# Bayesian Model Discrimination for Multiple Strata Capture-Recapture Data

### Ruth King and Stephen P. Brooks

### University of Cambridge

## Summary

In this paper we consider the problem of Bayesian model determination in the
context of the analysis of multiple-site
capture-recapture. Extending the work of Dupuis (1995),
we motivate a range of biologically plausible models and show how
the original Gibbs sampling algorithm of Dupuis can be extended to
obtain posterior model probabilities through the introduction of
reversible jump Markov chain Monte Carlo updates.

This model selection procedure improves upon previous analyses
in two distinct ways. First, if parameter estimates are of primary
interest, then Bayesian model averaging provides a robust
estimation technique which properly incorporates model
uncertainty in the resulting intervals. Second, by discriminating
between competing models, we are able to discern fine structure
within the data e.g., whether or not survival depends upon
age, year or location. Such questions are often of primary biological
importance and can only be addressed through model comparison techniques.

We examine the lizard data discussed in Dupuis (1995) and show that
most of the posterior mass is placed upon models
not previously considered for this data. We discuss model discrimination
and model averaging and focus upon the increased scientific understanding
of the data obtained via the Bayesian model comparison procedure.

### Keywords:

Arnason-Schwarz; capture-recapture; common lizard; migration;
model averaging; model selection;
reversible jump Markov chain Monte Carlo.

Appeared as King, R. and Brooks, S.P. (2002) "Bayesian Model Discrimination
for Multiple Strata Capture-Recapture Data".* Biometrika *
**89** pp 785-806