Reversible jump MCMC for nonparametric drift estimation for diffusion processes

Frank van der Meulen, Moritz Schauer and Harry van Zanten

Computational Statistics & Data Analysis, 2014, vol. 71, issue C, 615-632

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 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.

Keywords: Reversible jump Markov chain Monte Carlo; Discretely observed diffusion process; Data augmentation; Nonparametric Bayesian inference; Multiplicative scaling parameter; Series prior (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:71:y:2014:i:c:p:615-632

DOI: 10.1016/j.csda.2013.03.002

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