Jayanta K. Ghosh Memorial Session on Model Uncertainty
Organizer and Chair: James O. Berger, The Arts and Sciences Professor of Statistics, Department of Statistical Science, Duke University
Speakers
- Malgorzata Bogdan, Professory, Institute of Mathematics, Wroclaw University of Science and Technology
- Bertrand Clarke, Department Chair and Professor, Department of Statistics, University of Nebraska-Lincoln
- Malay Ghosh, Distinguished Professor, Department of Statistics, University of Florida
Friday, June 8, 10:00 a.m.-12:00 p.m. in STEW 214 AB
| Time | Speaker | Title |
|---|---|---|
| 10:00-10:40 a.m. | Malgorzata Bogdan | Model selection and multiple testing - a journey with Jayanta K. Ghosh |
| Abstract: I will talk about an exciting journey through the issues of model selection and multiple testing, which I took under an overly patient and gentle guidance of Jayanta. This journey is marked by the joint papers on the modified versions of Bayesian Information Criterion and the Benjamini-Hochberg correction for multiple testing, published e.g. in Genetics and Annals of Statistics, and its continuation with other colleagues lead to the development of the Sorted L-One Penalized Estimator and its adaptive version based on Bayesian ideas. | ||
| 10:40-11:20 a.m. | Bertrand Clarke | Estimating the VC dimension with applications to model selection |
|
Abstract: We derive an objective function that can be optimized to give an estimator of the Vapnik-Chervonenkis dimension for model selection in regression problems. We verify our estimator is consistent. Then, we verify it performs well compared to several other model selection techniques. We do this for simulated data, two benchmark data sets, and data from a designed agronomic experiment. |
||
| 11:20 a.m.-12:00 p.m. | Malay Ghosh | Bayesian multiple testing under sparsity |
|
Abstract: This talk reviews certain Bayesian procedures that have recently been proposed to address multiple testing under sparsity. Consider the problem of simultaneous testing for the means of independent normal observations. In this talk we study asymptotic optimality properties of certain multiple testing rules in a Bayesian decision theoretic framework, where the overall loss of a multiple testing rule is taken as the number of misclassi ed hypotheses. The multiple testing rules that are considered, include spike and slab priors as well as a general class of one- group shrinkage priors for the mean parameters. The latter is rich enough to include, among others, the families of three parameter beta, generalized double Pareto priors, and in particular the horseshoe, the normal-exponential-gamma and the Strawderman-Berger priors. Within the chosen asymptotic framework, the multiple testing rules under study asymptotically attain the risk of the Bayes Oracle. Some classical multiple testing procedures are also evaluated within the proposed Bayesian framework. |
||