|
Activity Number:
|
292
- Nonparametric and High-Dimensional Bayes: Uncertainty Quantification, Computation, and Posterior Contraction
|
|
Type:
|
Invited
|
|
Date/Time:
|
Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
|
|
Sponsor:
|
IMS
|
|
Abstract #309393
|
|
|
Title:
|
Posterior Convergence Rate and Sharp Minimaxity for Sparse Sequences
|
|
Author(s):
|
Ismaël Castillo*
|
|
Companies:
|
Sorbonne University
|
|
Keywords:
|
Bayesian posterior distributions;
Sharp minimaxity;
Sparsity;
Spike-and-Slab;
Empirical Bayes
|
|
Abstract:
|
In the sparse normal means model, we consider the question of deriving a sharp minimax rate for Bayesian posterior distributions. We will first describe some possible ways in which a posterior distribution can attain the sharp constant in the optimal rate for the quadratic risk in this setting. Next, we will focus on a prior distribution constructed by (marginal maximal likelihood) empirical Bayes calibration of a class of preliminary fixed-sparsity spike-and-slab priors. We will discuss a number of sharp optimality results for the corresponding posterior distribution as well as extensions to hierarchical Bayes priors, and conclude with a brief discussion.
|
Authors who are presenting talks have a * after their name.
Back to the full JSM 2020 program
|
