[00754] Regularization models and sampling algorithms in statistics and inverse problems
Session Date & Time :
00754 (1/2) : 1E (Aug.21, 17:40-19:20)
00754 (2/2) : 2C (Aug.22, 13:20-15:00)
Type : Proposal of Minisymposium
Abstract : Inverse problems involve the determination of unknown parameters from observational data and mathematical models linking those parameters to the data. Bayesian inference offers a framework to estimate the solution in terms of a posterior probability distribution. Oftentimes, the computation of the posterior requires application of Markov chain Monte Carlo (MCMC) methods. Direct implementation of these techniques becomes a challenge when the target parameters have a particular structure and are high-dimensional. This mini-symposium aims at presenting recent developments in sampling methods and prior/regularization models in statistics and inverse problems, including novel MCMC techniques, Monte Carlo estimators, and priors encoding structural information.
Felipe Uribe (Lappeenranta-Lahti University of Technology)
Jinglai Li (University of Birmingham)
Max Ehre (Technical University of Munich)
Nicolai Riis (Technical University of Denmark)
Dootika Vats (Indian Institute of Technology)
Heikki Haario (Lappeenranta-Lahti University of Technology)
Andi Wang (University of Bristol)
Matteo Croci (University of Texas at Austin)
Talks in Minisymposium :
[03567] Efficient Bernoulli Factory MCMC
Author(s) :
Dootika Vats (Indian Institute of Technology Kanpur)
Flávio Gonçalves (Universidade Federal de Minas Gerais)
Krzysztof Łatuszyński (University of Warwick)
Gareth Roberts (University of Warwick)
Abstract : Accept-reject based Markov chain Monte Carlo (MCMC) algorithms have traditionally utilised acceptance probabilities that can be explicitly written as a function of the ratio of the target density at the two contested points. This feature is rendered almost useless in Bayesian posteriors with unknown functional forms. We introduce a new family of MCMC acceptance probabilities that has the distinguishing feature of not being a function of the ratio of the target density at the two points. We present a stable Bernoulli factory that generates events within this class of acceptance probabilities. The efficiency of our methods rely on obtaining reasonable local upper or lower bounds on the target density and we present an application of MCMC on constrained spaces where this is reasonable.
[03923] Simulating rare events with Stein variational gradient descent
Author(s) :
Max Ehre (Technical University of Munich)
Iason Papaioannou (Technical University of Munich)
Daniel Straub (Technical University of Munich)
Abstract : Stein variational gradient descent (SVGD) is an approach to sampling from Bayesian posterior distributions. We repurpose SVGD for simulating rare events with probabilities 10^{-5} -- 10^{-12}. We employ a tempered version of SVGD to sample from an approximately optimal importance sampling density. Several examples are used to benchmark the efficacy of our approach against state-of-the-art methods for estimating rare event probabilities.
