Next Article in Journal
Optimal Multiuser Diversity in Multi-Cell MIMO Uplink Networks: User Scaling Law and Beamforming Design
Previous Article in Journal
On Entropy Test for Conditionally Heteroscedastic Location-Scale Time Series Models
Article Menu
Issue 8 (August) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(8), 391; https://doi.org/10.3390/e19080391

A Noninformative Prior on a Space of Distribution Functions

Applied Mathematics and Statistics, University of California, Santa Cruz, CA 95064, USA
*
Author to whom correspondence should be addressed.
Received: 20 June 2017 / Revised: 24 July 2017 / Accepted: 28 July 2017 / Published: 29 July 2017
(This article belongs to the Section Information Theory)
Full-Text   |   PDF [891 KB, uploaded 31 July 2017]

Abstract

In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information is available, the problem under study may possess an invariance under a transformation group that encodes a lack of information, leading to a unique prior—this idea was explored at length by E.T. Jaynes. Previous successful examples have included location-scale invariance under linear transformation, multiplicative invariance of the rate at which events in a counting process are observed, and the derivation of the Haldane prior for a Bernoulli success probability. In this paper we show that this method can be extended, by generalizing Jaynes, in two ways: (1) to yield families of approximately invariant priors; and (2) to the infinite-dimensional setting, yielding families of priors on spaces of distribution functions. Our results can be used to describe conditions under which a particular Dirichlet Process posterior arises from an optimal Bayesian analysis, in the sense that invariances in the prior and likelihood lead to one and only one posterior distribution. View Full-Text
Keywords: Bayesian nonparametrics; Dirichlet process; functional equations; Hyers–Ulam–Rassias stability; improper prior; invariance; optimal Bayesian analysis; transformation group Bayesian nonparametrics; Dirichlet process; functional equations; Hyers–Ulam–Rassias stability; improper prior; invariance; optimal Bayesian analysis; transformation group
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Terenin, A.; Draper, D. A Noninformative Prior on a Space of Distribution Functions. Entropy 2017, 19, 391.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top