Consistency of Bayesian nonparametric inference for discretely observed jump diffusions
نویسندگان
چکیده
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.
منابع مشابه
Consistent nonparametric Bayesian inference for discretely observed scalar diffusions
FRANK VAN DER MEULEN1 and HARRY VAN ZANTEN2 1Delft Institute of Applied Mathematics (DIAM), Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands. E-mail: [email protected] 2Department of Mathematics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: j....
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