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Robust Bayesian analysis of the binomial empirical Bayes problem
Author(s) -
Sivaganesan S.,
Berger James
Publication year - 1993
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315663
Subject(s) - bayes' theorem , moment (physics) , binomial distribution , statistics , mathematics , bayesian probability , range (aeronautics) , econometrics , binomial (polynomial) , interval (graph theory) , bayes estimator , combinatorics , physics , classical mechanics , materials science , composite material
Empirical Bayes estimation is considered for an i.i.d. sequence of binomial parameters θ i arising from an unknown prior distribution G (.). This problem typically arises in industrial sampling, where samples from lots are routinely used to estimate the lot fraction defective of each lot. Two related issues are explored. The first concerns the fact that only the first few moments of G are typically estimable from the data. This suggests consideration of the interval of estimates (e.g., posterior means) corresponding to the different possible G with the specified moments. Such intervals can be obtained by application of well‐known moment theory. The second development concerns the need to acknowledge the uncertainty in the estimation of the first few moments of G . Our proposal is to determine a credible set for the moments, and then find the range of estimates (e.g., posterior means) corresponding to the different possible G with moments in the credible set.