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The Blended Paradigm: A Bayesian Approach to Handling Outliers and Misspecified Models

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If you have a question about this talk, please contact Zoubin Ghahramani .

Bayesian methods have proven themselves to be enormously successful across a wide range of scientific problems, with analyses ranging from the simple one-sample problem to complicated hierarchical models. They have many well-documented advantages over competing methods. However, Bayesian methods run into difficulties for two major and prevalent classes of problems—handling data sets with outliers and dealing with model misspecification. In both cases, standard Bayesian analyses fall prey to the hubris that is an integral part of the Bayesian paradigm. The large sample behavior of the analysis is driven by the likelihood. We propose the use of restricted likelihood as a single solution to both of these problems. When working with restricted likelihood, we summarize the data, x, through a set of (insufficient) statistics T(x) and update our prior distribution with the likelihood of T(x) rather than the likelihood of x. By choice of T(x), we retain the main benefits of Bayesian methods while reducing the sensitivity of the analysis to selected features of the data. The talk will motivate the blended paradigm, discuss properties of the method and choice of T(x), cover the main computational strategies for its implementation, and illustrate its benefits. This is joint work with Yoonkyung Lee and John Lewis.

This talk is part of the Machine Learning @ CUED series.

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Faculty of Education, 184 Hills Road, Cambridge, CB2 8PQ, (Room G03, Mary Allan Building) Frankopan Hall, West Court, Jesus College, Jesus Lane, Cambridge, CB5 8BL https://cam-ac-uk.zoom.us/j/91513005909

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