Date of Graduation

11-2025

Document Type

Thesis

Degree Name

Master of Science in Mathematics (MS)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor/Mentor

Chakraborty, Avishek

Committee Member

Zhang, Qingyang

Second Committee Member

Plummer, Sean

Keywords

Bayesian Statistics; Chronic Diseases; Gibbs Sampling; Hierarchical Model; Markov Chain Monte Carlo; Spatial Analysis

Abstract

Chronic non-communicable diseases (NCDs), particularly hypertension and diabetes, are growing public health concerns in low- and middle-income countries like Bangladesh. These diseases often co-occur and exhibit notable spatial heterogeneity influenced by socio-demographic and environmental factors. This thesis presents a Bayesian multivariate spatial probit modelling framework to jointly analyze the prevalence of hypertension and diabetes using data from the 2022 Bangladesh Demographic and Health Survey (BDHS). The study incorporates individual-level covariates—such as age, sex, BMI, education, and wealth index—and a spatially structured random effects model, which is modelled via intrinsic Conditional Autoregressive (ICAR) priors at the district level. Gibbs sampling is employed to estimate model parameters and latent spatial effects. Results reveal significant spatial clustering in disease risk and strong associations between chronic conditions and socio-demographic factors. The joint modelling approach enhances estimation efficiency and facilitates the identification of high-risk districts where public health interventions are likely to have the most significant impact. Model performance is evaluated using the Deviance Information Criterion (DIC), effective parameter count, and Moran’s I statistic to confirm spatial dependencies. This research provides an integrated statistical tool for understanding the co-distribution of chronic diseases and supports evidence-based policy planning in Bangladesh.

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