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Optional Pólya tree and Bayesian inference. (English) Zbl 1189.62048

Summary: We introduce an extension of the Pólya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data. The resulting “optional Pólya tree” distribution has large support in total variation topology and yields posterior distributions that are also optional Pólya trees with computable parameter values.

MSC:

62F15 Bayesian inference
62G99 Nonparametric inference
60G57 Random measures
62G07 Density estimation
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