Robust Empirical Bayes Analyses of Event Rates

A number, I, of nominally similar items generate events (e.g. failures) at possibly different rates, or mean time intervals. This paper addresses the problem of appropriately pooling the data from the different sources. The approach is parametric empirical Bayes: true individual item rates are assumed to come from a fixed superpopulation. It is shown how parameters of a superpopulation model can be estimated from all of the data, and combined with individual unit history, can provide improved estimates of individual rates. The procedure can be robust: evidence that a particular rate is far off from the main body of rates permits that outlier to stand by itself, i.e. to resist pooling. Illustrative analyses of data are supplied. Keywords: Robustness; Population(Mathematics); and Charts.