ABSTRACT
This chapter presents four applications of the Bayesian hierarchical modelling approach that tackle a range of substantive problems at the area level in the social and public health sciences. In the process we demonstrate how, within the Bayesian approach to inference, certain statistical challenges arising from the modelling of spatial data can be addressed. In the first application, the aim is to identify the covariates that explain why some areas of a city are classified as high intensity crime areas (HIAs) whilst others are not. In the second, the aim is to assess the relationship between exposure to nitrogen oxide and stroke mortality at the small area level. The third application is an analysis of small area counts of new cases of malaria in a small region of India. The fourth application aims to model the spatial variation, at the small area scale, in the reported cases of violent sexual assault in Stockholm. Each case study presents certain statistical challenges, which is the reason for their inclusion. These challenges include: handling missing data, dealing with incompatible spatial units, handling overdispersion and zero inflation when modelling small area count data, dealing with spatially autocorrelated missing covariates, allowing for spatial heterogeneity in model parameters and providing reliable small area estimates.
