
Chapter 4
Inferential Models
Portions of the material in this chapter are from R. Martin and C. Liu, “Inferential
models: A framework for prior-free posterior probabilistic inference,” Journal of the
American Statistical Association 108, 301–313, 2013, reprinted by permission of the
American Statistical Association, www.amstat.org.
4.1 Introduction
Posterior probabilistic statistical inference without priors is an important but so far
elusive goal. Fisher’s fiducial inference, the Dempster–Shafer theory of belief func-
tions, and Bayesian inference with default priors are attempts to achieve this goal but,
as we explained in Chapter 2, so far none has ...