Progress towards ending AIDS as a public health threat by 2030 is not being made fast enough. Effective public health response requires accurate, timely, high-resolution estimates of epidemic and demographic indicators. Limitations of available data and statistical methodology make obtaining these estimates difficult.
I developed and applied Bayesian spatio-temporal methods to meet this challenge. First, I used scoring rules to compare models for area-level spatial structure with both simulated and real data. Second, I estimated district-level HIV risk group proportions, enabling behavioural prioritisation of prevention services, as put forward in the UNAIDS Global AIDS Strategy. Third, I developed a novel deterministic Bayesian inference method, combining adaptive Gauss-Hermite quadrature with principal component analysis, motivated by the Naomi district-level model of HIV indicators. In developing this method, I implemented integrated nested Laplace approximations using automatic differentiation, enabling use of this algorithm for a wider class of models. Together, the contributions in this thesis help to guide precision HIV policy in sub-Saharan Africa, as well as advancing Bayesian methods for spatio-temporal data.