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By McCrea, Rachel S.

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4 Model comparison Parameters in capture-recapture models may vary with respect to factors such as time, space, age and cohort. Thus there are typically many alternative models to be considered. The outcome of a classical analysis is frequently a single best model and the corresponding point and interval estimates for the parameters of that model, as a result of using methods to decide between the alternative models. We describe here several such methods which will be used throughout the book. 1 MODEL FITTING, AVERAGING AND COMPARISON Likelihood-ratio and score tests Likelihood-ratio and score tests allow us to compare nested models, where one is a special case of another.

D(x; θ i ) for all i. Such plots are called discrepancy plots. If the model describes the data x well, we would expect similar values for D(xi ; θ i ) and D(x; θ i ) for all i. 5. This approach necessarily depends on the prior distribution used, so that changing the prior changes the Bayesian p-value. Any appropriate measure of goodness-of-fit may be used, and it may be useful to select more than one, to obtain different perspectives on how the model may fail to describe the data (Gelman et al. 1996).

2010), in particular with regard to applying RJMCMC. Barker and Link (2013) present a version of RJMCMC in terms of Gibbs sampling, with advantages for calculating model probabilities; see also Link and Barker (2009). Possibly the earliest example of MCMC methods at use in capture-recapture is to be found in George and Robert (1992), where Gibbs sampling is used and all the conditional distributions are of standard form. In a period of just over 20 years, Bayesian methods have become firmly established for the analysis of capture-recapture data; see for example K´ery (2010) and K´ery and Schaub (2012).

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