277 lines
11 KiB
Matlab
277 lines
11 KiB
Matlab
function pdraw = prior_draw(BayesInfo, prior_trunc, uniform)
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% This function generate one draw from the joint prior distribution and
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% allows sampling uniformly from the prior support (uniform==1 when called with init==1)
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%
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% INPUTS
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% o init [integer] scalar equal to:
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% 1: first call to set up persistent variables
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% describing the prior
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% 0: subsequent call to get prior
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% draw
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% o uniform [integer] scalar used in initialization (init=1), equal to:
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% 1: sample uniformly from prior
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% support (overwrites prior shape used for sampling within this function)
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% 0: sample from joint prior distribution
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%
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% OUTPUTS
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% o pdraw [double] 1*npar vector, draws from the joint prior density.
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%
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%
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% SPECIAL REQUIREMENTS
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% none
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%
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% NOTE 1. Input arguments 1 and 2 are only needed for initialization.
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% NOTE 2. A given draw from the joint prior distribution does not satisfy BK conditions a priori.
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% NOTE 3. This code relies on bayestopt_ as created in the base workspace
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% by the preprocessor (or as updated in subsequent pieces of code and handed to the base workspace)
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%
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% Copyright © 2006-2023 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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persistent p6 p7 p3 p4 lb ub
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persistent uniform_index gaussian_index gamma_index beta_index inverse_gamma_1_index inverse_gamma_2_index weibull_index
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persistent uniform_draws gaussian_draws gamma_draws beta_draws inverse_gamma_1_draws inverse_gamma_2_draws weibull_draws
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if nargin>0
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p6 = BayesInfo.p6;
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p7 = BayesInfo.p7;
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p3 = BayesInfo.p3;
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p4 = BayesInfo.p4;
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bounds = prior_bounds(BayesInfo, prior_trunc);
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lb = bounds.lb;
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ub = bounds.ub;
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number_of_estimated_parameters = length(p6);
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if nargin>2 && uniform
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prior_shape = repmat(5,number_of_estimated_parameters,1);
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else
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prior_shape = BayesInfo.pshape;
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end
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beta_index = find(prior_shape==1);
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if isempty(beta_index)
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beta_draws = false;
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else
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beta_draws = true;
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end
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gamma_index = find(prior_shape==2);
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if isempty(gamma_index)
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gamma_draws = false;
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else
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gamma_draws = true;
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end
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gaussian_index = find(prior_shape==3);
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if isempty(gaussian_index)
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gaussian_draws = false;
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else
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gaussian_draws = true;
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end
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inverse_gamma_1_index = find(prior_shape==4);
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if isempty(inverse_gamma_1_index)
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inverse_gamma_1_draws = false;
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else
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inverse_gamma_1_draws = true;
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end
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uniform_index = find(prior_shape==5);
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if isempty(uniform_index)
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uniform_draws = false;
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else
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uniform_draws = true;
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end
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inverse_gamma_2_index = find(prior_shape==6);
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if isempty(inverse_gamma_2_index)
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inverse_gamma_2_draws = false;
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else
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inverse_gamma_2_draws = true;
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end
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weibull_index = find(prior_shape==8);
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if isempty(weibull_index)
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weibull_draws = false;
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else
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weibull_draws = true;
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end
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pdraw = NaN(number_of_estimated_parameters,1);
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return
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end
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if uniform_draws
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pdraw(uniform_index) = rand(length(uniform_index),1).*(p4(uniform_index)-p3(uniform_index)) + p3(uniform_index);
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out_of_bound = find( (pdraw(uniform_index)'>ub(uniform_index)) | (pdraw(uniform_index)'<lb(uniform_index)));
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while ~isempty(out_of_bound)
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pdraw(uniform_index) = rand(length(uniform_index),1).*(p4(uniform_index)-p3(uniform_index)) + p3(uniform_index);
