Bayesian Nonparametric Models for Modelling Ecological Data and Stochastic Processes for Modelling Species Interactions

In this thesis, we present four manuscripts, described in the second to fifth chapter. Chapter 2 presents a Bayesian nonparametric model for capture-recapture (CR) data collected at different sites and for several years. To estimate arrival and departure patterns at the different sites and years, we build an extension of the Dirichlet process, the Hierarchical Dependent Dirichlet process, which allows us to perform density estimation jointly across different sites and in the presence of covariates. In this case, we use a year-specific covariate, and model the correlation structure of the covariate across years using a multivariate Gaussian process. In Chapter 3, we present a model for estimating entry and exit patterns, as well as the population size, using count data (CD), by employing a Polya Tree (PT) prior. In Chapter 4 we present several extensions of chapter 3. More specifically, we extend the model to CR and to ring-recovery data and develop a joint model for CR and CD. In addition, we consider the case when multiple data-sets are modelled at the same time, by defining a hierarchical extension of the PT, which we define as Hierarchical Logistic PT. Finally, we extend the model to the case of long time series, by borrowing ideas from the Optional PT. Chapter 5 presents a spatial model to estimate interactions between multiple species using CR data. The model uses a vector of interaction point process (IPP), which allows us to estimate interactions between and within species. The use of an IPP leads to an intractable ratio of normalising constants (RNC), and hence we use the Monte Carlo Metropolis Hastings algorithm to approximate the RNC with an importance sampling estimate. The supplementary material for each paper is presented in the appendix.