Bayesian Hierarchical Mixture Models
When massive streams of data are collected, it is usually the case that different information sources contribute to different levels of knowledge, or inferences about subgroups may suffer from small or inadequate sample size. In these cases, Bayesian hierarchical models have been proven to be valuable, or even necessary, modelling tools that provide the required multi-level modelling structure to deal with the statistical inferential procedure. We investigate the need to generalize the inherent assumption of exchangeability which routinely accompanies these models. By modelling the second-stage parameters of a Bayesian hierarchical model as a finite mixture of normals with unknown number of components, we allow for parameter partitions so that exchangeability is assumed within each partition. This more general model formulation allows better understanding of the data generating mechanism and provides better parameter estimates and forecasts. We discuss choices of prior densities and MCMC implementation in problems in actuarial science, finance and genetics.
KeywordsFinite Mixture Dirichlet Process Bayesian Hierarchical Model Prior Density Prior Specification
The authors acknowledge financial support from the Royal Society (International Exchanges grant IE110977). The second author acknowledges financial support from the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) through the research funding program ARISTEIA-LIKEJUMPS.
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