A piecewise deterministic Monte Carlo method for diffusion bridges

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Abstract

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.

Original languageEnglish
Article number37
Number of pages21
JournalStatistics and Computing
Volume31
Issue number3
DOIs
Publication statusPublished - 2021

Keywords

  • Conditional diffusion
  • Diffusion bridge
  • Diffusion process
  • Faber–Schauder basis
  • High-dimensional simulation
  • Intractable target density
  • Local Zig-Zag sampler
  • Piecewise deterministic Monte Carlo

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