B0706
Title: Locally robust efficient Bayesian inference
Authors: Andriy Norets - Brown University (United States) [presenting]
Abstract: A framework for making Bayesian parametric models robust to local misspecification is proposed. Suppose in a baseline parametric model, a parameter of interest has an interpretation in a more general semiparametric model, and the baseline model is only locally misspecified. Bayesian and maximum likelihood estimators will generally be biased in these settings. Augmenting the baseline likelihood by a multiplicative factor is proposed that involves scores for the baseline model, the efficient scores for the encompassing semiparametric model, and an auxiliary parameter that has the same dimension as the parameter of interest. It is shown that this augmentation asymptotically results in a marginal posterior for the parameter of interest that is normal with the mean equal to the semiparametrically efficient estimator and the variance equal to the semiparametric efficiency bound. The augmented model nests the baseline model as a special case when the auxiliary parameter is zero. The approach should be especially useful when not only the parameters but other aspects of the distribution are of interest. An MCMC algorithm is developed for the augmented model estimation. The approach is illustrated in applications.
