Robust Empirical Bayes Analyses of Event Rates
Loading...
Authors
Gaver, Donald P.
O'Muircheartaigh, I.G.
Subjects
Reliability
Poisson process
Robustness
Empirical Bayes
Poisson process
Robustness
Empirical Bayes
Advisors
Date of Issue
1987-02
Date
Publisher
American Statistical Association and the American Society for Quality Control
Language
Abstract
A collection of I similar items generates point event histories; for example, machines experience failures or operators make mistakes. Suppose the intervals between events are modeled as iid exponential (λi , or the counts as Poisson (λ i t i ,) for the ith item. Furthermore, so as to represent between-item variability, each individual rate parameter, λ i , is presumed drawn from a fixed (super) population with density g λ (·; θ), θ being a vector parameter: a parametric empirical Bayes (PEB) setup. For g λ, specified alternatively as log-Student t(n) or gamma, we exhibit the results of numerical procedures for estimating superpopulation parameters ll and for describing pooled estimates of the individual rates, λ i , obtained via Bayes's formula. Three data sets are analyzed, and convenient explicit approximate formulas are furnished for λ iestimates. In the Student-t case, the individual estimates are seen to have a robust quality.
Type
Article
Description
The article of record as published may be found at https://doi.org/10.1080/00401706.1987.10488178
Series/Report No
Department
Operations Research (OR)
Organization
Identifiers
NPS Report Number
Sponsors
Office of Naval Research
Nuclear Safety and Analysis Department of the Electric Power Research Institute (EPRI)
Nuclear Safety and Analysis Department of the Electric Power Research Institute (EPRI)
Funder
Format
15 p.
Citation
Gaver, D. P., & O'Muircheartaigh, I. G. (1987). Robust empirical Bayes analyses of event rates. Technometrics, 29(1), 1-15.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.