Reversible jump MCMC for nonparametric drift estimation for diffusion processes
Artikel i vetenskaplig tidskrift, 2014

In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional diffusion. The drift is modeled by a scaled linear combination of basis functions with a Gaussian prior on the coefficients. The scaling parameter is equipped with a partially conjugate prior. The number of basis functions in the drift is equipped with a prior distribution as well. For continuous data, a reversible jump Markov chain algorithm enables the exploration of the posterior over models of varying dimension. Subsequently, it is explained how data-augmentation can be used to extend the algorithm to deal with diffusions observed discretely in time. Some examples illustrate that the method can give satisfactory results. In these examples a comparison is made with another existing method as well. © 2013 Elsevier B.V. All rights reserved.

Författare

Frank Van Der Meulen

TU Delft

Moritz Schauer

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Harry Van Zanten

Universiteit Van Amsterdam

Computational Statistics and Data Analysis

0167-9473 (ISSN)

Vol. 71 615-632

Ämneskategorier (SSIF 2025)

Sannolikhetsteori och statistik

DOI

10.1016/j.csda.2013.03.002

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Senast uppdaterat

2025-07-01