Bayesian decision making about small binomial rates
with uncertainty about prior
N.T. Longford
Abstract
We address the problem of deciding between two actions
related to the rate of faults in a process of manufacturing
many identical items.
The faults occur independently of each other and are rare,
so that the binomial distribution of their count in a given period
is well approximated by a Poisson.
We use prior information in the form of a set of so-called
plausible prior distributions
to reflect the difficulties and uncertainty inherent in the process
of capturing the expert's knowledge and opinions
in a format amenable to a Bayesian analysis.
Our analysis also incorporates an elicited set of plausible loss functions.
The American Statistician, 64, 164-169, 2010
June 2010.