Local exchangeability
Name
Download (1).pdf
Description
Published version
Size
255.34 KB
Format
Adobe PDF
Checksum (MD5)
6b8240069aa97f548dd993a4e23bf7c6
Author(s)
Campbell, Trevor
Syed, Saifuddin
Yang, Chiao-Yu
Jordan, Michael I
Broderick, Tamara
Date Issued
August 2023
Journal
Bernoulli
Publisher
Bernoulli Society for Mathematical Statistics and Probability
Citation
Trevor Campbell. Saifuddin Syed. Chiao-Yu Yang. Michael I. Jordan. Tamara Broderick. "Local exchangeability." Bernoulli 29 (3) 2084 - 2100, August 2023.
Version
Final published version
Abstract
Exchangeability—in which the distribution of an infinite sequence is invariant to reorderings of its elements—implies the existence of a simple conditional independence structure that may be leveraged in the design of statistical models and inference procedures. In this work, we study a relaxation of exchangeability in which this invariance need not hold precisely. We introduce the notion of local exchangeability—where swapping data associated with nearby covariates causes a bounded change in the distribution. We prove that locally exchangeable processes correspond to independent observations from an underlying measure-valued stochastic process. Using this main probabilistic result, we show that the local empirical measure of a finite collection of observations provides an approximation of the underlying measure-valued process and Bayesian posterior predictive distributions. The paper concludes with applications of the main theoretical results to a model from Bayesian nonparametrics and covariate-dependent permutation tests.
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3150/22-bej1533
