A Bayesian semi-parametric approach to small area estimation and forecasting: with application to estimating and forecasting mortality rates by country, age and sex.


Bayesian methods (1)

John Bryant (Statistics New Zealand)
Feifei Wang (Peking University)
Junni L. Zhang (Peking University) (Speaker)

Researchers and policymakers are often interested in estimating and forecasting rates cross-classified by several dimensions. We consider the case of simultaneously estimating and forecasting mortality rates, cross-classified by age, sex and country, for 40 countries in the Human Mortality Database. These rates have complicated interactions. For instance, age-sex profiles differ across countries, and are changing over time. Estimating and forecasting these interactions is challenging, particular when cell counts are small, as they are in some countries. We present a Bayesian semi-parametric approach to estimating and forecasting disaggregated rates. We model the area-level rates using a hierarchical ANOVA-type structure, with specialized priors for main effects and interactions. Priors for main effects and simple interactions are parametric, and weakly informative. For example, dynamic linear models with informative priors on year-to-year variability are used for time effects, and exchangeable priors are used for simple interactions. Priors for complicated interactions are non-parametric, and are based on Dirichlet process mixtures of tensor factorizations, with mixture probabilities varying over time. The mixture priors can represent complex interactions parsimoniously, and are suitable for forecasting. We demonstrate that the resulting estimates and forecasts have features of substantive interest that cannot be captured by previous approaches such as the Lee-Carter models and functional demographic models.