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dynare/matlab/prior_draw.m

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function pdraw = prior_draw(BayesInfo, prior_trunc, uniform) % --*-- Unitary tests --*--
% This function generate one draw from the joint prior distribution and
% allows sampling uniformly from the prior support (uniform==1 when called with init==1)
%
% INPUTS
% o init [integer] scalar equal to:
% 1: first call to set up persistent variables
% describing the prior
% 0: subsequent call to get prior
% draw
% o uniform [integer] scalar used in initialization (init=1), equal to:
% 1: sample uniformly from prior
% support (overwrites prior shape used for sampling within this function)
% 0: sample from joint prior distribution
%
% OUTPUTS
% o pdraw [double] 1*npar vector, draws from the joint prior density.
%
%
% SPECIAL REQUIREMENTS
% none
%
% NOTE 1. Input arguments 1 and 2 are only needed for initialization.
% NOTE 2. A given draw from the joint prior distribution does not satisfy BK conditions a priori.
% NOTE 3. This code relies on bayestopt_ as created in the base workspace
% by the preprocessor (or as updated in subsequent pieces of code and handed to the base workspace)
%
% Copyright © 2006-2017 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
persistent p6 p7 p3 p4 lb ub
persistent uniform_index gaussian_index gamma_index beta_index inverse_gamma_1_index inverse_gamma_2_index weibull_index
persistent uniform_draws gaussian_draws gamma_draws beta_draws inverse_gamma_1_draws inverse_gamma_2_draws weibull_draws
if nargin>0
p6 = BayesInfo.p6;
p7 = BayesInfo.p7;
p3 = BayesInfo.p3;
p4 = BayesInfo.p4;
bounds = prior_bounds(BayesInfo, prior_trunc);
lb = bounds.lb;
ub = bounds.ub;
number_of_estimated_parameters = length(p6);
if nargin>2 && uniform
prior_shape = repmat(5,number_of_estimated_parameters,1);
else
prior_shape = BayesInfo.pshape;
end
beta_index = find(prior_shape==1);
if isempty(beta_index)
beta_draws = false;
else
beta_draws = true;
end
gamma_index = find(prior_shape==2);
if isempty(gamma_index)
gamma_draws = false;
else
gamma_draws = true;
end
gaussian_index = find(prior_shape==3);
if isempty(gaussian_index)
gaussian_draws = false;
else
gaussian_draws = true;
end
inverse_gamma_1_index = find(prior_shape==4);
if isempty(inverse_gamma_1_index)
inverse_gamma_1_draws = false;
else
inverse_gamma_1_draws = true;
end
uniform_index = find(prior_shape==5);
if isempty(uniform_index)
uniform_draws = false;
else
uniform_draws = true;
end
inverse_gamma_2_index = find(prior_shape==6);
if isempty(inverse_gamma_2_index)
inverse_gamma_2_draws = false;
else
inverse_gamma_2_draws = true;
end
weibull_index = find(prior_shape==8);
if isempty(weibull_index)
weibull_draws = false;
else
weibull_draws = true;
end
pdraw = NaN(number_of_estimated_parameters,1);
return
end
if uniform_draws
pdraw(uniform_index) = rand(length(uniform_index),1).*(p4(uniform_index)-p3(uniform_index)) + p3(uniform_index);
out_of_bound = find( (pdraw(uniform_index)'>ub(uniform_index)) | (pdraw(uniform_index)'<lb(uniform_index)));
while ~isempty(out_of_bound)
pdraw(uniform_index) = rand(length(uniform_index),1).*(p4(uniform_index)-p3(uniform_index)) + p3(uniform_index);
out_of_bound = find( (pdraw(uniform_index)'>ub(uniform_index)) | (pdraw(uniform_index)'<lb(uniform_index)));
end
end
if gaussian_draws
