credint

 Computes credible interval(s) directly from a vector (or row-major matrix) of
 the posterior(s) obtained by bayesian bootstrap.

 -- Function File: CI = credint (BOOTSTAT)
 -- Function File: CI = credint (BOOTSTAT, PROB)

     'CI = credint (BOOTSTAT)' computes 95% credible intervals directly from
     the vector, or rows* of the matrix in BOOTSTAT, where BOOTSTAT contains
     posterior (or Bayesian bootstrap) statistics, such as those generated
     using the `bootbayes` function (or the `bootlm` function with the method
     set to 'bayesian'). The credible intervals are shortest probability
     intervals (SPI), which represent a more computationally stable version
     of the highest posterior density interval [1,2].

        * The matrix should have dimensions P * NBOOT, where P corresponds to
          the number of parameter estimates and NBOOT corresponds to the number
          of posterior (or Bayesian bootstrap) samples.

     'CI = credint (BOOTSTAT, PROB)' returns credible intervals, where PROB is
     numeric and sets the lower and upper bounds of the credible interval(s).
     The value(s) of PROB must be between 0 and 1. PROB can either be:
       <> scalar: To set the central mass of shortest probability intervals
                  to 100*PROB%
       <> vector: A pair of probabilities defining the lower and upper
                  percentiles of the credible interval(s) as 100*(PROB(1))%
                  and 100*(PROB(2))% respectively.
          The default value of PROB is the scalar: 0.95, for a 95% shortest 
          posterior credible interval.

  Bibliography:
  [1] Liu, Gelman & Zheng (2015). Simulation-efficient shortest probability
        intervals. Statistics and Computing, 25(4), 809–819. 
  [2] Gelman (2020) Shortest Posterior Intervals.
        https://discourse.mc-stan.org/t/shortest-posterior-intervals/16281/16

  credint (version 2023.09.03)
  Author: Andrew Charles Penn
  https://www.researchgate.net/profile/Andrew_Penn/

  Copyright 2019 Andrew Charles Penn
  This program 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.

  This program 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 this program.  If not, see http://www.gnu.org/licenses/

Demonstration 1

 % Input univariate dataset
 y = [5.18 2.71 2.69 6.09 4.23 10.7 3.71 13.13 19.28 6.61].';

 % 95% credible interval for the mean 
 [stats, bootstat] = bootbayes (y);
 CI = credint (bootstat,0.95)           % 95% shortest probability interval
 CI = credint (bootstat,[0.025,0.975])  % 95% equal-tailed interval

 % Please be patient, the calculations will be completed soon...

CI =

       4.5724       10.951

CI =

       4.7304       11.208

Package: statistics-resampling