diff --git a/matlab/@dprior/dprior.m b/matlab/@dprior/dprior.m
index c98f27a3e6a92f77b441e7d674f30b84f89b348b..189dcad7dd3937a24179f4a2c06f0ba8c64f73ba 100644
--- a/matlab/@dprior/dprior.m
+++ b/matlab/@dprior/dprior.m
@@ -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.
@@ -48,6 +49,7 @@ classdef dprior
if isfield(bayestopt_, 'p5'), o.p5 = bayestopt_.p5; end
if isfield(bayestopt_, 'p6'), o.p6 = bayestopt_.p6; end
if isfield(bayestopt_, 'p7'), o.p7 = bayestopt_.p7; end
+ if isfield(bayestopt_, 'p11'), o.p11 = bayestopt_.p11; end
bounds = prior_bounds(bayestopt_, PriorTrunc);
o.lb = bounds.lb;
o.ub = bounds.ub;
@@ -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(bayestopt_, 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