Awhile ago I was invited by Keying Ye to contribute to a book of essays, Frontier of Statistical Decision Making and Bayesian Analysis, in honor of the great Jim Berger. Here’s my chapter, which begins:

Jim Berger has made important contributions in many areas of Bayesian statistics, most notably on the topics of statistical decision theory and prior distributions. It is the latter subject which I shall discuss here. I will focus on they applied work of my collaborators and myself, not out of any claim for its special importance but because these are the examples with which I am most familiar. A discussion of the role of the prior distribution in several applied examples will perhaps be more interesting than the alternative of surveying the gradual progress of Bayesian inference in political science (or any other specific applied field).

I will go through four examples that illustrate different sorts of prior distributions as well as my own progress–in parallel with the rest of the statistical research community–in developing tools for including prior information in statistical analyses . . .