Summary
A process is said to be exchangeable if each finite-dimensional distribution is symmetric, or invariant under coordinate permutation. The definition suggests that exchangeability can have no role in statistical models for dependence, in which the units are overtly nonexchangeable on account of diffe...
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| Format: | Text |
| Language: | English |
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2004
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| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.3948 http://galton.uchicago.edu/techreports/tr544.pdf |
| Summary: | A process is said to be exchangeable if each finite-dimensional distribution is symmetric, or invariant under coordinate permutation. The definition suggests that exchangeability can have no role in statistical models for dependence, in which the units are overtly nonexchangeable on account of differences in covariate values. The theme of this paper is that this narrow view is mistaken for two reasons. First, every regression model is a set of processes in which the distributions are indexed by the finite restrictions of the covariate, and regression exchangeability is defined naturally with this in mind. Second, regression exchangeability has a number of fundamental implications connected with lack of interference (Cox, 1958a) and absence of unmeasured covariates (Greenland, Robins and Pearl 1999). This paper explores the role of exchangeability in a range of regression models, including generalized linear models, biased-sampling models (Vardi, 1985), block factors and random-effects models, models for spatial dependence, and growth-curve models. The fundamental distinction between parameter estimation and sample-space prediction is a recurring theme. Key words: block factor; classification factor; causal model; counterfactual; crossover design; empirical Bayes; exchangeable prior process; factorial model; interaction; interference; likelihood principle; penalized likelihood; prediction; random-effects model; smoothing spline; 1 |
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