Open Access
Translator Disclaimer
2017 A novel approach to Bayesian consistency
Minwoo Chae, Stephen G. Walker
Electron. J. Statist. 11(2): 4723-4745 (2017). DOI: 10.1214/17-EJS1369


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.


Download Citation

Minwoo Chae. Stephen G. Walker. "A novel approach to Bayesian consistency." Electron. J. Statist. 11 (2) 4723 - 4745, 2017.


Received: 1 May 2017; Published: 2017
First available in Project Euclid: 24 November 2017

zbMATH: 06816631
MathSciNet: MR3729657
Digital Object Identifier: 10.1214/17-EJS1369

Primary: 62G05 , 62G20
Secondary: 62G07

Keywords: Kullback–Leibler divergence , Lévy–Prokhorov metric , mixture of Student’s $t$ distributions , posterior consistency , Total variation


Vol.11 • No. 2 • 2017
Back to Top