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out_of_bound = find( (pdraw(uniform_index)'>ub(uniform_index)) | (pdraw(uniform_index)'<lb(uniform_index)));
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end
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end
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if gaussian_draws
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pdraw(gaussian_index) = randn(length(gaussian_index),1).*p7(gaussian_index) + p6(gaussian_index);
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out_of_bound = find( (pdraw(gaussian_index)'>ub(gaussian_index)) | (pdraw(gaussian_index)'<lb(gaussian_index)));
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while ~isempty(out_of_bound)
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pdraw(gaussian_index(out_of_bound)) = randn(length(gaussian_index(out_of_bound)),1).*p7(gaussian_index(out_of_bound)) + p6(gaussian_index(out_of_bound));
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out_of_bound = find( (pdraw(gaussian_index)'>ub(gaussian_index)) | (pdraw(gaussian_index)'<lb(gaussian_index)));
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end
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end
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if gamma_draws
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pdraw(gamma_index) = gamrnd(p6(gamma_index),p7(gamma_index))+p3(gamma_index);
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out_of_bound = find( (pdraw(gamma_index)'>ub(gamma_index)) | (pdraw(gamma_index)'<lb(gamma_index)));
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while ~isempty(out_of_bound)
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pdraw(gamma_index(out_of_bound)) = gamrnd(p6(gamma_index(out_of_bound)),p7(gamma_index(out_of_bound)))+p3(gamma_index(out_of_bound));
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out_of_bound = find( (pdraw(gamma_index)'>ub(gamma_index)) | (pdraw(gamma_index)'<lb(gamma_index)));
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end
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end
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if beta_draws
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pdraw(beta_index) = (p4(beta_index)-p3(beta_index)).*betarnd(p6(beta_index),p7(beta_index))+p3(beta_index);
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out_of_bound = find( (pdraw(beta_index)'>ub(beta_index)) | (pdraw(beta_index)'<lb(beta_index)));
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while ~isempty(out_of_bound)
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pdraw(beta_index(out_of_bound)) = (p4(beta_index(out_of_bound))-p3(beta_index(out_of_bound))).*betarnd(p6(beta_index(out_of_bound)),p7(beta_index(out_of_bound)))+p3(beta_index(out_of_bound));
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out_of_bound = find( (pdraw(beta_index)'>ub(beta_index)) | (pdraw(beta_index)'<lb(beta_index)));
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end
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end
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if inverse_gamma_1_draws
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pdraw(inverse_gamma_1_index) = ...
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sqrt(1./gamrnd(p7(inverse_gamma_1_index)/2,2./p6(inverse_gamma_1_index)))+p3(inverse_gamma_1_index);
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out_of_bound = find( (pdraw(inverse_gamma_1_index)'>ub(inverse_gamma_1_index)) | (pdraw(inverse_gamma_1_index)'<lb(inverse_gamma_1_index)));
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while ~isempty(out_of_bound)
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pdraw(inverse_gamma_1_index(out_of_bound)) = ...
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sqrt(1./gamrnd(p7(inverse_gamma_1_index(out_of_bound))/2,2./p6(inverse_gamma_1_index(out_of_bound))))+p3(inverse_gamma_1_index(out_of_bound));
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out_of_bound = find( (pdraw(inverse_gamma_1_index)'>ub(inverse_gamma_1_index)) | (pdraw(inverse_gamma_1_index)'<lb(inverse_gamma_1_index)));
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end
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end
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if inverse_gamma_2_draws
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pdraw(inverse_gamma_2_index) = ...
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1./gamrnd(p7(inverse_gamma_2_index)/2,2./p6(inverse_gamma_2_index))+p3(inverse_gamma_2_index);
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out_of_bound = find( (pdraw(inverse_gamma_2_index)'>ub(inverse_gamma_2_index)) | (pdraw(inverse_gamma_2_index)'<lb(inverse_gamma_2_index)));
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while ~isempty(out_of_bound)
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pdraw(inverse_gamma_2_index(out_of_bound)) = ...
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1./gamrnd(p7(inverse_gamma_2_index(out_of_bound))/2,2./p6(inverse_gamma_2_index(out_of_bound)))+p3(inverse_gamma_2_index(out_of_bound));
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out_of_bound = find( (pdraw(inverse_gamma_2_index)'>ub(inverse_gamma_2_index)) | (pdraw(inverse_gamma_2_index)'<lb(inverse_gamma_2_index)));
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end
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end
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if weibull_draws
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pdraw(weibull_index) = wblrnd(p7(weibull_index), p6(weibull_index)) + p3(weibull_index);
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out_of_bound = find( (pdraw(weibull_index)'>ub(weibull_index)) | (pdraw(weibull_index)'<lb(weibull_index)));
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while ~isempty(out_of_bound)
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pdraw(weibull_index(out_of_bound)) = wblrnd(p7(weibull_index(out_of_bound)),p6(weibull_index(out_of_bound)))+p3(weibull_index(out_of_bound));
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out_of_bound = find( (pdraw(weibull_index)'>ub(weibull_index)) | (pdraw(weibull_index)'<lb(weibull_index)));
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end
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end
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return % --*-- 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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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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ndraws = 1e5;
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m0 = BayesInfo.p1; %zeros(14,1);
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v0 = diag(BayesInfo.p2.^2); %zeros(14);
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% Call the tested routine
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try
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% Initialization of prior_draws.
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prior_draw(BayesInfo, prior_trunc, false);
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% Do simulations in a loop and estimate recursively the mean and teh variance.
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for i = 1:ndraws
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draw = transpose(prior_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;
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m0 = m1;
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end
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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(abs(m0-BayesInfo.p1)<3e-3);
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t(3) = all(all(abs(v0-diag(BayesInfo.p2.^2))<5e-3));
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end
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T = all(t);
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%@eof:1
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