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The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic Markov process. Similar to the L\u00e9vy\u2013Ciesielski construction of a Brownian motion, we expand the diffusion path in a truncated Faber\u2013Schauder basis. The coefficients within the basis are sampled using a Zig-Zag sampler. A key innovation is the use of the<jats:italic>fully local<\/jats:italic>algorithm for the Zig-Zag sampler that allows to exploit the sparsity structure implied by the dependency graph of the coefficients and by the<jats:italic>subsampling<\/jats:italic>technique to reduce the complexity of the algorithm. We illustrate the performance of the proposed methods in a number of examples.<\/jats:p>","DOI":"10.1007\/s11222-021-10008-8","type":"journal-article","created":{"date-parts":[[2021,4,20]],"date-time":"2021-04-20T08:04:02Z","timestamp":1618905842000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A piecewise deterministic Monte Carlo method for diffusion bridges"],"prefix":"10.1007","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0185-5804","authenticated-orcid":false,"given":"Joris","family":"Bierkens","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2026-261X","authenticated-orcid":false,"given":"Sebastiano","family":"Grazzi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7246-8612","authenticated-orcid":false,"given":"Frank","family":"van der Meulen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3310-7915","authenticated-orcid":false,"given":"Moritz","family":"Schauer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,4,20]]},"reference":[{"key":"10008_CR1","unstructured":"Andrieu, C., Livingstone, S.: Peskun-Tierney ordering for Markov chain and process Monte Carlo: beyond the reversible scenario (2019). arXiv:1906.06197"},{"key":"10008_CR2","unstructured":"Andrieu, C. et al.: Hypocoercivity of Piecewise Deterministic Markov Process-Monte Carlo. 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