Dirichlet-Multinomial distribution

A demo of random number generation, density evaluation, and distribution fitting for the Dirichlet-Mutlinomial distribution

Contents

Generate Dirichlet-Multinomial random vectors

clear;
% reset random seed
s = RandStream('mt19937ar','Seed',2);
RandStream.setGlobalStream(s);
% sample size
n = 100;
% # bins
d = 5;
% true parameter values
alpha = 1:d;
% set batch sizes (ranges from 25 to 50)
batchsize = 25+unidrnd(25,n,1);
% generate random vectors
X = dirmnrnd(batchsize,alpha,n);

Evaluate Dirichlet-Multinomial (log) pdf at true parameter value

logL = dirmnpdfln(X,alpha);
display(sum(logL));

  -1.0282e+03

Fit Dirichlet-Multinomial distribution

tic;
[alpha_hat, stats_dm] = dirmnfit(X);
toc;
display([alpha_hat, stats_dm.se]);
display(stats_dm);

figure;
plot(stats_dm.logL_iter);
xlabel('iteration');
ylabel('log-likelihood');

Elapsed time is 0.009744 seconds.
    0.9495    0.1300
    2.1979    0.2670
    2.7269    0.3231
    3.9027    0.4525
    4.7257    0.5470


stats_dm = 

  struct with fields:

           BIC: 2.0753e+03
           AIC: 2.0623e+03
           dof: 5
    iterations: 6
          logL: -1.0261e+03
     logL_iter: [1×6 double]
            se: [5×1 double]
      gradient: [5×1 double]
           LRT: 445.1073
        pvalue: 0

Published with MATLAB® R2017a