Shrinkage and Selection for High-Dimensional Bayesian Estimating Equations

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Bayesian inference typically relies on specification of a likelihood as a key ingredient. Recently, likelihood-free approaches have become popular to avoid 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 generalized estimating equations with correlated responses, or in the use of M-estimators for robust regression avoiding the distributional assumptions on the errors. In the high-dimensional case, sparsity in both parameter estimates and number of estimating equations can be accomplished via a Bayesian empirical likelihood approach via careful specification of prior distributions.