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.
|Citazione:||Camerlenghi, F., Lijoi, A., & Pruenster, I. (2015). Nonparametric hierarchical models based on completely random measures. In CFE-CMStatistics 2015 Book of Abstracts.|
|Carattere della pubblicazione:||Scientifica|
|Presenza di un coautore afferente ad Istituzioni straniere:||No|
|Titolo:||Nonparametric hierarchical models based on completely random measures|
|Autori:||Camerlenghi, F; Lijoi, A; Pruenster, I|
|Data di pubblicazione:||2015|
|Nome del convegno:||8th International Conference of the ERCIM|
|Appare nelle tipologie:||02 - Intervento a convegno|