On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm

• 成果类型: Article
• 署名作者: Roberts, GO; Stramer, O
• 署名单位: Lancaster University; University of Iowa
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/88.3.603
• 发表日期: 2001
• 页码: 603621
• 关键词: time-series; CONVERGENCE; distributions; rates

摘要

In this paper, we introduce a new Markov chain Monte Carlo approach to Bayesian analysis of discretely observed diffusion processes. We treat the paths between any two data points as missing data. As such, we show that, because of full dependence between the missing paths and the volatility of the diffusion, the rate of convergence of basic algorithms can be arbitrarily slow if the amount of the augmentation is large. We offer a transformation of the diffusion which breaks down dependency between the transformed missing paths and the volatility of the diffusion. We then propose two efficient Markov chain Monte Carlo algorithms to sample from the posterior-distribution of the transformed missing observations and the parameters of the diffusion. We apply our results to examples involving simulated data and also to Eurodollar short-rate data.