dynare/matlab/posterior_moments.m

function [post_mean, post_median, post_var, hpd_interval, post_deciles, density] = posterior_moments(xx,info,mh_conf_sig)
% 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.
%
% part of DYNARE, copyright Dynare Team (2005-2008)
% Gnu Public License.

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);
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];

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)]);

density = [];
if info
    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.  
    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);
end