ABSTRACT
In general, Bayesian approaches are more computationally intensive than frequentist approaches, hence this limited their use historically. However, due to the advances in computing power, Bayesian methods have emerged as an increasingly effective and practical alternative to the corresponding frequentist methods. This chapter discusses how to incorporate the empirical likelihood (EL) in the Bayesian framework by showing a novel approach for developing the nonparametric Bayesian posterior expectation, nonparametric analog of James–Stein estimation, and the nonparametric Bayesian confidence interval estimation. The asymptotic approximations to the new distribution-free posterior expectations are developed and shown to be quite accurate, even in the finite sample setting. The chapter explains posterior expectations of general functionals and nonparametric analog of James–Stein estimation.
