Abstract
Functionals of random probability measures are probabilistic objects whose properties are studied in different fields. They also play an important role in Bayesian Nonparametrics: understanding the behavior of a finite dimensional feature of a flexible and infinite-dimensional prior is crucial for prior elicitation. In particular distributions of means of nonparametric priors have been the object of thorough investigation in the literature. We target the inverse path: the determination of the parameter measure of a random probability measure giving rise to a fixed mean distribution. This direction yields a better understanding of the sets of mean distributions of notable nonparametric priors, giving moreover a way to directly enforce prior information, without losing inferential power. Here we summarize and report results obtained in [6] for the Dirichlet process, the normalized stable random measure and the Pitman–Yor process, with an application to mixture models.
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The authors are grateful to the Editor and two anonymous Referees for their insightful comments and suggestions.
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Gaffi, F., Lijoi, A., Prünster, I. (2022). Specification of the Base Measure of Nonparametric Priors via Random Means. In: Argiento, R., Camerlenghi, F., Paganin, S. (eds) New Frontiers in Bayesian Statistics. BAYSM 2021. Springer Proceedings in Mathematics & Statistics, vol 405. Springer, Cham. https://doi.org/10.1007/978-3-031-16427-9_9
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