Elerian, Ola; Chib, Siddhartha; Shephard, Neil Likelihood inference for discretely observed nonlinear diffusions. (English) Zbl 1017.62068 Econometrica 69, No. 4, 959-993 (2001). Summary: This paper is concerned with the Bayesian estimation of nonlinear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis-Hastings algorithm, in conjunction with the Euler-Maruyama discretization scheme, are used to sample the posterior distribution of the latent data and the model parameters. Techniques for computing the likelihood function, the marginal likelihood, and diagnostic measures (all based on the MCMC output) are developed. Examples using simulated and real data are presented and discussed in detail. Cited in 141 Documents MSC: 62M05 Markov processes: estimation; hidden Markov models 62F15 Bayesian inference PDFBibTeX XMLCite \textit{O. Elerian} et al., Econometrica 69, No. 4, 959--993 (2001; Zbl 1017.62068) Full Text: DOI Link