Comparing normal random samples,
with uncertainty about the priors and utilities
N.T. Longford
Abstract
We study the problem of deciding which of two normal random samples,
at least one of them of small size, has greater expected value.
Unlike in the standard Bayesian approach,
in which a single prior distribution and a single loss function are declared,
we assume that a set of plausible priors and a set of plausible loss functions
are elicited from the expert (the client or the sponsor of the analysis).
The choice of the sample that has greater expected value
is based on equilibrium priors, allowing for an impasse
if for some plausible priors and loss functions choosing one
and for others the other sample is associated with smaller expected loss.
To appear in Scandinavian Journal of Statistics
March 2011