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Center for Nonlinear Studies |
The ideals of exact modeling, and of putting off approximations as long as possible, make Bayesian practice both successful and difficult. To address the difficulties, Bayesian statisticians have created mechanically-interpretable languages in which to write statistical models and questions about them, and computer implementations that calculate answers. However, none of these languages have a well-defined semantics, so there is no way to tell whether unexpected behavior in an implementation is a bug or a feature. Functional programming researchers have created probabilistic programming languages with well-defined semantics. However, because the languages lack critical features, Bayesians cannot use them in their day-to-day work. For example, all but one lack probabilistic onditioning. In short, Bayesians have made languages that are useful but that they cannot trust, and others have made languages that are trustworthy but that Bayesians cannot use. My dissertation work is to create mechanically interpretable languages that are trustworthy and useful to practicing Bayesian statisticians. I expect many of the techniques and theoretical tools I develop - such as extending the foundations of mathematics to make it more like a programming language while preserving existing theorems - to transfer to creating such languages for other areas of applied mathematics.
Host: Chris Tomkins, Complex Data Analysis Techniques & Applications (C-DATA) Applied Modern Physics (Group P-21)