ST790 — Imprecise-Probabilistic Foundations of Statistics & Data Science (Fall 2022)
Probability theory plays an important role in statistics, machine learning, and data science more generally, as the language commonly used to describe uncertainty. But probability theory can’t satisfactorily describe all kinds of uncertainty. For example, in statistical inference problems, we’re often in an a priori state of ignorance when it comes to the values of unknown model parameters, but probability simply can’t capture ignorance. More importantly, when we’re uncertain about aspects of the data-generating process, the “error probabilities” that our statistical methods are designed to control aren’t precise probabilities, so some degree of imprecision is needed. Fortunately, there is a well-developed theory of imprecise probability, a generalization of ordinary/precise probability that is sufficiently rich to handle the issues identified above, and more. Unfortunately, the important connection between imprecise probability and statistics/data science is (arguably) yet to be fully understood and appreciated.
This course aims to help close this gap between imprecise probability & statistics in two ways:
- introduce the essentials of imprecise probability to a (mostly) statistical audience
- expose some of the opportunities for imprecise-probabilistic insights and techniques to positively impact statistics and data science.
This is an official/credit-earning course for Statistics PhD students at NC State University, but since many others might find this topic of interest, the instructor is making all of the course material (lecture videos, slides, etc.) publicly available here on this site, under the Course Materials tab. Everyone is welcome to participate in an unofficial/non-credit-earning capacity.
Non-NC State students who wish to participate in a “near-official” capacity should contact the instructor for additional information.