Kou S C, Olding Benjamin P, Lysy Martin, Liu Jun S
Department of Statistics, Harvard University.
J Am Stat Assoc. 2012 Dec;107(500):1558-1574. doi: 10.1080/01621459.2012.720899.
Diffusion process models are widely used in science, engineering and finance. Most diffusion processes are described by stochastic differential equations in continuous time. In practice, however, data is typically only observed at discrete time points. Except for a few very special cases, no analytic form exists for the likelihood of such discretely observed data. For this reason, parametric inference is often achieved by using discrete-time approximations, with accuracy controlled through the introduction of missing data. We present a new multiresolution Bayesian framework to address the inference difficulty. The methodology relies on the use of multiple approximations and extrapolation, and is significantly faster and more accurate than known strategies based on Gibbs sampling. We apply the multiresolution approach to three data-driven inference problems - one in biophysics and two in finance - one of which features a multivariate diffusion model with an entirely unobserved component.
扩散过程模型在科学、工程和金融领域有着广泛应用。大多数扩散过程由连续时间的随机微分方程描述。然而，在实际中，数据通常仅在离散时间点上被观测到。除了少数非常特殊的情况外，对于这种离散观测数据的似然性不存在解析形式。因此，参数推断通常通过使用离散时间近似来实现，通过引入缺失数据来控制精度。我们提出了一个新的多分辨率贝叶斯框架来解决推断难题。该方法依赖于使用多种近似和外推，并且比基于吉布斯采样的已知策略显著更快、更准确。我们将多分辨率方法应用于三个数据驱动的推断问题——一个在生物物理学中，两个在金融领域——其中一个问题具有一个完全不可观测成分的多元扩散模型。
