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Robust Inference via the Blended Paradigm

The blended paradigm provides a means of achieving robust inference within the Bayesian framework. We seek to improve inference when the sampling distribution posited for the data does not fully capture the data generating process. This paper focuses on the use of robust estimators of location and scale (e.g., Huber estimators) in a Bayesian context. An underlying model induces a distribution for the estimators. This induced distribution yields a likelihood which is used to update from the prior distribution to the posterior distribution. We empirically show that good choices of robust estimators can produce posteriors that are more concentrated around the target value than those based on the full data, reducing both the bias and variance of the posterior mean. The success of the method is illustrated in simulations and in an application for estimation of the speed of light.