3 papers
math.PR2025
Asymptotic analysis of rare events in high dimensions
Anya Katsevich, Alexander Katsevich
Understanding rare events is critical across domains ranging from signal processing to reliability and structural safety, extreme-weather forecasting, and insurance. The analysis o…
math.ST2025
A unified theory of the high-dimensional Laplace approximation with application to Bayesian inverse problems
Anya Katsevich, Vladimir Spokoiny
The Laplace approximation (LA) to posteriors is a ubiquitous tool to simplify Bayesian computation, particularly in the high-dimensional settings arising in Bayesian inverse proble…
math.CA2025
The Laplace asymptotic expansion in high dimensions
Anya Katsevich
We prove that the classical Laplace asymptotic expansion (AE) of , extends to the high-dimensional regime in which may grow large w…