Estimating immigration using a Bayesian integrated population model: choice of parametrization and priors

Abstract

Bayesian integrated population modelling provides a natural tool for estimating immigration into a single study population when we have indices of population size, mark–recapture data and fecundity data. We consider the choice of both the parametrization of immigration and its prior. Using a simulation study for a model that is typical of those used for short-live bird species, we assess the effect of specifying immigration in terms of the number of immigrants each year, as opposed to an immigration rate. We also assess the effect of the assumption of independence of the data sets, which is commonly required in such modelling. If immigration is occurring, our results suggest that parametrizing the model in terms of number of immigrants will provide a more precise estimate, compared to a parametrization involving an immigration rate, even if we wish to estimate the rate. If there is little or no immigration, use of a model parametrized in terms of an immigration rate can result in overestimation, whereas a model in which immigration is specified as a number offers the possibility to use priors that have a negative lower bound with the consequence that immigration is correctly estimated. Use of such a model appears to be robust to the assumption of independence being wrong, our results for independent and dependent data sets being remarkably similar in terms of the distribution, across all simulations, of the posterior means and standard deviations.