Seminar Details

Seminar Details

Monday

May 6

3:30 pm

## Hierarchical Partition Models

### Guido Consonni

Seminar

University of Pavia - Departments of Economics & Quantitative Methods

Consider I "experiments" for which the object of investigation is regarded to be broadly similar (e.g. survival rate of patients treated with the same drug in I distinct studies/hospitals; monthly sales of a specific product in I branches of the same company; educational performance of students in I schools or districts). Often the sample size in each experiment is too small to obtain separate reliable estimates of parameters or predictions. As a consequence, some degree of {\em borrowing strength} among experiments seems mandatory. However the traditional exchangeability assumption of experiment-specific parameters is often not satisfactory because of heterogeneity between studies. When relevant covariates are available, one may try to adjust for these. Sometimes, however, a less structured, and perhaps more exploratory, approach is called for.

Hierarchical partition models provide such an exploratory approach for these problems. They postulate that first-stage-parameters are only partially exchangeable; however the very nature of their aggregation is itself modelled, in order to let the data suggest which {\em partition} of the experiments is more likely to represent the underlying structure. The output of the analysis is twofold: a parameter estimate, or prediction, for each experiment (or subsets of experiments), together with a posterior distribution on the collection of all entertained partitions. The latter, which may be regarded as a form of Bayesian cluster analysis, can be subsequently employed to average the former, according to the Bayesian Model Averaging paradigm.

The talk will describe the general methodology in the setting of binomial experiments, with special emphasis on ongoing research aimed at applying MCMC methods in the space of partitions.