Bayesian Elicitation Diagnostics

An elicitation diagnostic forms a question that compares the information in the prior
distribution with the information in the given sample. One elicitation diagnostic identifies
a family of prior distributions that are so diffuse that they are practically equivalent to the
"completely" diffuse prior. Another elicitation diagnostic identifies a family of prior
distributions that concentrate enough mass in the neighborhood of zero that they are
practically equivalent to the dogmatic prior which sets a parameter exactly equal to zero.
The question that is asked is whether the subject's prior distribution falls in either of
these two classes. If an affirmative answer can be given to either of these two elicitation
questions then there is no need to go to the expense of a more accurate elicitation of the
prior distribution.
KEYWORDSR:egression diagnostics, Bayesian regression, prior elicitation.
1. INTRODUCTION
MOSTREAL ECONOMETRIC ESTIMATES are built implicitly on approximate prior
distributions. For example, a common method of estimating a linear regression
is to omit variables that have t values less than some critical level. When a
variable is omitted, the regression coefficient is treated as if it were certainly
zero, but this is clearly only an approximation since, if this opinion were actually
entertained, the variable would have been omitted in the first place, and no
pretesting would have occurred.
Though the prior distribution implicit in most estimates is only approximate,
the adequacy of the approximation is never formally stated. Specifically, no
answer is given to the question: How concentrated must the prior distribution
be in order to act as if it were dogmatically concentrated? An elicitation
diagnostic answers this question.