Date of Graduation

7-2026

Document Type

Thesis

Degree Name

Master of Science in Statistics and Analytics (MS)

Degree Level

Graduate

Department

Statistics and Analytics

Advisor/Mentor

Chakraborty, Avishek

Committee Member

Zhang, Qingyang

Second Committee Member

Majumder, Reetam

Keywords

binary regression, South Africa, spatial regression models, plant abundance data, bivariate binary, univariate binary

Abstract

Analyzing species distributions is of prime interest in ecological research. Prevalence of a species usually depends on several environmental and topographic features not all of which can be quantified or measured. Spatial random effects play an important role as a surrogate for missing features that can explain similarity in species prevalence patterns between neighboring locations. In this thesis, we focus on a dataset on abundance of plants in the southern part of South Africa. First, we build a hierarchical Bayesian model for binary regression, using the probit link, on presence/ absence of a species based on available covariates. Since the covariate values are available at an areal scale, we assume the probabilities do not change within an areal unit. Next, we introduce random effects one per areal unit, in the regression equation. The proximity between areal units is quantified using a binary adjacency matrix and the intrinsic conditionally autoregressive prior distribution is used to represent spatial dependence between random effects from neighboring units. Finally, we demonstrate how the univariate regression equations for two different plants can be merged in a bivariate framework that allows for inter-species correlation. Markov chain Monte Carlo algorithms are described for parameter estimation and inference. Since many areal units lacked sampling coverage, posterior samples are used to predict the probability of presence/ absence throughout the region. Multiple diagnostic tools are used to assess the effects of covariates, spatial random effects, and the correlation parameter. Our analysis reveals significant improvement in model fit due to addition of spatial random effects and a modest positive interspecies correlation. This thesis is organized as follows. In Chapter 1, we provide overview of the purpose and utility of spatial models and Bayesian inference. Chapter 2 describes the univariate and bivariate hierarchical models for presence/absence including the posterior sampling distributions and model assessment tools. Chapter 3 describes the plant abundance datasets, implements the proposed models and presents the numerical and graphical outputs of the analysis. In Chapter 4, we discuss possible directions of future research with this dataset.

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