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.0001 function [post_mean, post_median, post_var, hpd_interval, post_deciles, density] = posterior_moments(xx,info,mh_conf_sig) 0002 % Computes posterior mean, median, variance, HPD interval, deciles, and density from posterior draws. 0003 % 0004 % INPUTS 0005 % xx [double] Vector of posterior draws (or prior draws ;-) 0006 % info [integer] If equal to one the posterior density is estimated. 0007 % mh_config_sig [double] Scalar between 0 and 1 specifying the size of the HPD interval. 0008 % 0009 % 0010 % OUTPUTS 0011 % post_mean [double] Scalar, posterior mean. 0012 % post_median [double] Scalar, posterior median. 0013 % post_var [double] Scalar, posterior variance. 0014 % hpd_interval [double] Vector (1*2), Highest Probability Density interval 0015 % post_deciles [double] Vector (9*1), deciles of the posterior distribution. 0016 % density [double] Matrix (n*2), non parametric estimate of the posterior density. First and second 0017 % columns are respectively abscissa and ordinate coordinates. 0018 % 0019 % SPECIAL REQUIREMENTS 0020 % Other matlab routines distributed with Dynare: mh_optimal_bandwidth.m 0021 % kernel_density_estimate.m. 0022 % 0023 0024 % Copyright (C) 2005-2010 Dynare Team 0025 % 0026 % This file is part of Dynare. 0027 % 0028 % Dynare is free software: you can redistribute it and/or modify 0029 % it under the terms of the GNU General Public License as published by 0030 % the Free Software Foundation, either version 3 of the License, or 0031 % (at your option) any later version. 0032 % 0033 % Dynare is distributed in the hope that it will be useful, 0034 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0035 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0036 % GNU General Public License for more details. 0037 % 0038 % You should have received a copy of the GNU General Public License 0039 % along with Dynare. If not, see <http://www.gnu.org/licenses/>. 0040 0041 xx = xx(:); 0042 xx = sort(xx); 0043 0044 0045 post_mean = mean(xx); 0046 post_median = median(xx); 0047 post_var = var(xx); 0048 0049 number_of_draws = length(xx); 0050 hpd_draws = round((1-mh_conf_sig)*number_of_draws); 0051 kk = zeros(hpd_draws,1); 0052 jj = number_of_draws-hpd_draws; 0053 for ii = 1:hpd_draws 0054 kk(ii) = xx(jj)-xx(ii); 0055 jj = jj + 1; 0056 end 0057 [kmin,idx] = min(kk); 0058 hpd_interval = [xx(idx) xx(idx)+kmin]; 0059 0060 post_deciles = xx([round(0.1*number_of_draws) ... 0061 round(0.2*number_of_draws) ... 0062 round(0.3*number_of_draws) ... 0063 round(0.4*number_of_draws) ... 0064 round(0.5*number_of_draws) ... 0065 round(0.6*number_of_draws) ... 0066 round(0.7*number_of_draws) ... 0067 round(0.8*number_of_draws) ... 0068 round(0.9*number_of_draws)]); 0069 0070 density = []; 0071 if info 0072 number_of_grid_points = 2^9; % 2^9 = 512 !... Must be a power of two. 0073 if post_var > 1e-12 0074 bandwidth = 0; % Rule of thumb optimal bandwidth parameter. 0075 kernel_function = 'gaussian'; % Gaussian kernel for Fast Fourrier Transform approximaton. 0076 optimal_bandwidth = mh_optimal_bandwidth(xx,number_of_draws,bandwidth,kernel_function); 0077 [density(:,1),density(:,2)] = kernel_density_estimate(xx,number_of_grid_points,... 0078 number_of_draws,optimal_bandwidth,kernel_function); 0079 else 0080 density = NaN(number_of_grid_points,2); 0081 end 0082 end