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Additional info for Analysis of Capture-Recapture Data
For any model M(θ), with d-dimensional parameter vector θ, we form the likelihood L(θ; x). 1 Forming likelihoods A characteristic of capture-reencounter data is the need to deal with partial information, due to the fact that wild animals can be diﬃcult to find. We can construct likelihoods in diﬀerent ways, as we shall see, and one of these is individual-by-individual, taking account of the various alternatives when animals are not encountered. In such cases an eﬃcient approach may be provided by using the theory of hidden Markov models; see Zucchini and MacDonald (1999).
Diagnostic goodness-of-fit tests in capture-recapture take place before model-fitting. They are designed to check for particular departures from a standard model, and whether the model needs to be improved. 1 Bayesian inference Introduction Choice of prior distributions, and the influence of priors, will be discussed in examples throughout the book. For a scalar parameter θ the Jeﬀreys prior has the form, π(θ) ∝ J(θ), and is invariant to reparameterisation. 1) readily provides the joint posterior distribution π(θ|x) for all of the model parameters, θ.
6. We start with the simplest case of model M0 . 1 Model M0 Under model M0 there is constant capture probability, p. 3), in which the capture probability was time dependent, we deduce the likelihood, L(N, p; X) ∝ N! pS. (1 − p)N T −S. (N − D)! The maximum-likelihood estimate of p is given by pˆ = S.