A piecewise deterministic Monte Carlo method for diffusion bridges
Journal article, 2021

We introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic Markov process. Similar to the Lévy–Ciesielski construction of a Brownian motion, we expand the diffusion path in a truncated Faber–Schauder basis. The coefficients within the basis are sampled using a Zig-Zag sampler. A key innovation is the use of the fully local algorithm for the Zig-Zag sampler that allows to exploit the sparsity structure implied by the dependency graph of the coefficients and by the subsampling technique to reduce the complexity of the algorithm. We illustrate the performance of the proposed methods in a number of examples.

Intractable target density

Local Zig-Zag sampler

Piecewise deterministic Monte Carlo

High-dimensional simulation

Diffusion bridge

Conditional diffusion

Diffusion process

Faber–Schauder basis

Author

Joris Bierkens

Delft Institute of Applied Mathematics

Sebastiano Grazzi

Delft Institute of Applied Mathematics

Frank Van Der Meulen

Delft Institute of Applied Mathematics

Moritz Schauer

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Statistics and Computing

0960-3174 (ISSN) 1573-1375 (eISSN)

Vol. 31 3 37

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Signal Processing

DOI

10.1007/s11222-021-10008-8

More information

Latest update

6/24/2021