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function [post_mean, post_median, post_var, hpd_interval, post_deciles, density] = posterior_moments(xx,info,mh_conf_sig,kernel_options)
% Computes posterior mean, median, variance, HPD interval, deciles, and density from posterior draws.
%
% INPUTS
% xx [double] Vector of posterior draws (or prior draws ;-)
% info [integer] If equal to one the posterior density is estimated.
% mh_config_sig [double] Scalar between 0 and 1 specifying the size of the HPD interval.
%
%
% OUTPUTS
% post_mean [double] Scalar, posterior mean.
% post_median [double] Scalar, posterior median.
% post_var [double] Scalar, posterior variance.
% hpd_interval [double] Vector (1*2), Highest Probability Density interval
% post_deciles [double] Vector (9*1), deciles of the posterior distribution.
% density [double] Matrix (n*2), non parametric estimate of the posterior density. First and second
% columns are respectively abscissa and ordinate coordinates.
%
% SPECIAL REQUIREMENTS
% Other matlab routines distributed with Dynare: mh_optimal_bandwidth.m
% kernel_density_estimate.m.
%
% Copyright (C) 2005-2017 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/>.
if nargin<4
number_of_grid_points = 2^9; % 2^9 = 512 !... Must be a power of two.
bandwidth = 0; % Rule of thumb optimal bandwidth parameter.
kernel_function = 'gaussian'; % Gaussian kernel for Fast Fourrier Transform approximaton.
else
number_of_grid_points = kernel_options.gridpoints;
bandwidth = kernel_options.bandwidth;
kernel_function = kernel_options.kernel_function;
end
xx = xx(:);
xx = sort(xx);
post_mean = mean(xx);
post_median = median(xx);
post_var = var(xx);
number_of_draws = length(xx);
hpd_draws = round((1-mh_conf_sig)*number_of_draws);
if hpd_draws>2
kk = zeros(hpd_draws,1);
jj = number_of_draws-hpd_draws;
for ii = 1:hpd_draws
kk(ii) = xx(jj)-xx(ii);
jj = jj + 1;
end
[kmin,idx] = min(kk);
hpd_interval = [xx(idx) xx(idx)+kmin];
else
hpd_interval=NaN(1,2);
end
if length(xx)>9
post_deciles = xx([round(0.1*number_of_draws) ...
round(0.2*number_of_draws) ...
round(0.3*number_of_draws) ...
round(0.4*number_of_draws) ...
round(0.5*number_of_draws) ...
round(0.6*number_of_draws) ...
round(0.7*number_of_draws) ...
round(0.8*number_of_draws) ...
round(0.9*number_of_draws)]);
else
post_deciles=NaN(9,1);
end
density = [];
if info
if post_var > 1e-12
optimal_bandwidth = mh_optimal_bandwidth(xx,number_of_draws,bandwidth,kernel_function);
[density(:,1),density(:,2)] = kernel_density_estimate(xx,number_of_grid_points,...
number_of_draws,optimal_bandwidth,kernel_function);
else
density = NaN(number_of_grid_points,2);
end
end
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