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A hierarchical dependent Dirichlet process prior for modelling bird migration patterns in the UK. (English) Zbl 1439.62218
Summary: Environmental changes in recent years have been linked to phenological shifts which in turn are linked to the survival of species. The work in this paper is motivated by capture-recapture data on blackcaps collected by the British Trust for Ornithology as part of the Constant Effort Sites monitoring scheme. Blackcaps overwinter abroad and migrate to the UK annually for breeding purposes. We propose a novel Bayesian nonparametric approach for expressing the bivariate density of individual arrival and departure times at different sites across a number of years as a mixture model. The new model combines the ideas of the hierarchical and the dependent Dirichlet process, allowing the estimation of site-specific weights and year-specific mixture locations, which are modelled as functions of environmental covariates using a multivariate extension of the Gaussian process. The proposed modelling framework is extremely general and can be used in any context where multivariate density estimation is performed jointly across different groups and in the presence of a continuous covariate.
##### MSC:
 62P10 Applications of statistics to biology and medical sciences; meta analysis 62P12 Applications of statistics to environmental and related topics 62N05 Reliability and life testing 62H11 Directional data; spatial statistics 60G15 Gaussian processes 92B25 Biological rhythms and synchronization
Rcpp; R
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