Translator Disclaimer
2019 Data-driven priors and their posterior concentration rates
Ryan Martin, Stephen G. Walker
Electron. J. Statist. 13(2): 3049-3081 (2019). DOI: 10.1214/19-EJS1600

Abstract

In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a prior? In this paper, we develop a general strategy for constructing a data-driven or empirical prior and sufficient conditions for the corresponding posterior distribution to achieve a certain concentration rate. The idea is that the prior should put sufficient mass on parameter values for which the likelihood is large. An interesting byproduct of this data-driven centering is that the asymptotic properties of the posterior are less sensitive to the prior shape which, in turn, allows users to work with priors of computationally convenient forms while maintaining the desired rates. General results on both adaptive and non-adaptive rates based on empirical priors are presented, along with illustrations in density estimation, nonparametric regression, and high-dimensional normal models.

Citation

Download Citation

Ryan Martin. Stephen G. Walker. "Data-driven priors and their posterior concentration rates." Electron. J. Statist. 13 (2) 3049 - 3081, 2019. https://doi.org/10.1214/19-EJS1600

Information

Received: 1 June 2018; Published: 2019
First available in Project Euclid: 20 September 2019

zbMATH: 07113711
MathSciNet: MR4010592
Digital Object Identifier: 10.1214/19-EJS1600

Subjects:
Primary: 62C12, 62E20
Secondary: 62G07, 62G08

JOURNAL ARTICLE
33 PAGES


SHARE
Vol.13 • No. 2 • 2019
Back to Top