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The computational cost of blocking for sampling discretely observed diffusions

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Mider, Marcin, Jenkins, Paul, Pollock, Murray and Roberts, Gareth O. (2022) The computational cost of blocking for sampling discretely observed diffusions. Methodology and Computing in Applied Probability . doi:10.1007/s11009-022-09949-y ISSN 1387-5841. (In Press)

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Official URL: https://doi.org/10.1007/s11009-022-09949-y

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Abstract

Many approaches for conducting Bayesian inference on discretely observed diffusions involve imputing diffusion bridges between observations. This can be computationally challenging in settings in which the temporal horizon between subsequent observations is large, due to the poor scaling of algorithms for simulating bridges as observation distance increases. It is common in practical settings to use a blocking scheme, in which the path is split into a (user-specified) number of overlapping segments and a Gibbs sampler is employed to update segments in turn. Substituting the independent simulation of diffusion bridges for one obtained using blocking introduces an inherent trade-off: we are now imputing shorter bridges at the cost of introducing a dependency between subsequent iterations of the bridge sampler. This is further complicated by the fact that there are a number of possible ways to implement the blocking scheme, each of which introduces a different dependency structure between iterations. Although blocking schemes have had considerable empirical success in practice, there has been no analysis of this trade-off nor guidance to practitioners on the particular specifications that should be used to obtain a computationally efficient implementation. In this article we conduct this analysis and demonstrate that the expected computational cost of a blocked path-space rejection sampler applied to Brownian bridges scales asymptotically at a cubic rate with respect to the observation distance and that this rate is linear in the case of the Ornstein-Uhlenbeck process. Numerical experiments suggest applicability both of the results of our paper and of the guidance we provide beyond the class of linear diffusions considered.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics
Q Science > QC Physics

Divisions:

Faculty of Science, Engineering and Medicine > Science > Statistics

Library of Congress Subject Headings (LCSH):

Bayesian statistical decision theory , Diffusion , Gaussian processes, Markov processes, Monte Carlo method

Journal or Publication Title:

Methodology and Computing in Applied Probability

Publisher:

Springer

ISSN:

1387-5841

Official Date:

2022

Dates:

Date	Event
2022	Published
14 July 2022	Available
10 March 2022	Accepted

DOI:

10.1007/s11009-022-09949-y

Status:

Peer Reviewed

Publication Status:

In Press

Access rights to Published version:

Open Access (Creative Commons)

Date of first compliant deposit:

6 April 2022

Date of first compliant Open Access:

6 April 2022

RIOXX Funder/Project Grant:

Project/Grant ID	RIOXX Funder Name	Funder ID
EP/L016710/1	[EPSRC] Engineering and Physical Sciences Research Council	http://dx.doi.org/10.13039/501100000266
EP/R018561/1	[EPSRC] Engineering and Physical Sciences Research Council	http://dx.doi.org/10.13039/501100000266
EP/K014463/1	[EPSRC] Engineering and Physical Sciences Research Council	http://dx.doi.org/10.13039/501100000266
EP/K034154/1	Engineering and Physical Sciences Research Council	http://dx.doi.org/10.13039/501100000266
EP/N510129/1	[EPSRC] Engineering and Physical Sciences Research Council	http://dx.doi.org/10.13039/501100000266