© 2002 by Biometrika Trust
Bayesian model discrimination for multiple strata capture-recapture data
1 The Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, U.Kr.king{at}statslab.cam.ac.uk s.p.brooks{at}statslab.cam.ac.uk
Extending the work of Dupuis (1995), we motivate a range of biologically plausible models for multiple-site capture-recapture and show how the original Gibbs sampling algorithm of Dupuis can be extended to obtain posterior model probabilities using reversible jump Markov chain Monte Carlo.This model selection procedure improves upon previous analyses in two distinct ways. First, Bayesian model averaging provides a robust parameter estimation technique which properly incorporates model uncertainty in the resulting intervals. Secondly, by discriminating among perhaps millions of competing models, we are able to discern fine structure within the data and thereby answer questions of primary biological importance. We demonstrate how reversible jump Markov chain Monte Carlo methods provide the only viable method for exploring model spaces of this size. 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 these 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.
Key Words: Arnason–Schwarz; Capture-recapture; Common lizard; Migration; Model averaging; Model selection; Reversible jump Markov chain Monte Carlo
Received April 2001. Revised November 2001
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