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FDS Statistics & Data Science Seminar
High-dimensional Laplace-type asymptotics
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Speaker: Anya Katsevich (MIT) NSF Postdoctoral Fellow Massachusetts Institute of Technology Monday, February 24, 2025 11:30AM - 1:00PM Lunch at 11:30am in room 1307
Talk from 12:00-1:00pm in room 1327A Location: Yale Institute for Foundations of Data Science, Kline Tower 13th Floor, Room 1327, New Haven, CT 06511 and via Webcast: https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=5affe167-3578-4fe4-98f1-b233012bcd93 |
Abstract: We derive an asymptotic expansion of posterior integrals in the regime in which dimension grows together with sample size. We also present related work on the accuracy of the Laplace approximation (LA) to high-dimensional posterior densities, and derive a higher-order correction to the LA. These results are both theoretically significant and useful for the computations involved e.g. in Bayesian model selection and construction of credible sets. Finally, we prove the tightest known high-dimensional Bernstein-von Mises theorem, closing the long-standing gap between conditions for asymptotic normality in Bayesian and frequentist inference.
Our expansion of posterior integrals, which are naturally of Laplace type for large sample size, is also of theoretical significance in asymptotic analysis. It fills the gap in the theory between the classical fixed-dimensional regime dating back to Laplace, and more recent work on the asymptotic expansion of infinite-dimensional Laplace-type integrals due to Ben Arous.
Speaker bio: Anya Katsevich is an NSF postdoctoral fellow in the mathematics department at MIT. She earned her PhD in mathematics at the Courant Institute at NYU, where she was a DOE Computational Sciences Graduate Fellow. Her research interests center around asymptotic methods with applications in statistics and probability.
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