ABSTRACT Multivariate stochastic differential equations (SDEs) are commonly used in many applications. Statistical inference based on discretely observed data requires estimating the transition density, which is unknown for most models. Typically, one would estimate the transition density and use the approximation for statistical inference. However, many estimation methods will fail when the observations are too sparse or when the SDE models have a hierarchical structure. In a Bayesian approach, we explore the posterior distribution of the SDE model parameters. In the Markov Chain Monte Carlo algorithm, we use data augmentation to understand how the approximation of the transition density affects the inference procedure. We give guidelines on balancing the computational demands with the need to provide reliable and accurate posterior inference. Simulations are used to evaluate these guidelines. We demonstrate these methods on the analysis of oceanography tracer measurements.

中文翻译：

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随机微分方程数据增强策略研究

摘要 多元随机微分方程 (SDE) 常用于许多应用。基于离散观察数据的统计推断需要估计转换密度，这对于大多数模型来说是未知的。通常，人们会估计转换密度并使用近似值进行统计推断。然而，当观测值过于稀疏或 SDE 模型具有层次结构时，许多估计方法将失败。在贝叶斯方法中，我们探索了 SDE 模型参数的后验分布。在马尔可夫链蒙特卡罗算法中，我们使用数据增强来理解转移密度的近似如何影响推理过程。我们给出了平衡计算需求与提供可靠和准确的后验推断的需要的指南。模拟用于评估这些指南。我们在海洋学示踪剂测量分析中展示了这些方法。