University of Washington - Department of Statistics
For generalized HIV epidemics, where the prevalence among pregnant women is consistently over 1%, the Bayesian melding has been used as the basis for the probabilistic HIV prevalence projections by UNAIDS and WHO. It combines expert opinion, past trends in inputs and outputs, and provides a framework for assessing uncertainty in mechanistic models in general. I will present an Incremental Mixture Importance Sampling (IMIS) algorithm which improves the sampling efficiency of the Bayesian melding while retaining its essential simplicity and transparency. It gives a good picture of the uncertainty when the posterior distribution tends to be multimodal and to feature nonlinear sharp ridges. It also leads to a simple estimator of the integrated likelihood that is the basis for Bayesian model comparison and model averaging.
For low-level and concentrated HIV epidemics, where transmission is not sustained out-side at-risk populations, it is more important to estimate the size of populations that are most likely to acquire and transmit HIV. We develop a Bayesian hierarchical model for developing local and national size estimates of HIV at-risk populations and assessing the uncertainty of the estimates. It incorporates multiple commonly used data sources including mapping data, survey, intervention, capture-recapture and estimate/guestimate from other organizations; and has the potential exibility of dealing with missing data, allowing the heterogeneous distributions of at-risk population across districts and combining the uncertainty of the size estimation with the uncertainty of HIV prevalence. The basic model has been applied to the size estimation of injecting drug users and female sex workers in Bangladesh.