd) = sqrt((o.p7(jd)-1)./o.p6(jd));
end
end
end
if o.isinvgamma2
jd = intersect(o.idinvgamma2, find(id));
if ~isempty(jd)
if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd))) || any(isnan(o.p3(jd)))
error('dprior::mean: Some hyperparameters are missing (inverse gamma type 2 distribution).')
end
% s → o.p6, ν → o.p7
switch name
case 'mean'
m(jd) = o.p3(jd) + o.p6(jd)./(o.p7(jd)-2);
case 'median'
m(jd) = o.p3(jd) + 1.0/gaminv(.5, o.p7(jd)/2.0, 2.0/o.p6(jd));
case 'std'
m(jd) = sqrt(2./(o.p7(jd)-4)).*o.p6(jd)./(o.p7(jd)-2);
case 'mode'
m(jd) = o.p6(jd)./(o.p7(jd)+2);
end
end
end
if o.isweibull
jd = intersect(o.idweibull, find(id));
if ~isempty(jd)
if any(isnan(o.p6(jd))) || any(isnan(o.p7(jd))) || any(isnan(o.p3(jd)))
error('dprior::mean: Some hyperparameters are missing (weibull distribution).')
end
% k → o.p6 (shape parameter), λ → o.p7 (scale parameter)
% See https://en.wikipedia.org/wiki/Weibull_distribution
switch name
case 'mean'
m(jd) = o.p3(jd) + o.p7(jd).*gamma(1+1./o.p6(jd));
case 'median'
m(jd) = o.p3(jd) + o.p7(jd).*log(2).^(1./o.p6(jd));
case 'std'
m(jd) = o.p7(jd).*sqrt(gamma(1+2./o.p6(jd))-gamma(1+1./o.p6(jd)).^2);
case 'mode'
m(jd) = 0;
hd = o.p6(jd)>1;
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)));
end
end
end
switch name
case 'mean'
o.p1 = m;
case 'median'
o.p11 = m;
case 'std'
o.p2 = m;
case 'mode'
o.p5 = m;
end
end
end
function m = mean(o, resetmoments)
% Return the prior mean.
%
% INPUTS
% - o [dprior]
% - resetmoments [logical] Force the computation of the prior mean
%
% OUTPUTS
% - m [double] n×1 vector, prior mean
if nargin<2, resetmoments = false; end
if any(isnan(o.p1)), resetmoments = true; end
if resetmoments, o.p1 = NaN(size(o.p1)); o.moments('mean');
end
m = o.p1;
end
function m = variance(o, resetmoments)
% Return the prior variance.
%
% INPUTS
% - o [dprior]
% - resetmoments [logical] Force the computation of the prior variance
%
% OUTPUTS
% - m [double] n×1 vector, prior variance
if nargin<2, resetmoments = false; end
if any(isnan(o.p2)), resetmoments = true; end
if resetmoments, o.p2 = NaN(size(o.p2)); o.moments('std'); end
m = o.p2.^2;
end
function m = median(o, resetmoments)
% Return the prior median.
%
% INPUTS
% - o [dprior]
% - resetmoments [logical] Force the computation of the prior median
%
% OUTPUTS
% - m [double] n×1 vector, prior median
if nargin<2, resetmoments = false; end
if any(isnan(o.p11)), resetmoments = true; end
if resetmoments, o.p11 = NaN(size(o.p11)); o.moments('median'); end
m = o.p11;
end
function m = mode(o, resetmoments)
% Return the prior mode.
%
% INPUTS
% - o [dprior]
% - resetmoments [logical] Force the computation of the prior mode
%
% OUTPUTS
% - m [double] n×1 vector, prior mode
if nargin<2, resetmoments = false; end
if any(isnan(o.p5)), resetmoments = true; end
if resetmoments, o.p5 = NaN(size(o.p5)); o.moments('mode'); end
m = o.p5;
end
end % methods
end % classdef --*-- Unit tests --*--
@ -750,6 +1007,7 @@ end % classdef --*-- Unit tests --*--
%$ try
%$ Prior = dprior(BayesInfo, prior_trunc, false);
%$ mu = NaN(14,1);
%$ std = NaN(14,1);
%$
%$ for i=1:14
%$ % Define conditional density (it's also a marginal since priors are orthogonal)
@ -759,6 +1017,7 @@ end % classdef --*-- Unit tests --*--
%$ density = @(x) f(x)/m; % rescaling is required since the probability mass depends on the conditioning.