pdraw(gaussian_index) = randn(length(gaussian_index),1).*p7(gaussian_index) + p6(gaussian_index);
out_of_bound = find( (pdraw(gaussian_index)'>ub(gaussian_index)) | (pdraw(gaussian_index)'<lb(gaussian_index)));
while ~isempty(out_of_bound)
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));
out_of_bound = find( (pdraw(gaussian_index)'>ub(gaussian_index)) | (pdraw(gaussian_index)'<lb(gaussian_index)));
end
end
if gamma_draws
pdraw(gamma_index) = gamrnd(p6(gamma_index),p7(gamma_index))+p3(gamma_index);
out_of_bound = find( (pdraw(gamma_index)'>ub(gamma_index)) | (pdraw(gamma_index)'<lb(gamma_index)));
while ~isempty(out_of_bound)
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));
out_of_bound = find( (pdraw(gamma_index)'>ub(gamma_index)) | (pdraw(gamma_index)'<lb(gamma_index)));
end
end
if beta_draws
pdraw(beta_index) = (p4(beta_index)-p3(beta_index)).*betarnd(p6(beta_index),p7(beta_index))+p3(beta_index);
out_of_bound = find( (pdraw(beta_index)'>ub(beta_index)) | (pdraw(beta_index)'<lb(beta_index)));
while ~isempty(out_of_bound)
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));
out_of_bound = find( (pdraw(beta_index)'>ub(beta_index)) | (pdraw(beta_index)'<lb(beta_index)));
end
end
if inverse_gamma_1_draws
pdraw(inverse_gamma_1_index) = ...
sqrt(1./gamrnd(p7(inverse_gamma_1_index)/2,2./p6(inverse_gamma_1_index)))+p3(inverse_gamma_1_index);
out_of_bound = find( (pdraw(inverse_gamma_1_index)'>ub(inverse_gamma_1_index)) | (pdraw(inverse_gamma_1_index)'<lb(inverse_gamma_1_index)));
while ~isempty(out_of_bound)
pdraw(inverse_gamma_1_index(out_of_bound)) = ...
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));
out_of_bound = find( (pdraw(inverse_gamma_1_index)'>ub(inverse_gamma_1_index)) | (pdraw(inverse_gamma_1_index)'<lb(inverse_gamma_1_index)));
end
end
if inverse_gamma_2_draws
pdraw(inverse_gamma_2_index) = ...
1./gamrnd(p7(inverse_gamma_2_index)/2,2./p6(inverse_gamma_2_index))+p3(inverse_gamma_2_index);
out_of_bound = find( (pdraw(inverse_gamma_2_index)'>ub(inverse_gamma_2_index)) | (pdraw(inverse_gamma_2_index)'<lb(inverse_gamma_2_index)));
while ~isempty(out_of_bound)
pdraw(inverse_gamma_2_index(out_of_bound)) = ...
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));
out_of_bound = find( (pdraw(inverse_gamma_2_index)'>ub(inverse_gamma_2_index)) | (pdraw(inverse_gamma_2_index)'<lb(inverse_gamma_2_index)));
end
end
if weibull_draws
pdraw(weibull_index) = wblrnd(p7(weibull_index), p6(weibull_index)) + p3(weibull_index);
out_of_bound = find( (pdraw(weibull_index)'>ub(weibull_index)) | (pdraw(weibull_index)'<lb(weibull_index)));
while ~isempty(out_of_bound)
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));
out_of_bound = find( (pdraw(weibull_index)'>ub(weibull_index)) | (pdraw(weibull_index)'<lb(weibull_index)));
end
end
%@test:1
%$ % 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;
%$ m0 = BayesInfo.p1; %zeros(14,1);
%$ v0 = diag(BayesInfo.p2.^2); %zeros(14);
%$
%$ % Call the tested routine
%$ try
%$ % Initialization of prior_draws.
%$ prior_draw(BayesInfo, prior_trunc, false);
%$ % Do simulations in a loop and estimate recursively the mean and teh variance.
%$ for i = 1:ndraws
%$ draw = transpose(prior_draw());
%$ m1 = m0 + (draw-m0)/i;
%$ m2 = m1*m1';
%$ 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
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