6 papers
Neural Backward Filtering Forward Guiding
Gefan Yang, Frank van der Meulen, Stefan Sommer
Inference in nonlinear continuous stochastic processes on trees is challenging, particularly when observations are sparse and the topology is complex. Exact smoothing via Doob's $h…
Semi-parametric Bernstein-von Mises Theorem in a Parabolic PDE Problem
Adel Magra, Frank van der Meulen, Aad van der Vaart
We consider the heat equation with absorption in a bounded domain of , where both the scalar diffusivity and the absorption function are unknown. We investigate a Bay…
Guided filtering and smoothing for infinite-dimensional diffusions
Thorben Pieper-Sethmacher, Daniele Avitabile, Frank van der Meulen
We consider the filtering and smoothing problems for an infinite-dimensional diffusion process X, observed through a finite-dimensional representation at discrete points in time. A…
Neural Guided Diffusion Bridges
Gefan Yang, Frank van der Meulen, Stefan Sommer
We propose a novel method for simulating conditioned diffusion processes (diffusion bridges) in Euclidean spaces. By training a neural network to approximate bridge dynamics, our a…
Backward Filtering Forward Guiding
Frank van der Meulen, Moritz Schauer, Stefan Sommer
We develop a general methodological framework for probabilistic inference in discrete- and continuous-time stochastic processes evolving on directed acyclic graphs (DAGs). The proc…
Simulation of infinite-dimensional diffusion bridges
Thorben Pieper-Sethmacher, Frank van der Meulen, Aad van der Vaart
Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridg…