2023-04-26 10:34:25 +02:00
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classdef dprior
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properties
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p6 = []; % Prior first hyperparameter.
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p7 = []; % Prior second hyperparameter.
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p3 = []; % Lower bound of the prior support.
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p4 = []; % Upper bound of the prior support.
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lb = []; % Truncated prior lower bound.
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ub = []; % Truncated prior upper bound.
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uniform_index = []; % Index for the uniform priors.
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gaussian_index = []; % Index for the gaussian priors.
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gamma_index = []; % Index for the gamma priors.
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beta_index = []; % Index for the beta priors.
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inverse_gamma_1_index = []; % Index for the inverse gamma type 1 priors.
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inverse_gamma_2_index = []; % Index for the inverse gamma type 2 priors.
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weibull_index = []; % Index for the weibull priors.
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uniform_draws = false;
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gaussian_draws = false;
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gamma_draws = false;
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beta_draws = false;
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inverse_gamma_1_draws = false;
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inverse_gamma_2_draws = false;
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weibull_draws = false;
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end
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methods
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function o = dprior(BayesInfo, PriorTrunc, Uniform)
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% Class constructor.
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%
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% INPUTS
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% - BayesInfo [struct] Informations about the prior distribution, aka bayestopt_.
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% - PriorTrunc [double] scalar, probability mass to be excluded, aka options_.prior_trunc
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% - Uniform [logical] scalar, produce uniform random deviates on the prior support.
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%
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% OUTPUTS
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% - o [dprior] scalar, prior object.
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%
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% REQUIREMENTS
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% None.
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o.p6 = BayesInfo.p6;
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o.p7 = BayesInfo.p7;
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o.p3 = BayesInfo.p3;
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o.p4 = BayesInfo.p4;
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bounds = prior_bounds(BayesInfo, PriorTrunc);
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o.lb = bounds.lb;
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o.ub = bounds.ub;
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if nargin>2 && Uniform
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prior_shape = repmat(5, length(o.p6), 1);
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else
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prior_shape = BayesInfo.pshape;
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end
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o.beta_index = find(prior_shape==1);
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if ~isempty(o.beta_index)
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o.beta_draws = true;
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end
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o.gamma_index = find(prior_shape==2);
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if ~isempty(o.gamma_index)
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o.gamma_draws = true;
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end
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o.gaussian_index = find(prior_shape==3);
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if ~isempty(o.gaussian_index)
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o.gaussian_draws = true;
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end
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o.inverse_gamma_1_index = find(prior_shape==4);
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if ~isempty(o.inverse_gamma_1_index)
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o.inverse_gamma_1_draws = true;
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end
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o.uniform_index = find(prior_shape==5);
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if ~isempty(o.uniform_index)
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o.uniform_draws = true;
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end
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o.inverse_gamma_2_index = find(prior_shape==6);
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if ~isempty(o.inverse_gamma_2_index)
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o.inverse_gamma_2_draws = true;
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end
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o.weibull_index = find(prior_shape==8);
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if ~isempty(o.weibull_index)
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o.weibull_draws = true;
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end
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end
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function p = draw(o)
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% Return a random draw from the prior distribution.
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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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% - p [double] m×1 vector, random draw from the prior distribution (m is the number of estimated parameters).
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%
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% REMARKS
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% None.
