Hierarchical bayesian modeling with elicited prior information

Conditionally independent hierarchical models (CIHMs) have proven useful in problems where modest numbers of observations are made on a collection of k similar experimental units. In CIHMs, the observation vector Y i for the i-th unit has a distribution indexed by a unit-specific parameter vector θi,. The unit-specific parameter vectors are i.i.d. with distributions indexed by a common hyperparameter vector λ This paper presents a general methodology for subjective Bayesian inference in CIHMs. An analyst (e.g., a statistician) specifies a pre-elicitation prior distribution for the parameter vector ξ at the final stage of the hierarchy. “Data”, in the form of elicited probability statements, are then collected from a substantive expert and are used to obtain an estimate , yielding a fitted hyperprior for λ. This hyperprior can then be updated subsequent to observing the sample data in order to conduct Bayesian posterior inference about the first and second-stage parameter vectors and λ. The approach is ill...