231 lines
8.9 KiB
Matlab
231 lines
8.9 KiB
Matlab
function ds = olsgibbs(ds, eqtag, BetaPriorExpectation, BetaPriorVariance, s2, nu, ndraws, discarddraws, thin, fitted_names_dict)
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%function ds = olsgibbs(ds, eqtag, BetaPriorExpectation, BetaPriorVariance, s2, nu, ndraws, discarddraws, thin, fitted_names_dict)
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% Implements Gibbs Sampling for univariate linear model.
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%
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% INPUTS
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% - ds [dseries] dataset.
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% - eqtag [string] name of equation tag to estimate.
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% - BetaPriorExpectation [double] vector with n elements, prior expectation of β.
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% - BetaPriorVariance [double] n*n matrix, prior variance of β.
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% - s2 [double] scalar, first hyperparameter for h.
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% - nu [integer] scalar, second hyperparameter for h.
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% - ndraws [integer] scalar, total number of draws (Gibbs sampling)
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% - discarddraws [integer] scalar, number of draws to be discarded.
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% - thin [integer] scalar, if thin == N, save every Nth draw (default is 1).
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% - fitted_names_dict [cell] Nx2 or Nx3 cell array to be used in naming fitted
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% values; first column is the equation tag,
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% second column is the name of the
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% associated fitted value, third column
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% (if it exists) is the function name of
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% the transformation to perform on the
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% fitted value.
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%
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% OUTPUTS
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% - ds [dseries] dataset updated with fitted value
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%
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% SPECIAL REQUIREMENTS
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% dynare must have been run with the option: json=compute
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% Copyright (C) 2018-2019 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 <http://www.gnu.org/licenses/>.
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global M_ oo_ options_
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%% Check input
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if nargin < 7 || nargin > 10
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error('Incorrect number of arguments passed to olsgibbs')
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end
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if isempty(ds) || ~isdseries(ds)
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error('The 1st argument must be a dseries')
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end
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if ~ischar(eqtag)
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error('The 2nd argument must be a string')
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end
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if ~isvector(BetaPriorExpectation)
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error('The 3rd argument must be a vector')
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else
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if ~isempty(BetaPriorExpectation)
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BetaPriorExpectation = transpose(BetaPriorExpectation(:));
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end
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end
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if ~ismatrix(BetaPriorVariance) || length(BetaPriorExpectation)~=length(BetaPriorVariance)
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error('The 4th argument (BetaPriorVariance) must be a square matrix with the same dimension as the third argument (BetaPriorExpectation)')
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else
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warning('off', 'MATLAB:singularMatrix')
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BetaInversePriorVariance = eye(length(BetaPriorVariance))/BetaPriorVariance;
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warning('on', 'MATLAB:singularMatrix')
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end
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if ~isreal(s2)
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error('The 5th argument (s2) must be a double')
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end
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if ~isint(nu)
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error('The 6th argument (nu) must be an integer')
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end
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if ~isint(ndraws)
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error('The 7th argument (ndraws) must be an integer')
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end
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if nargin <= 7
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discarddraws = 0;
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else
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if ~isint(discarddraws)
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error('The 8th argument (discardeddraws), if provided, must be an integer')
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else
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if discarddraws >= ndraws
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error('The 8th argument (discardeddraws) must be smaller than the 7th argument (ndraws)')
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end
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end
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end
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if nargin <= 8
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thin = 1;
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else
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if ~isint(thin)
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error('The 9th argument, must be an integer')
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end
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end
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if nargin <= 9
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fitted_names_dict = {};
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else
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if ~isempty(fitted_names_dict) && ...
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(~iscell(fitted_names_dict) || ...
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(size(fitted_names_dict, 2) < 2 || size(fitted_names_dict, 2) > 3))
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error('The 10th argument must be an Nx2 or Nx3 cell array');
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end
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end
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%% Parse equation
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[Y, lhssub, X, fp, lp] = common_parsing(ds, get_ast({eqtag}), true);
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lhsname = Y{1}.name;
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Y = Y{1}.data;
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X = X{1};
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fp = fp{1};
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lp = lp{1};
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pnames = X.name;
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N = size(X.data, 1);
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X = X.data;
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%% Estimation (see Koop, Gary. Bayesian Econometrics. 2003. Chapter 4.2)
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PosteriorDegreesOfFreedom = N + nu;
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n = length(pnames);
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assert(n==length(BetaPriorExpectation), 'the length prior mean for beta must be the same as the number of parameters in the equation to be estimated.');
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h = 1.0/s2*nu; % Initialize h to the prior expectation.
