Open Access
August 2019 Consistency of Bayesian nonparametric inference for discretely observed jump diffusions
Jere Koskela, Dario Spanò, Paul A. Jenkins
Bernoulli 25(3): 2183-2205 (August 2019). DOI: 10.3150/18-BEJ1050


We introduce verifiable criteria for weak posterior consistency of Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients 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. We also show that priors built from discrete nets, wavelet expansions, and Dirichlet mixture models satisfy our conditions. This generalises known results by incorporating jumps into previous work on unit diffusions with uniformly Lipschitz drift coefficients.


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Jere Koskela. Dario Spanò. Paul A. Jenkins. "Consistency of Bayesian nonparametric inference for discretely observed jump diffusions." Bernoulli 25 (3) 2183 - 2205, August 2019.


Received: 1 October 2015; Revised: 1 November 2017; Published: August 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07066254
MathSciNet: MR3961245
Digital Object Identifier: 10.3150/18-BEJ1050

Keywords: Bayesian statistics , Dirichlet mixture model prior , discrete net prior , jump diffusion , nonparametric inference , posterior consistency

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 3 • August 2019
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