%$ % Compute the conditional expectation
%$ mu(i) = integral(@(x) x.*density(x), p3(i), p4(i));
%$ std(i) = sqrt(integral(@(x) ((x-mu(i)).^2).*density(x), p3(i), p4(i)));
%$ end
%$
%$ t(1) = true;
@ -768,6 +1027,95 @@ end % classdef --*-- Unit tests --*--
%$
%$ if t(1)
%$ t(2) = all(abs(mu-.4)<1e-6);
%$ t(3) = all(abs(std-.2)<1e-6);
%$ end
%$ T = all(t);
%@eof:4
%@test:5
%$ % Fill global structures with required fields...
%$ prior_trunc = 1e-10;
%$ p0 = repmat([1; 2; 3; 4; 5; 6; 8], 2, 1); % Prior shape
%$ p1 = .4*ones(14,1); % Prior mean
%$ p2 = .2*ones(14,1); % Prior std.
%$ p3 = NaN(14,1);
%$ p4 = NaN(14,1);
%$ p5 = NaN(14,1);
%$ p6 = NaN(14,1);
%$ p7 = NaN(14,1);
%$
%$ for i=1:14
%$ switch p0(i)
%$ case 1
%$ % Beta distribution
%$ p3(i) = 0;
%$ p4(i) = 1;
%$ [p6(i), p7(i)] = beta_specification(p1(i), p2(i)^2, p3(i), p4(i));
%$ p5(i) = compute_prior_mode([p6(i) p7(i)], 1);
%$ case 2
%$ % Gamma distribution
%$ p3(i) = 0;
%$ p4(i) = Inf;
%$ [p6(i), p7(i)] = gamma_specification(p1(i), p2(i)^2, p3(i), p4(i));
%$ p5(i) = compute_prior_mode([p6(i) p7(i)], 2);
%$ case 3
%$ % Normal distribution
%$ p3(i) = -Inf;
%$ p4(i) = Inf;
%$ p6(i) = p1(i);
%$ p7(i) = p2(i);
%$ p5(i) = p1(i);
%$ case 4
%$ % Inverse Gamma (type I) distribution
%$ p3(i) = 0;
%$ p4(i) = Inf;
%$ [p6(i), p7(i)] = inverse_gamma_specification(p1(i), p2(i)^2, p3(i), 1, false);
%$ p5(i) = compute_prior_mode([p6(i) p7(i)], 4);
%$ case 5
%$ % Uniform distribution
%$ [p1(i), p2(i), p6(i), p7(i)] = uniform_specification(p1(i), p2(i), p3(i), p4(i));
%$ p3(i) = p6(i);
%$ p4(i) = p7(i);
%$ p5(i) = compute_prior_mode([p6(i) p7(i)], 5);
%$ case 6
%$ % Inverse Gamma (type II) distribution
%$ p3(i) = 0;
%$ p4(i) = Inf;
%$ [p6(i), p7(i)] = inverse_gamma_specification(p1(i), p2(i)^2, p3(i), 2, false);
%$ p5(i) = compute_prior_mode([p6(i) p7(i)], 6);
%$ case 8
%$ % Weibull distribution
%$ p3(i) = 0;
%$ p4(i) = Inf;
%$ [p6(i), p7(i)] = weibull_specification(p1(i), p2(i)^2, p3(i));
%$ p5(i) = compute_prior_mode([p6(i) p7(i)], 8);
%$ otherwise
%$ error('This density is not implemented!')
%$ end
%$ end
%$
%$ BayesInfo.pshape = p0;
%$ BayesInfo.p1 = p1;
%$ BayesInfo.p2 = p2;
%$ BayesInfo.p3 = p3;
%$ BayesInfo.p4 = p4;
%$ BayesInfo.p5 = p5;
%$ BayesInfo.p6 = p6;
%$ BayesInfo.p7 = p7;
%$
%$ % Call the tested routine
%$ try
%$ Prior = dprior(BayesInfo, prior_trunc, false);
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ if t(1)
%$ t(2) = all(Prior.mean()==.4);
%$ t(3) = all(ismembertol(Prior.mean(true),.4));
%$ t(4) = all(ismembertol(Prior.variance(),.04));
%$ t(5) = all(ismembertol(Prior.variance(true),.04));
%$ end
%$ T = all(t);
%@eof:5