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%
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% EXAMPLE
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%
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% >> Prior = dprior(bayestopt_, options_.prior_trunc);
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% >> d = Prior.draw()
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p = NaN(rows(o.lb), 1);
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if o.uniform_draws
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p(o.uniform_index) = rand(length(o.uniform_index),1).*(o.p4(o.uniform_index)-o.p3(o.uniform_index)) + o.p3(o.uniform_index);
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out_of_bound = find( (p(o.uniform_index)>o.ub(o.uniform_index)) | (p(o.uniform_index)<o.lb(o.uniform_index)));
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while ~isempty(out_of_bound)
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p(o.uniform_index) = rand(length(o.uniform_index), 1).*(o.p4(o.uniform_index)-o.p3(o.uniform_index)) + o.p3(o.uniform_index);
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out_of_bound = find( (p(o.uniform_index)>o.ub(o.uniform_index)) | (p(o.uniform_index)<o.lb(o.uniform_index)));
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end
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end
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if o.gaussian_draws
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p(o.gaussian_index) = randn(length(o.gaussian_index), 1).*o.p7(o.gaussian_index) + o.p6(o.gaussian_index);
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out_of_bound = find( (p(o.gaussian_index)>o.ub(o.gaussian_index)) | (p(o.gaussian_index)<o.lb(o.gaussian_index)));
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while ~isempty(out_of_bound)
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p(o.gaussian_index(out_of_bound)) = randn(length(o.gaussian_index(out_of_bound)), 1).*o.p7(o.gaussian_index(out_of_bound)) + o.p6(o.gaussian_index(out_of_bound));
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out_of_bound = find( (p(o.gaussian_index)>o.ub(o.gaussian_index)) | (p(o.gaussian_index)<o.lb(o.gaussian_index)));
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end
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end
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if o.gamma_draws
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p(o.gamma_index) = gamrnd(o.p6(o.gamma_index), o.p7(o.gamma_index))+o.p3(o.gamma_index);
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out_of_bound = find( (p(o.gamma_index)>o.ub(o.gamma_index)) | (p(o.gamma_index)<o.lb(o.gamma_index)));
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while ~isempty(out_of_bound)
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p(o.gamma_index(out_of_bound)) = gamrnd(o.p6(o.gamma_index(out_of_bound)), o.p7(o.gamma_index(out_of_bound)))+o.p3(o.gamma_index(out_of_bound));
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out_of_bound = find( (p(o.gamma_index)>o.ub(o.gamma_index)) | (p(o.gamma_index)<o.lb(o.gamma_index)));
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end
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end
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if o.beta_draws
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p(o.beta_index) = (o.p4(o.beta_index)-o.p3(o.beta_index)).*betarnd(o.p6(o.beta_index), o.p7(o.beta_index))+o.p3(o.beta_index);
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out_of_bound = find( (p(o.beta_index)>o.ub(o.beta_index)) | (p(o.beta_index)<o.lb(o.beta_index)));
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while ~isempty(out_of_bound)
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p(o.beta_index(out_of_bound)) = (o.p4(o.beta_index(out_of_bound))-o.p3(o.beta_index(out_of_bound))).*betarnd(o.p6(o.beta_index(out_of_bound)), o.p7(o.beta_index(out_of_bound)))+o.p3(o.beta_index(out_of_bound));
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out_of_bound = find( (p(o.beta_index)>o.ub(o.beta_index)) | (p(o.beta_index)<o.lb(o.beta_index)));
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end
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end
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if o.inverse_gamma_1_draws
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p(o.inverse_gamma_1_index) = ...
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sqrt(1./gamrnd(o.p7(o.inverse_gamma_1_index)/2, 2./o.p6(o.inverse_gamma_1_index)))+o.p3(o.inverse_gamma_1_index);
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out_of_bound = find( (p(o.inverse_gamma_1_index)>o.ub(o.inverse_gamma_1_index)) | (p(o.inverse_gamma_1_index)<o.lb(o.inverse_gamma_1_index)));
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while ~isempty(out_of_bound)
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p(o.inverse_gamma_1_index(out_of_bound)) = ...
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sqrt(1./gamrnd(o.p7(o.inverse_gamma_1_index(out_of_bound))/2, 2./o.p6(o.inverse_gamma_1_index(out_of_bound))))+o.p3(o.inverse_gamma_1_index(out_of_bound));
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2023-06-04 08:07:28 +02:00
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out_of_bound = find( (p(o.inverse_gamma_1_index)>o.ub(o.inverse_gamma_1_index)) | (p(o.inverse_gamma_1_index)<o.lb(o.inverse_gamma_1_index)));
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2023-04-26 10:34:25 +02:00
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end
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end
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if o.inverse_gamma_2_draws
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p(o.inverse_gamma_2_index) = ...
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1./gamrnd(o.p7(o.inverse_gamma_2_index)/2, 2./o.p6(o.inverse_gamma_2_index))+o.p3(o.inverse_gamma_2_index);
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out_of_bound = find( (p(o.inverse_gamma_2_index)>o.ub(o.inverse_gamma_2_index)) | (p(o.inverse_gamma_2_index)<o.lb(o.inverse_gamma_2_index)));
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while ~isempty(out_of_bound)
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p(o.inverse_gamma_2_index(out_of_bound)) = ...
