Introduction to Bayesian Nonparametric Methods for Missing Data

Bayesian nonparametrics is a powerful approach for missing data. This course will provide an overview of flexible Bayesian nonparametric (BNP) methods for modeling joint or conditional distributions and functional relationships, and their interplay with missing data. We will emphasize the importance of making untestable assumptions to identify estimands of interest, such as missing at random assumptions. Unlike parametric methods, the BNP approach can account for possible violations of assumptions and minimize concerns about model misspecification. The overall strategy is to first specify BNP models for observed data and then to specify uncheckable assumptions to identify estimands of interest. The course is divided into three main parts. Part I develops the key concepts in missing data (including identifiability and sensitivity parameters) and reviews relevant concepts in Bayesian inference. Part II introduces the fundamental BNP tools required to address missing data problems. Part III shows how the BNP approach can be applied in a variety of case studies. The datasets in the case studies come from electronic health records (EHR) data and randomized clinical trials. The R code and/or packages used to run the data examples will be provided to the attendees at a specific github site. The course will be based on half of the recently published book, Daniels, Linero, and Roy (2023) Bayesian nonparametric approaches for causal inference and missing data. Chapman & Hall/CRC Press.