MIT Media Lab note (1998; revised 11/19/2001)

By rejecting the use of a prior distribution over parameters, orthodox
statistics is forced to focus on *estimators*, functions which guess
parameter values, and to invent heuristics for choosing among estimators.
Two popular heuristics are *unbiasedness* and *maximum
likelihood*. Since these heuristics are not consistent with Bayes'
rule, they are also not consistent with the axioms of common sense from
which Bayes' rule is derived. Hence we expect there to be situations in
which they violate common sense and indeed it is not hard to find such
situations. This paper reviews a few simple, realistic scenarios where
pathologies occur with either the unbiasedness heuristic or the maximum
likelihood heuristic.

Last modified: Fri Dec 10 14:30:08 GMT 2004