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Title: Regularized exponentially tilted empirical likelihood for Bayesian inference Authors:  Eunseop Kim - The Ohio State University (United States) [presenting]
Steven MacEachern - The Ohio State University (United States)
Mario Peruggia - The Ohio State University (United States)
Abstract: Empirical likelihood extends the use of likelihood to models defined through moment conditions with minimal distributional assumptions. A likelihood closely related to empirical likelihood, called the exponentially tilted empirical likelihood, arises as a nonparametric Bayesian procedure with the prior that favors distributions close to the empirical distribution. Despite its desirable asymptotic properties, the so-called empty set problem or the convex hull constraint limits its use for Bayesian inference. We propose a hybrid method for the exponentially tilted empirical likelihood that is free from the empty set problem. The method introduces an auxiliary exponential family distribution and applies exponential tilting to the mixture of the empirical distribution and the auxiliary distribution. The auxiliary distribution prevents the empty set problem and regularizes the likelihood by forming an exponential family. We demonstrate that the method stabilizes the posterior distribution in the full parameter space, enabling more efficient posterior sampling with relatively small sample sizes.