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We argue for the use of separate exchangeability as a modeling principle inBayesian inference, especially for nonparametric Bayesian models. While in someareas, such as random graphs, separate and (closely related) jointexchangeability are widely used, and it naturally arises for example in simplemixed models, it is curiously underused for other applications. We brieflyreview the definition of separate exchangeability. We then discuss two specificmodels that implement separate exchangeability. One example is about nestedrandom partitions for a data matrix, defining a partition of columns and nestedpartitions of rows, nested within column clusters. Many recently proposedmodels for nested partitions implement partially exchangeable models. We arguethat inference under such models in some cases ignores important features ofthe experimental setup. The second example is about setting up separatelyexchangeable priors for a nonparametric regression model when multiple sets ofexperimental units are involved.

Separate Exchangeability as Modeling Principle in Bayesian Nonparametrics