A Bayesian Semiparametric Jolly-Seber Model with Individual Heterogeneity: An Application to Migratory Mallards at Stopover

Abstract

We propose a Bayesian hierarchical Jolly-Seber model that can account for individual heterogeneity in departure and the dependence of arrival time on covariates. Additionally, our model provides a semiparametric functional form for modeling capture probabilities. The model is flexible and can be used to estimate the stopover duration and stopover population size, which are key to stopover duration analysis. From the modeling perspective, our model allows for individual heterogeneity in departure due to a continuous intrinsic factor that varies with time and individual. A stochastic process is considered to model the change of this intrinsic factor over time. Moreover, our model links extrinsic factors to capture probabilities and arrival time. Consequently, our proposed model enables us to draw inference about the impacts of the intrinsic factor on departure, and extrinsic factors on both capture outcome and arrival time. Through the use of a semiparametric model for capture probabilities, we allow the data to suggest the functional relationship between extrinsic factors and capture probabilities rather than relying on an imposed parametric model. By using data augmentation, we develop a well customized Markov chain Monte Carlo algorithm that is free of tuning. We demonstrate the effectiveness of our model through a motivating example of stopover duration analysis for mallards (Anas platyrhynchos) studied during fall migration in Sweden.