论文标题
增强的伪划分的大都市 - 用于部分观察到的扩散过程
Augmented pseudo-marginal Metropolis-Hastings for partially observed diffusion processes
论文作者
论文摘要
我们使用在离散时间可能不完整且遭受测量误差的数据，考虑了非线性，多元扩散过程的推断问题，满足了ITôStochastic微分方程（SDE）。我们的起点是一种最先进的相关伪核心大都市 - 悬挂算法，该算法使用相关的粒子过滤器来诱导连续的可能性估计之间的强和正相关。但是，除非测量误差或SDE的尺寸很小，否则相关性可以通过粒子滤波器中的重采样步骤侵蚀。因此，我们提出了一种新颖的增强方案，该方案允许在观察时间的潜在过程值进行调节，从而完全避免了重新采样步骤的需求。我们将观察时间的不确定性与额外的吉布斯步骤整合在一起。建立了生成的伪划分方案与现有的扩散过程推理方案之间的连接，从而提供了一个包含Gibbs采样和伪边缘方案的统一推理框架。该方法应用于增加复杂性的三个示例。我们发现，与竞争方法相比，我们的方法可实现总体效率的大幅提高。
We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying Itô stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our starting point is a state-of-the-art correlated pseudo-marginal Metropolis-Hastings algorithm, that uses correlated particle filters to induce strong and positive correlation between successive likelihood estimates. However, unless the measurement error or the dimension of the SDE is small, correlation can be eroded by the resampling steps in the particle filter. We therefore propose a novel augmentation scheme, that allows for conditioning on values of the latent process at the observation times, completely avoiding the need for resampling steps. We integrate over the uncertainty at the observation times with an additional Gibbs step. Connections between the resulting pseudo-marginal scheme and existing inference schemes for diffusion processes are made, giving a unified inference framework that encompasses Gibbs sampling and pseudo marginal schemes. The methodology is applied in three examples of increasing complexity. We find that our approach offers substantial increases in overall efficiency, compared to competing methods.
