Three-Toed Sloth

"Robust Bayesian inference via coarsening" (Next Week at the Statistics Seminar)

Attention conservation notice: Only of interest if you (1) care allocating precise fractions of a whole belief over a set of mathematical models when you know none of them is actually believable, and (2) will be in Pittsburgh on Monday.

As someone who thinks Bayesian inference is only worth considering under mis-specification, next week's first talk is of intense interest.

Jeff Miller, "Robust Bayesian inference via coarsening" (arxiv:1506.06101)

Abstract: The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a Bayesian procedure, particularly when the data set is large. We introduce a simple, coherent approach to Bayesian inference that improves robustness to small departures from the model: rather than conditioning on the observed data exactly, one conditions on the event that the model generates data close to the observed data, with respect to a given statistical distance. When closeness is defined in terms of relative entropy, the resulting "coarsened posterior" can be approximated by simply raising the likelihood to a certain fractional power, making the method computationally efficient and easy to implement in practice. We illustrate with real and simulated data, and provide theoretical results.

Time and place: 4 pm on Monday, 15 February 2016, in 125 Scaife Hall

As always, the talk is free and open to the public.

Enigmas of Chance; Bayes, Anti-Bayes