Monte Carlo Seminar| Alexandare Bouchard-Côté| Computational Lebesgue Integration
Автор: Monte Carlo Seminar
Загружено: 2025-09-23
Просмотров: 178
Speaker: Alexandre Bouchard-Côté (University of British Columbia)
Title: Computational Lebesgue integration
Abstract: In many modern applications in science and engineering, we seek to reconstruct a complicated object x from noisy data y, for example, one may seek to reconstruct an evolutionary tree from sequencing data. In principle, Bayesian statistics provides a broad framework to approach such problems, by modelling knowns and unknowns as random variables X and Y. Since the notion of a posterior distribution, X|Y, is defined under very general conditions, Bayesian inference is in a sense universal for the purpose of data analysis. In contrast, other inferential setups often require, among other things, for x to be real-valued in order to use approximations such as those based on the central limit theorem.
However, this generality hinges on being able to approximate expectations with respect to an arbitrary measure. Can we develop generic sampling methods in such an unstructured context? Surprisingly, practical methodologies are indeed possible. I will describe some of our work in the area with a focus on recent developments based on regenerative MCMC, particle methods, and non-reversibility. My group is also working on making these complex Monte Carlo methods easy to use: check out https://pigeons.run/dev/, a package that allows users to leverage clusters of 1000s of nodes to speed up difficult Monte Carlo problems without requiring knowledge of distributed algorithms.
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