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1./gamrnd(o.p7(o.inverse_gamma_2_index(out_of_bound))/2, 2./o.p6(o.inverse_gamma_2_index(out_of_bound)))+o.p3(o.inverse_gamma_2_index(out_of_bound));
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out_of_bound = find( (p(o.inverse_gamma_2_index)>o.ub(o.inverse_gamma_2_index)) | (p(o.inverse_gamma_2_index)<o.lb(o.inverse_gamma_2_index)));
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end
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end
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if o.weibull_draws
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p(o.weibull_index) = wblrnd(o.p7(o.weibull_index), o.p6(o.weibull_index)) + o.p3(o.weibull_index);
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out_of_bound = find( (p(o.weibull_index)>o.ub(o.weibull_index)) | (p(o.weibull_index)<o.lb(o.weibull_index)));
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while ~isempty(out_of_bound)
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p(o.weibull_index(out_of_bound)) = wblrnd(o.p7(o.weibull_index(out_of_bound)), o.p6(o.weibull_index(out_of_bound)))+o.p3(o.weibull_index(out_of_bound));
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out_of_bound = find( (p(o.weibull_index)>o.ub(o.weibull_index)) | (p(o.weibull_index)<o.lb(o.weibull_index)));
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end
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end
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end
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function P = draws(o, n)
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% Return n independent random draws from the prior distribution.
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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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% - P [double] m×n matrix, random draw from the prior distribution.
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%
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% REMARKS
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% If the Parallel Computing Toolbox is available, the main loop is run in parallel.
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%
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% EXAMPLE
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%
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% >> Prior = dprior(bayestopt_, options_.prior_trunc);
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% >> Prior.draws(1e6)
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P = NaN(rows(o.lb), 1);
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parfor i=1:n
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P(:,i) = draw(o);
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end
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end
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end % methods
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end % classdef --*-- Unit tests --*--
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%@test:1
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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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%$
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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);
|
|
|
|
|
|
%$ case 6
|
|
|
|
|
|
%$ % Inverse Gamma (type II) distribution
|
|
|
|
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|
%$ 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
|
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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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|
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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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|
%$
|
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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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%$
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%$ ndraws = 1e5;
|
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|
%$ m0 = BayesInfo.p1; %zeros(14,1);
|
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|
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%$ v0 = diag(BayesInfo.p2.^2); %zeros(14);
|
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%$
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|
%$ % Call the tested routine
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%$ try
|
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|
%$ % Instantiate dprior object
|
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|
|
%$ o = dprior(BayesInfo, prior_trunc, false);
|
|
|
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|
|
%$ % Do simulations in a loop and estimate recursively the mean and the variance.
|
|
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|
|
|
%$ for i = 1:ndraws
|
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|
|
|
%$ draw = o.draw();
|
|
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|
|
|
%$ m1 = m0 + (draw-m0)/i;
|
|
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|
|
|
%$ m2 = m1*m1';
|
|
|
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|
|
%$ v0 = v0 + ((draw*draw'-m2-v0) + (i-1)*(m0*m0'-m2'))/i;
|
|
|
|
|
|
%$ m0 = m1;
|
|
|
|
|
|
%$ end
|
|
|
|
|
|
%$ t(1) = true;
|
|
|
|
|
|
%$ catch
|
|
|
|
|
|
%$ t(1) = false;
|
|
|
|
|
|
%$ end
|
|
|
|
|
|
%$
|
|
|
|
|
|
%$ if t(1)
|
|
|
|
|
|
%$ t(2) = all(abs(m0-BayesInfo.p1)<3e-3);
|
|
|
|
|
|
%$ t(3) = all(all(abs(v0-diag(BayesInfo.p2.^2))<5e-3));
|
|
|
|
|
|
%$ end
|
|
|
|
|
|
%$ T = all(t);
|
|
|
|
|
|
%@eof:1
|
|
|
|
|
|
|
|
|
|
|
|
%@test:2
|
|
|
|
|
|
%$ % 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;
|
|
|
|
|
|
%$
|
|
|
|
|
|
%$ ndraws = 1e5;
|
|
|
|
|
|
%$
|
|
|
|
|
|
%$ % Call the tested routine
|
|
|
|
|
|
%$ try
|
|
|
|
|
|
%$ % Instantiate dprior object.
|
|
|
|
|
|
%$ o = dprior(BayesInfo, prior_trunc, false);
|
|
|
|
|
|
%$ X = o.draws(ndraws);
|
|
|
|
|
|
%$ m = mean(X, 2);
|
|
|
|
|
|
%$ v = var(X, 0, 2);
|
|
|
|
|
|
%$ t(1) = true;
|
|
|
|
|
|
%$ catch
|
|
|
|
|
|
%$ t(1) = false;
|
|
|
|
|
|
%$ end
|
|
|
|
|
|
%$
|
|
|
|
|
|
%$ if t(1)
|
|
|
|
|
|
%$ t(2) = all(abs(m-BayesInfo.p1)<3e-3);
|
|
|
|
|
|
%$ t(3) = all(all(abs(v-BayesInfo.p2.^2)<5e-3));
|
|
|
|
|
|
%$ end
|
|
|
|
|
|
%$ T = all(t);
|
|
|
|
|
|
%@eof:2
|
