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2023 | OriginalPaper | Chapter

13. Capture-Recapture: Bayesian Methods

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Abstract

This chapter outlines the development of Bayesian methods for estimating abundance in closed population capture-recapture models. We describe model development prior to the use of Markov chain Monte Carlo (MCMC), which relied on mathematical derivation of the posterior distribution for relatively simple models. The rapid development of Bayesian models after the introduction of MCMC is reviewed and includes models that allow for behavioral effects due to previous capture, individual heterogeneity, and dependence between capture occasions (or list dependence).
We consider in detail Bayesian estimation of abundance in the presence of individual heterogeneity. It is a difficult problem due to one parameter (abundance) defining the dimensionality of another parameter (capture probability). Prior choice for closed population capture-recapture models is discussed. This includes priors that attempt to include little to no prior information (non-informative), priors that attempt to include external information (informative), and priors that incorporate a weaker form of the information available (weakly informative).

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Footnotes
1
Technically the beta distribution with \(\alpha =0\) and \(\gamma =0\) is undefined. What is meant is that the prior is \(f(p) \propto p^{-1}(1-p)^{-1}\), the limit of a beta distribution as \(\alpha \rightarrow 0\), \(\gamma \rightarrow 0\).
 
2
In practice, the value of \(\pi _{0}\) at \(\mu ^{(t)}\) is required in the previous iteration of the algorithm. It is more efficient to “carry forward” this quantity than reevaluate it.
 
3
Schofield and Barker (2008) considered open population models where the times of entry and exit to the population are included as latent variables. Wright et al. (2009) allowed for uncertain identification and included the true identities as a latent variable.
 
4
Noted that Gelman et al. (2008) defined their prior with the assumption that the input variables have mean 0 and standard deviation 0.5.
 
5
The posterior summaries are those given by Link (2014).
 
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Metadata
Title
Capture-Recapture: Bayesian Methods
Author
Matthew R. Schofield
Copyright Year
2023
DOI
https://doi.org/10.1007/978-3-031-39834-6_13

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