Exchangeability and regression models

Abstract

This chapter explores the relation between exchangeability, a concept from stochastic processes, and regression models in which the observed process is modulated by a covariate. A stochastic process is a collection of random variables, usually an infinite set, though not necessarily an ordered sequence. A process is said to be exchangeable if each finite-dimensional distribution is symmetric, or invariant under coordinate permutation. Regression models are statistical models for dependence, specifying the way in which a response variable depends on known explanatory variables or factors. The role of exchangeability is explored in a range of regression models, including generalized linear models, biased-sampling models, block factors and random-effects models, models for spatial dependence, and growth-curve models. Causal inference, counterfactuals, and its relation to exchangeability are discussed.