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function results_struct = geweke_chi2_test(results1,results2,results_struct,options)
% results_struct = geweke_chi2_test(results1,results2,results_struct,options)
% PURPOSE: computes Geweke's chi-squared test for two sets of MCMC sample draws
%
% INPUTS
% results1 [1 by (4+n_taper*2) vector] vector with post. mean,
% std, NSE_iid, RNE_iid, and tapered NSE and RNE
% for chain part 1
% results2 [1 by (4+n_taper*2) vector] vector with post. mean,
% std, NSE_iid, RNE_iid, and tapered NSE and RNE
% for chain part 2
% results_struct [structure] results structure generated by geweke_moments
% Dynareoptions [structure]
%
% OUTPUTS
% results_struct [structure] containing the following fields:
% pooled_mean Pooled mean of the chain parts, weighted
% with precision
% rpooled_nse Pooled NSE of the chain parts, weighted
% with precision
% prob_chi2_test p-value of Chi2-test for equality of
% means in both chain parts
% -----------------------------------------------------------------
%
% SPECIAL REQUIREMENTS
% None.
% Copyright (C) 2013-2017 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 <http://www.gnu.org/licenses/>.
%
% ------------------------------------------------
% REFERENCES: Geweke (1992), `Evaluating the accuracy of sampling-based
% approaches to the calculation of posterior moments', in J.O. Berger,
% J.M. Bernardo, A.P. Dawid, and A.F.M. Smith (eds.) Proceedings of
% the Fourth Valencia International Meeting on Bayesian Statistics,
% pp. 169-194, Oxford University Press
% Geweke (1999): `Using simulation methods for Bayesian econometric models:
% Inference, development and communication', Econometric Reviews, 18(1),
% 1-73
% written by: Johannes Pfeifer,
% based on code by James P. LeSage, who in turn
% drew on MATLAB programs written by Siddartha Chib
for k=1:length(options.convergence.geweke.taper_steps)+1
NSE=[results1(:,3+(k-1)*2) results2(:,3+(k-1)*2)];
means=[results1(:,1) results2(:,1)];
diff_Means=means(:,1)-means(:,2);
sum_of_weights=sum(1./(NSE.^2),2);
pooled_mean=sum(means./(NSE.^2),2)./sum_of_weights;
pooled_NSE=1./sqrt(sum_of_weights);
test_stat=diff_Means.^2./sum(NSE.^2,2);
p = 1-chi2cdf(test_stat,1);
results_struct.pooled_mean(:,k) = pooled_mean;
results_struct.pooled_nse(:,k) = pooled_NSE;
results_struct.prob_chi2_test(:,k) = p;
end
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