Professor Daniel Yekutieli

Department of Statistics and Operations Research

School of Mathematical Sciences (Schreiber #207)

Tel Aviv University

Title: Distribution-Free Bayesian multivariate predictive inference

Abstract: I will introduce a Bayesian multivariate predictive inference framework. The basis for this framework is a hierarchical Bayesian model, that is a mixture of finite Polya trees corresponding to multiple dyadic partitions of the unit cube. Given a sample of observations from an unknown multivariate distribution, the posterior predictive distribution is used to model and generate future observations from the unknown distribution.

The modeling approach is distribution free; it may be applied to categorical and continuous variables with missing values and doesn’t distinguish between explanatory and dependent variables. Thus, it may be used to evaluate the joint, marginal, and conditional distribution of any subset of variables given any other subset of variables. We implement conformal prediction algorithms to construct prediction sets that provide exact nominal conditional coverage probability for the outcome variables for given values of the explanatory variables.

I will illustrate use of the methodology on several simulated examples, for estimating average treatment effect in an observational study and for performing a binary expansion test for independence.

The talks will be both in-person at Chapman Hall 435 and on Zoom: https://unc.zoom.us/j/96417451559.