Hierarchical bayesian modeling with elicited prior information
Title:
Hierarchical bayesian modeling with elicited prior information
Author:
Steffey, Duane
Appeared in:
Communications in statistics
Paging:
Volume 21 (1992) nr. 3 pages 799-821
Year:
1992
Contents:
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 Yi 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 [image omitted] , yielding a fitted hyperprior [image omitted] for λ. This hyperprior can then be updated subsequent to observing the sample data [image omitted] in order to conduct Bayesian posterior inference about the first and second-stage parameter vectors [image omitted] and λ. The approach is illustrated with a CIHM for binomial observations applied to baseball data that were originally analyzed by Efron and Morris (1975) and Morris (1983) using parametric empirical Bayes (PEB) methods. Here, prior probability statements are elicted from a baseball expert, and a fully Bayesian analysis is conducted for the first-stage parameter, yielding approximate posterior probability intervals. These intervals are found to be substantially shorter than the corresponding PEB intervals, yet retain the stated probability of coverage.
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