  Minimum message length is a general Bayesian principle for model selection
and parameter estimation that is based on information theory. This paper
applies the minimum message length principle to a small-sample model selection
problem involving Poisson and geometric data models. Since MML is a Bayesian
principle, it requires prior distributions for all model parameters. We
introduce three candidate prior distributions for the unknown model parameters
with both light- and heavy-tails. The performance of the MML methods is
compared with objective Bayesian inference and minimum description length
techniques based on the normalized maximum likelihood code. Simulations show
that our MML approach with a heavy-tail prior distribution provides an
excellent performance in all tests.
