期刊
COMPUTATIONAL STATISTICS & DATA ANALYSIS
卷 71, 期 -, 页码 615-632出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.csda.2013.03.002
关键词
Reversible jump Markov chain Monte Carlo; Discretely observed diffusion process; Data augmentation; Nonparametric Bayesian inference; Multiplicative scaling parameter; Series prior
资金
- Netherlands Organization for Scientific Research (NWO) via the STAR Mathematics Cluster
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. (C) 2013 Elsevier B.V. All rights reserved.
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