134 lines
4.7 KiB
Matlab
134 lines
4.7 KiB
Matlab
function surgibbs(ds, param_names, beta0, A, ndraws, discarddraws, thin, eqtags)
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%function surgibbs(ds, param_names, beta0, A, ndraws, discarddraws, thin, eqtags)
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% Implements Gibbs Samipling for SUR
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%
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% INPUTS
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% ds [dseries] data
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% param_names [cellstr] list of parameters to estimate
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% beta0 [vector] prior values (in order of param_names)
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% A [matrix] prior distribution variance (in order of
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% param_names)
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% ndraws [int] number of draws
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% discarddraws [int] number of draws to discard
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% thin [int] if thin == N, save every Nth draw
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% eqtags [cellstr] names of equation tags to estimate. If empty,
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% estimate all equations
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%
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% OUTPUTS
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% none
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%
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% SPECIAL REQUIREMENTS
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% none
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% Copyright (C) 2017-2018 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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%% The notation that follows comes from Section 2.2 of
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% Ando, Tomohiro and Zellner, Arnold. 2010. Hierarchical Bayesian Analysis of the
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% Seemingly Unrelated Regression and Simultaneous Equations Models Using a
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% Combination of Direct Monte Carlo and Importance Sampling Techniques.
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% Bayesian Analysis Volume 5, Number 1, pp. 65-96.
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global M_ oo_
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%% Check input
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assert(nargin >= 5 && nargin <= 8, 'Incorrect number of arguments passed to surgibbs');
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assert(isdseries(ds), 'The 1st argument must be a dseries');
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assert(iscellstr(param_names), 'The 2nd argument must be a cellstr');
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assert(isvector(beta0) && length(beta0) == length(param_names), ...
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'The 3rd argument must be a vector with the same length as param_names and the same ');
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if isrow(beta0)
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beta0 = beta0';
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end
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assert(ismatrix(A) && all(all((A == A'))) && length(beta0) == size(A, 2), ...
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'The 4th argument must be a symmetric matrix with the same dimension as beta0');
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assert(isint(ndraws), 'The 5th argument must be an integer');
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if nargin == 5
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discarddraws = 0;
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else
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assert(isint(discarddraws), 'The 6th argument, if provided, must be an integer');
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end
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if nargin == 6
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thin = 1;
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else
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assert(isint(thin), 'The 7th argument, if provided, must be an integer');
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end
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%% Estimation
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% Notation from:
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% Ando, Tomohiro and Zellner, Arnold. Hierarchical Bayesian Analysis of
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% the Seemingly Unrelated Regression and Simultaneous Equations Models
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% Using a Combination of Direct Monte Carlo and Importance Sampling
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% Techniques. Bayesian Analysis. 2010. pp 67-70.
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if nargin == 8
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[nobs, pidxs, X, Y, m] = sur(ds, param_names, eqtags);
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else
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[nobs, pidxs, X, Y, m] = sur(ds, param_names);
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end
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beta = beta0;
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A = inv(A);
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thinidx = 1;
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drawidx = 1;
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nparams = length(param_names);
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oo_.surgibbs.betadraws = zeros(floor((ndraws-discarddraws)/thin), nparams);
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for i = 1:ndraws
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% Draw Omega, given X, Y, Beta
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resid = reshape(Y - X*beta, nobs, m);
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Omega = rand_inverse_wishart(m, nobs, chol(inv(resid'*resid/nobs)));
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% Draw beta, given X, Y, Omega
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tmp = kron(inv(Omega), eye(nobs));
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tmp1 = X'*tmp*X;
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Omegabar = inv(tmp1 + A);
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betahat = tmp1\X'*tmp*Y;
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betabar = Omegabar*(tmp1*betahat+A*beta0);
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beta = rand_multivariate_normal(betabar', chol(Omegabar), nparams)';
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if i > discarddraws
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if thinidx == thin
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oo_.surgibbs.betadraws(drawidx, :) = beta';
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thinidx = 1;
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drawidx = drawidx + 1;
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else
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thinidx = thinidx + 1;
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end
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end
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end
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% save parameter values
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oo_.surgibbs.beta = (sum(oo_.surgibbs.betadraws)/rows(oo_.surgibbs.betadraws))';
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M_.params(pidxs) = oo_.surgibbs.beta;
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%% Print Output
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dyn_table('Gibbs Sampling on SUR', {}, {}, param_names, ...
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{'Parameter Value'}, 4, oo_.surgibbs.beta);
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%% Plot
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figure
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nrows = 5;
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ncols = floor(nparams/nrows);
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if mod(nparams, nrows) ~= 0
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ncols = ncols + 1;
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end
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for j = 1:length(param_names)
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M_.params(strmatch(param_names{j}, M_.param_names, 'exact')) = oo_.surgibbs.beta(j);
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subplot(nrows, ncols, j)
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histogram(oo_.surgibbs.betadraws(:, j))
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hc = histcounts(oo_.surgibbs.betadraws(:, j));
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line([oo_.surgibbs.beta(j) oo_.surgibbs.beta(j)], [min(hc) max(hc)], 'Color', 'red');
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title(param_names{j}, 'Interpreter', 'none')
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end
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