Electronic Journal of Statistics

A novel approach to Bayesian consistency

Minwoo Chae and Stephen G. Walker

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It is well-known that the Kullback–Leibler support condition implies posterior consistency in the weak topology, but is not sufficient for consistency in the total variation distance. There is a counter–example. Since then many authors have proposed sufficient conditions for strong consistency; and the aim of the present paper is to introduce new conditions with specific application to nonparametric mixture models with heavy–tailed components, such as the Student-$t$. The key is a more focused result on sets of densities where if strong consistency fails then it fails on such densities. This allows us to move away from the traditional types of sieves currently employed.

Article information

Electron. J. Statist., Volume 11, Number 2 (2017), 4723-4745.

Received: May 2017
First available in Project Euclid: 24 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62G07: Density estimation

Kullback–Leibler divergence Lévy–Prokhorov metric mixture of Student’s $t$ distributions posterior consistency total variation

Creative Commons Attribution 4.0 International License.


Chae, Minwoo; Walker, Stephen G. A novel approach to Bayesian consistency. Electron. J. Statist. 11 (2017), no. 2, 4723--4745. doi:10.1214/17-EJS1369. https://projecteuclid.org/euclid.ejs/1511492460

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