Abstract:
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Random partition models, such as the Chinese restaurant process, allow a Bayesian model to flexibly borrow strength. While many partition priors are exchangeable, we propose a nonexchangeable prior based on a focal partition, a Bayesian's prior guess for the unknown partition. We show how our approach modifies the Chinese restaurant process so that certain partitions, similar to the focal partition, have higher probability. This distribution has a vector of weight parameters that vary between zero and infinity, where a vector of zeros correspond to the original Chinese restaurant process and a vector of infinity yields a point mass distribution at the focal partition. Our approach is similar to other recent works, however, in contrast, we have a tractable normalizing constant and can individually weight sets in the focal partition to one’s prior belief. These features allow for a straightforward computational approach implemented in an R library. We demonstrate the capability of our approach in an application.
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