A piecewise deterministic Monte Carlo method for diffusion bridges
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We introduce the use of the Zig-Zag sampler to the problem of sampling of 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 a local version of the Zig-Zag sampler that allows to exploit the sparse dependency structure of the coefficients of the Faber-Schauder expansion to reduce the complexity of the algorithm. We illustrate the performance of the proposed methods in a number of examples. Contrary to some other Markov Chain Monte Carlo methods, our approach works well in case of strong nonlinearity in the drift and multimodal distributions of sample paths.
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