[图书][B] Bayesian non-linear statistical inverse problems

R Nickl - 2023 - statslab.cam.ac.uk
Mathematics in Zurich has a long and distinguished tradition, in which the writing of lecture
notes volumes and research monographs plays a prominent part. The Zurich Lectures in …

On diffusion models for amortized inference: Benchmarking and improving stochastic control and sampling

M Sendera, M Kim, S Mittal, P Lemos… - arXiv preprint arXiv …, 2024 - arxiv.org
We study the problem of training diffusion models to sample from a distribution with a given
unnormalized density or energy function. We benchmark several diffusion-structured …

Dimension Free Nonasymptotic Bounds on the Accuracy of High-Dimensional Laplace Approximation

V Spokoiny - SIAM/ASA Journal on Uncertainty Quantification, 2023 - SIAM
This paper aims at revisiting the classical results on Laplace approximation in a modern
nonasymptotic and dimension-free form. Such an extension is motivated by applications to …

Heavy-tailed Bayesian nonparametric adaptation

S Agapiou, I Castillo - The Annals of Statistics, 2024 - projecteuclid.org
We provide the rest of the proofs of the results contained in the main article, some technical
lemmas as well as additional simulations corroborating the theory. We also provide a …

A special issue on Bayesian inference: challenges, perspectives and prospects

CP Robert, J Rousseau - Philosophical Transactions of …, 2023 - royalsocietypublishing.org
This special issue is dedicated to Sir Adrian Smith, whose contributions to Bayesian analysis
have deeply impacted the field (or rather fields) of Bayesian inference, decision theory and …

Improved off-policy training of diffusion samplers

M Sendera, M Kim, S Mittal, P Lemos… - The Thirty-Eighth …, 2024 - research.ed.ac.uk
We study the problem of training diffusion models to sample from a distribution with a given
unnormalized density or energy function. We benchmark several diffusion-structured …

On log-concave approximations of high-dimensional posterior measures and stability properties in non-linear inverse problems

J Bohr, R Nickl - Annales de l'Institut Henri Poincare (B) …, 2024 - projecteuclid.org
The problem of efficiently generating random samples from high-dimensional and non-log-
concave posterior measures arising in nonlinear regression problems is considered …

Less Interaction with Forward Models in Langevin Dynamics: Enrichment and Homotopy

M Eigel, R Gruhlke, D Sommer - SIAM Journal on Applied Dynamical Systems, 2024 - SIAM
Ensemble methods have become ubiquitous for the solution of Bayesian inference
problems. State-of-the-art Langevin samplers such as the ensemble Kalman sampler (EKS) …

Bernstein-von Mises theorems for time evolution equations

R Nickl - arXiv preprint arXiv:2407.14781, 2024 - arxiv.org
We consider a class of infinite-dimensional dynamical systems driven by non-linear
parabolic partial differential equations with initial condition $\theta $ modelled by a Gaussian …

Sampling from Boltzmann densities with physics informed low-rank formats

P Hagemann, J Schütte, D Sommer, M Eigel… - arXiv preprint arXiv …, 2024 - arxiv.org
Our method proposes the efficient generation of samples from an unnormalized Boltzmann
density by solving the underlying continuity equation in the low-rank tensor train (TT) format …