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Celebrating StatisticsPapers in honour of Sir David Cox on his 80th birthday$
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A. C. Davison, Yadolah Dodge, and N. Wermuth

Print publication date: 2005

Print ISBN-13: 9780198566540

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198566540.001.0001

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Exchangeability and regression models

Exchangeability and regression models

(p.89) 4 Exchangeability and regression models
Celebrating Statistics

Peter McCullagh

Oxford University Press

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.

Keywords:   causality, covariates, estimation, homologous factor, interaction, interference, permutation of units, prediction, regression

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