Hierarchical capture-recapture models

A defining feature of capture-recapture is missing data due to imperfect detection of individuals. The standard approach used to deal with the missing data is to integrate (or sum) over all the possible unknown values. The missing data is completely removed and the resulting likelihood is in terms of the observed data. The problem with this approach is that often biologically unnatural parameters are chosen to make the integration (summation) tractable. A related consequence is that latent variables of interest, such as the population size and the number of births are only available as derived quantities. As they are not explicitly in the model they are not available to be used in the model as covariates to describe population dynamics. Therefore, models including density dependence are unable to be examined using standard methods. Instead of explicitly integrating out missing data, we choose to include it using data augmentation. Instead of being removed, the missing data is now present in the likelihood as if it were actually observed. This means that we are able to specify models in terms of the data we would like to have observed, instead of the data we actually did observe. Having the complete data allows us to separate the processes of demographic interest from the sampling process. The separation means that we can focus on specifying the model for the demographic processes without worrying about

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