Reversible jump MCMC for nonparametric drift estimation for diffusion processes
Abstract
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 function 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.
Cite
@article{arxiv.1206.4910,
title = {Reversible jump MCMC for nonparametric drift estimation for diffusion processes},
author = {Frank van der Meulen and Moritz Schauer and Harry van Zanten},
journal= {arXiv preprint arXiv:1206.4910},
year = {2017}
}