Open Access
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


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.


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Ryan Martin. Stephen G. Walker. "Data-driven priors and their posterior concentration rates." Electron. J. Statist. 13 (2) 3049 - 3081, 2019.


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

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

Keywords: Adaptation , data-dependent prior , Density estimation , Empirical Bayes , Nonparametric regression

Vol.13 • No. 2 • 2019
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