Unleashing the Power of Inferential Models

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This course provides an introduction to the latest development in statistical inference: Inferential Models (IMs). Developed by Ryan Martin and Chuanhai Liu in 2010s, the IMs framework offers a new approach to prior-free and frequency-calibrated probabilistic inference that is motivated by Fisher's fiducial argument and the Dempster-Shafer theory of belief functions.

In this course, students will review traditional inferential methods, including Bayesian argument, Fisher's fiducial argument, and Jerzy Neyman's school of thought, before diving into the basics of IMs. They will learn how IMs extend the Bayes theorem without priors and explore the marginalization methods used in IMs.

By examining unsolved problems from an IMs perspective, including the Behrens-Fisher problem and the many-normal-means problem, students will gain a deeper understanding of probabilistic reasoning and valid uncertainty quantification. They will also learn about the future research directions in this field.

This course is designed for students who are highly motivated to tackle unsolved problems in the field of statistical inference and are eager to gain a deep understanding of IMs. Upon completion of the course, students will have a comprehensive understanding of this cutting-edge field and be equipped to contribute to future research.