A piecewise deterministic Monte Carlo method for diffusion bridges
Artikel i vetenskaplig tidskrift, 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.

High-dimensional simulation

Diffusion process

Diffusion bridge

Intractable target density

Faber–Schauder basis

Conditional diffusion

Piecewise deterministic Monte Carlo

Local Zig-Zag sampler

Författare

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, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Statistics and Computing

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

Vol. 31 3 37

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Signalbehandling

DOI

10.1007/s11222-021-10008-8

Mer information

Senast uppdaterat

2021-05-06