Hypothesis Testing: A Minimax Perspective

6 units · Graduate

All Semesters: 6 units Hypothesis testing is a fundamental task in statistics: given data, we want to decide which of two competing explanations (hypotheses) generated it. As statistical models become higher-dimensional and more complex, determining whether reliable testing is possible (and designing procedures that achieve optimal performance) becomes increasingly challenging. This course will be an introduction to minimax hypothesis testing, which aims to characterize the smallest separation between hypotheses that permits reliable testing. Our primary focus will be on the interplay between optimal tests and matching information-theoretic lower bounds, as well as on understanding when testing is easier than learning the underlying distribution. This course will be theory-oriented. Prerequisites: ( 10-601 or 15-781) and (36-725 or 36-705)