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

我们考虑非线性、多元扩散过程的推断问题，满足 Itô 随机微分方程 (SDE)，使用可能不完整且受测量误差影响的离散时间的数据。我们的出发点是最先进的相关伪边际 Metropolis-Hastings 算法，该算法使用相关粒子滤波器在连续似然估计之间产生强正相关。然而，除非测量误差或 SDE 的维度很小，否则相关性可能会被粒子滤波器中的重采样步骤侵蚀。因此，我们提出了一种新的增强方案，它允许在观察时间对潜在过程的值进行调节，完全避免了重新采样步骤的需要。我们将观察时间的不确定性与额外的 Gibbs 步骤相结合。得到的伪边际方案和现有的扩散过程推理方案之间建立了联系，给出了一个统一的推理框架，包括吉布斯采样和伪边际方案。该方法应用于三个越来越复杂的例子。我们发现，与竞争方法相比，我们的方法大大提高了整体效率