"Learning from data: Bayesian methods and (some) machine learning"

Courses: OSU Physics 8820 and OU PHYS 6601

Physics 8820 at Ohio State University is taught by Dick Furnstahl and PHYS 6601 at Ohio University is taught by Daniel Phillips.

Overview

Physics is an empirical science. This means that any serious attempt to do physics involves trying to wrest truth from data. In this course we will discuss how Bayesian statistics provides a mathematically consistent framework for deriving inferences from data and quantifying the strength of those inferences.

While most physics Ph.D. students are taught some standard (frequentist) statistics as part of their course work, relatively few encounter Bayesian methods until they are engaged in research. But Bayesian methods provide a coherent and compelling framework to think about inference, and so can be applied to many important questions in physics. The overall learning goal of this course is to show students who have had little or no previous exposure to Bayes’ theorem how it can be applied to the extraction of model parameters from data as well as how to use it to compare the efficacy of different models. We will also discuss machine learning tools for data analysis: simple ones such as Gaussian Processes, and more modern ones such as Neural Networks.

Learning outcomes

Upon completion of this course students should be able to:

• Apply the rules of probability to derive posterior probability distributions for simple problems involving prior information on parameters and various standard likelihood functions.
• Perform Bayesian parameter estimation, including in cases where marginalization over nuisance parameters is required.
• Use Monte Carlo sampling to generate posterior probability distributions and identify problems where standard sampling is likely to fail.
• Apply model comparison methods and explain what the results mean; e.g., computing an evidence ratio.
• Explain machine learning from a Bayesian perspective and employ a testing and training data set to develop and validate a Gaussian-process model.
• Employ these methods in the context of specific physics problems (examples in class will be often taken from nuclear physics, but they have more general applicability).
• Be able to understand, appreciate, and criticize the growing literature on Bayesian statistics and machine learning for physics applications.

Topics

The following topics will be covered (this is not an exclusive list):

• Basics of Bayesian statistics
• Bayesian parameter estimation
• Why Bayes is better
• MCMC sampling
• Assigning probabilities
• Model selection
• Model checking
• Gaussian processes
• Special topic: Bayesian methods and machine learning. [Note: we will not cover machine *earning in great detail, but learn about connections to Bayesian methods, e.g., with Bayesian neural networks as a working example.]
• Special topic: emulators