A very active line of research in Bayesian statistics has aimed at defining and investigating general classes of nonparametric priors. A notable example, which includes the Dirichlet process, is obtained through normalization or transformation of completely random measures. These have been extensively studied for the exchangeable setting. However in a large variety of applied problems data are heterogeneous, being generated by different, though related, experiments; in such situations partial exchangeability is a more appropriate assumption. In this spirit we propose a nonparametric hierarchical model based on transformations of completely random measures, which extends the hierarchical Dirichlet process. The model allows us to handle related groups of observations, creating a borrowing of strength between them. From the theoretical viewpoint, we analyze the induced partition structure, which plays a pivotal role in a very large number of inferential problems. The resulting partition probability function has a feasible expression, suitable to address predictionin its generality, as suggested by de Finetti. Finally we propose a set of applications which include inference on genomic and survival data.

Camerlenghi, F., Lijoi, A., Pruenster, I. (2015). Nonparametric hierarchical models based on completely random measures. In CFE-CMStatistics 2015 Book of Abstracts.

Nonparametric hierarchical models based on completely random measures

Camerlenghi F;
2015

Abstract

A very active line of research in Bayesian statistics has aimed at defining and investigating general classes of nonparametric priors. A notable example, which includes the Dirichlet process, is obtained through normalization or transformation of completely random measures. These have been extensively studied for the exchangeable setting. However in a large variety of applied problems data are heterogeneous, being generated by different, though related, experiments; in such situations partial exchangeability is a more appropriate assumption. In this spirit we propose a nonparametric hierarchical model based on transformations of completely random measures, which extends the hierarchical Dirichlet process. The model allows us to handle related groups of observations, creating a borrowing of strength between them. From the theoretical viewpoint, we analyze the induced partition structure, which plays a pivotal role in a very large number of inferential problems. The resulting partition probability function has a feasible expression, suitable to address predictionin its generality, as suggested by de Finetti. Finally we propose a set of applications which include inference on genomic and survival data.
No
abstract
Bayesian nonparametrics
English
8th International Conference of the ERCIM
9789963222704
Camerlenghi, F., Lijoi, A., Pruenster, I. (2015). Nonparametric hierarchical models based on completely random measures. In CFE-CMStatistics 2015 Book of Abstracts.
Camerlenghi, F; Lijoi, A; Pruenster, I
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/184902
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