Hierarchical Model for Species Abundance Using Efficient Dimension Reduction for Lattice Data

• Activity Number: 71 - Environmental Applications of Bayesian Methods
• Type: Contributed
• Date/Time: Sunday, July 30, 2017 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ghadeer Mahdi* and Avishek Chakraborty and Mark Arnold
• Companies: University of Arkansas and University of Arkansas and University of Arkansas
• Keywords: Areal spatial data ; Conditional Autoregressive Prior ; Graph Laplacian ; Reversible Jump MCMC ; Species Abundance ; Spectral Decomposition

Abstract

Stochastic models for analyzing species abundance patterns are gaining importance because of their multiple utilities. The Cape Floristic Region in South Africa provides a rich class of such species data for analysis. The entire region is mapped into around 37,000 grid cells and measurements on climate and soil characteristics are available at each of them. However, data on species prevalence is sparse due to poor sampling coverage. Implementation of a hierarchical spatial model on the entire region for predictive purpose would be challenging. The conditional autoregressive (CAR) prior, specifically suited for this kind of datasets, requires sequential updating, is computationally inefficient and suffers from poor mixing. We propose an alternative approach using the spectral properties of the adjacency matrix. We use an adaptive, truncated basis function expansion to approximate the spatial effect. We show that the commonly used CAR prior is a special case of the proposed model. We also take into account the non-availability of plant habitat due to land transformation. Post-estimation, we present maps and tables to summarize the abundance distribution.