Likelihood Inference for Discretely Observed Nonlinear Diffusions
用贝叶斯方法估计离散观测的非线性随机微分方程，通过引入潜在辅助数据填补缺失扩散，并用MCMC算法估计参数和潜在数据，适合处理金融或物理中的连续时间模型。
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.