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Inferential models: A framework for prior-free posterior probabilistic inference
journal contribution
posted on 2014-08-20, 00:00 authored by Ryan Martin, Chuanhai LiuPosterior probabilistic statistical inference without priors is an important but so
far elusive goal. Fisher's ducial inference, Dempster{Shafer theory of belief func-
tions, and Bayesian inference with default priors are attempts to achieve this goal
but, to date, none has given a completely satisfactory picture. This paper presents a
new framework for probabilistic inference, based on inferential models (IMs), which
not only provides data-dependent probabilistic measures of uncertainty about the
unknown parameter, but does so with an automatic long-run frequency calibration
property. The key to this new approach is the identi cation of an unobservable
auxiliary variable associated with observable data and unknown parameter, and the
prediction of this auxiliary variable with a random set before conditioning on data.
Here we present a three-step IM construction, and prove a frequency-calibration
property of the IM's belief function under mild conditions. A corresponding opti-
mality theory is developed, which helps to resolve the non-uniqueness issue. Several
examples are presented to illustrate this new approach.
Funding
This work is partially supported by the U.S. National Science Foundation, grants DMS-1007678, DMS-1208841, and DMS-1208833.
History
Publisher Statement
Post print version of article may differ from published version. This is an electronic version of an article published in Journal of the American Statistical Association. Journal of the American Statistical Association is available online at: http://www.informaworld.com/smpp/ DOI: 10.1080/01621459.2012.747960Publisher
Taylor & FrancisLanguage
- en_US
issn
0162-1459Issue date
2013-03-01Usage metrics
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