Title: In nonparametric and high-dimensional models, ignorability is an informative prior
Authors: Antonio Linero - University of Texas at Austin (United States) [presenting]
Abstract: In problems with substantial missing data one in general must model two distinct data generating processes: the outcome process which generates the outcome and the missing data mechanism which determines the outcomes that we observe. Under the ignorability assumption, however, likelihood-based inference for the outcome process does not depend on the missing data mechanism so that only the outcome process needs to be modeled; because of this simplification, ignorability is often used as a baseline assumption. We study the implications of ignorability in the Bayesian context when there are high-dimensional nuisance parameters. We argue that ignorability is typically incompatible with sensible prior beliefs about the degree of selection bias, and show that for many problems ignorability directly implies that the selection bias is small with high prior probability. As examples, we consider semiparametric regression with Gaussian processes, high-dimensional ridge regression, and spike-and-slab priors.