Koskela, Jere, Spanò, Dario and Jenkins, Paul (2019) Consistency of Bayesian nonparametric inference for discretely observed jump diffusions. Bernoulli, 25 (3). pp. 2183-2205. doi:10.3150/18-BEJ1050 ISSN 1350-7265.

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Abstract

We introduce verifiable criteria for weak posterior consistency of Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient in arbitrary dimension. The criteria are expressed in terms of coefficients of the SDEs describing the process, and do not depend on intractable quantities such as transition densities. In particular, we are able to show that posterior consistency can be verified under Gaussian and Dirichlet mixture model priors. Previous methods of proof have failed for these families due to restrictive regularity assumptions on drift functions, which we are able to circumvent using coupling.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Nonparametric statistics
Journal or Publication Title:	Bernoulli
Publisher:	Int Statistical Institute
ISSN:	1350-7265
Official Date:	June 2019
Dates:	Date Event June 2019 Published 12 June 2019 Available 14 June 2018 Accepted 12 June 2015 Submitted
Volume:	25
Number:	3
Page Range:	pp. 2183-2205
DOI:	10.3150/18-BEJ1050
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	17 July 2018
Date of first compliant Open Access:	17 June 2019
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/HO23364/1 (EPSRC), EP/L018497/1 (EPSRC)
Related URLs:	Publisher
Open Access Version:	ArXiv

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