Reversible jump MCMC for nonparametric drift estimation for diffusion processes

Frank van der Meulen; Moritz Schauer; Harry van Zanten

doi:10.1016/j.csda.2013.03.002

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arXiv · 1206.4910

Reversible jump MCMC for nonparametric drift estimation for diffusion processes

Frank van der Meulen·Moritz Schauer·Harry van Zanten

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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.

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BibTeX RIS

Frank van der Meulen, Moritz Schauer, Harry van Zanten. 2012-06-21. Reversible jump MCMC for nonparametric drift estimation for diffusion processes. https://doi.org/10.1016/j.csda.2013.03.002

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