Formal Rules for Selecting Prior Distributions:
A Review and Annotated Bibliography
Robert E. Kass
and Larry Wasserman
has become the dominant philosophical
foundation for Bayesian inference. Yet,
in practice, most Bayesian analyses are performed
with so-called ``noninformative'' priors,
that is, priors constructed
by some formal rule.
We review the plethora of techniques for
constructing such priors, and
discuss some of the practical and philosophical
issues that arise when they are used.
We give special emphasis to Jeffreys's rules and discuss the
evolution of his point of view about the interpretation of priors,
unique representation of
toward the notion that they should be
chosen by convention. We conclude that the problems raised by the
research on priors chosen by formal rules are serious and may not be
dismissed lightly; when sample sizes are small
(relative to the number of parameters being estimated) it is dangerous
to put faith in any ``default'' solution;
but when asymptotics take over, Jeffreys's rules and
their variants remain reasonable choices.
We also provide
an annotated bibliography.
Key words and phrases:
Entropy, Fisher information,
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