  The problem of assigning probability distributions which objectively reflect
the prior information available about experiments is one of the major stumbling
blocks in the use of Bayesian methods of data analysis. In this paper the
method of Maximum (relative) Entropy (ME) is used to translate the information
contained in the known form of the likelihood into a prior distribution for
Bayesian inference. The argument is inspired and guided by intuition gained
from the successful use of ME methods in statistical mechanics. For experiments
that cannot be repeated the resulting "entropic prior" is formally identical
with the Einstein fluctuation formula. For repeatable experiments, however, the
expected value of the entropy of the likelihood turns out to be relevant
information that must be included in the analysis. The important case of a
Gaussian likelihood is treated in detail.
