Statistics Seminar: Bondell -- Do you have a moment? Bayesian inference using estimating equations via empirical likelihood

Do you have a moment? Bayesian inference using estimating equations via empirical
likelihood

Speaker: Professor Howard Bondell, University of Melbourne 
Time: 2-3PM Friday 21 Oct
Location: Carslaw Lecture Theatre 373 (note the change in room), or 
Zoom at
https://uni-sydney.zoom.us/j/89779295453 

Bayesian inference typically relies on specification of a likelihood as a key
ingredient.  Recently, likelihood-free approaches have become popular to avoid
specification of potentially intractable likelihoods.  Alternatively, in the Frequentist
context, estimating equations are a popular choice for inference corresponding to an
assumption on a set of moments (or expectations) of the underlying distribution, rather
than its exact form.  Common examples are in the use of generalised estimating equations
with correlated responses, or in the use of M-estimators for robust regression avoiding
the distributional assumptions on the errors.  In this talk, I will discuss some of the
motivation behind empirical likelihood, and how it can be used to incorporate a fully
Bayesian analysis into these settings where only specification of moments is desired.
This allows one to then take advantage of prior distributions that have been developed
to accomplish various shrinkage tasks, both theoretically and in practice.  I will
further discuss computational issues that arise due to non-convexity of the support of
this likelihood and the corresponding posterior, and show how this can be rectified to
allow for MCMC and variational approaches to perform posterior inference.