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periods = 1;
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linee = 1;
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% Posterior Simulation
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oo_.olsgibbs.(eqtag).draws = zeros(floor((ndraws-discarddraws)/thin), n+3);
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for i=1:discarddraws
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% Set conditional distribution of β
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InverseConditionalPoseriorVariance = BetaInversePriorVariance + h*(X'*X);
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cholConditionalPosteriorVariance = chol(InverseConditionalPoseriorVariance\eye(n), 'upper');
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ConditionalPosteriorExpectation = (BetaPriorExpectation*BetaInversePriorVariance + h*(Y'*X))/InverseConditionalPoseriorVariance;
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% Draw beta | Y, h
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beta = rand_multivariate_normal(ConditionalPosteriorExpectation, cholConditionalPosteriorVariance, n);
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% draw h | Y, beta
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resids = Y - X*transpose(beta);
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s2_ = (resids'*resids + nu*s2)/PosteriorDegreesOfFreedom;
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h = gamrnd(PosteriorDegreesOfFreedom/2.0, 2.0/(PosteriorDegreesOfFreedom*s2_));
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end
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for i = discarddraws+1:ndraws
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% Set conditional distribution of β
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InverseConditionalPoseriorVariance = BetaInversePriorVariance + h*(X'*X);
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cholConditionalPosteriorVariance = chol(InverseConditionalPoseriorVariance\eye(n), 'upper');
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ConditionalPosteriorExpectation = (BetaPriorExpectation*BetaInversePriorVariance + h*(Y'*X))/InverseConditionalPoseriorVariance;
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% Draw beta | Y, h
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beta = rand_multivariate_normal(ConditionalPosteriorExpectation, cholConditionalPosteriorVariance, n);
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% draw h | Y, beta
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resids = Y - X*transpose(beta);
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s2_ = (resids'*resids + nu*s2)/PosteriorDegreesOfFreedom;
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h = gamrnd(PosteriorDegreesOfFreedom/2.0, 2.0/(PosteriorDegreesOfFreedom*s2_));
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R2 = 1-var(resids)/var(Y);
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if isequal(periods, thin)
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oo_.olsgibbs.(eqtag).draws(linee, 1:n) = beta;
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oo_.olsgibbs.(eqtag).draws(linee, n+1) = h;
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oo_.olsgibbs.(eqtag).draws(linee, n+2) = s2_;
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oo_.olsgibbs.(eqtag).draws(linee, n+3) = R2;
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periods = 1;
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linee = linee+1;
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else
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periods = periods+1;
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end
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end
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%% Save posterior moments.
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oo_.olsgibbs.(eqtag).posterior.mean.beta = mean(oo_.olsgibbs.(eqtag).draws(:,1:n))';
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oo_.olsgibbs.(eqtag).posterior.mean.h = mean(oo_.olsgibbs.(eqtag).draws(:,n+1));
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oo_.olsgibbs.(eqtag).posterior.variance.beta = cov(oo_.olsgibbs.(eqtag).draws(:,1:n));
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oo_.olsgibbs.(eqtag).posterior.variance.h = var(oo_.olsgibbs.(eqtag).draws(:,n+1));
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oo_.olsgibbs.(eqtag).s2 = mean(oo_.olsgibbs.(eqtag).draws(:,n+2));
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oo_.olsgibbs.(eqtag).R2 = mean(oo_.olsgibbs.(eqtag).draws(:,n+3));
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% Yhat
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idx = 0;
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yhatname = [eqtag '_olsgibbs_FIT'];
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if ~isempty(fitted_names_dict)
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idx = strcmp(fitted_names_dict(:,1), eqtag);
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if any(idx)
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yhatname = fitted_names_dict{idx, 2};
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end
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end
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oo_.olsgibbs.(eqtag).Yhat = dseries(X*oo_.olsgibbs.(eqtag).posterior.mean.beta, fp, yhatname) + lhssub{1};
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% Apply correcting function for Yhat if it was passed
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if any(idx) ...
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&& length(fitted_names_dict(idx, :)) == 3 ...
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&& ~isempty(fitted_names_dict{idx, 3})
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oo_.olsgibbs.(eqtag).Yhat = ...
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feval(fitted_names_dict{idx, 3}, oo_.olsgibbs.(eqtag).Yhat);
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end
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ds = [ds oo_.olsgibbs.(eqtag).Yhat];
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% Compute and save posterior densities.
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for i=1:n
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xx = oo_.olsgibbs.(eqtag).draws(:,i);
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nn = length(xx);
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bandwidth = mh_optimal_bandwidth(xx, nn, 0, 'gaussian');
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[x, f] = kernel_density_estimate(xx, 512, nn, bandwidth,'gaussian');
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oo_.olsgibbs.(eqtag).posterior.density.(pnames{i}) = [x, f];
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end
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% Update model's parameters with posterior mean.
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for j = 1:length(pnames)
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isj = strcmp(M_.param_names, pnames{j});
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M_.params(isj) = oo_.olsgibbs.(eqtag).posterior.mean.beta(j);
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end
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%% Print Output
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if ~options_.noprint
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ttitle = ['Bayesian estimation (with Gibbs sampling) of equation ''' eqtag ''''];
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preamble = {['Dependent Variable: ' lhsname{:}], ...
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sprintf('No. Independent Variables: %d', size(X,2)), ...
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sprintf('Observations: %d from %s to %s\n', size(X,1), fp.char, lp.char)};
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afterward = {sprintf('s^2: %f', oo_.olsgibbs.(eqtag).s2), sprintf('R^2: %f', oo_.olsgibbs.(eqtag).R2)};
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dyn_table(ttitle, preamble, afterward, pnames, {'Posterior mean', 'Posterior std.'}, 4, [oo_.olsgibbs.(eqtag).posterior.mean.beta, sqrt(diag(oo_.olsgibbs.(eqtag).posterior.variance.beta))]);
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end
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end
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