Data Augmentation for Diffusions

摘要: The problem of formal likelihood-based (either classical or Bayesian) inference for discretely observed multidimensional diffusions is particularly challenging. In principle, this involves data augmentation the observation to give representations entire diffusion trajectory. Most currently proposed methodology splits broadly into two classes: either through discretization idealized approaches continuous-time setup use standard finite-dimensional methodologies model. connections between these have not been well studied. This article provides a unified framework that brings together approaches, demonstrating connections, and in some cases surprising differences. As result, we provide, first time, theoretical justification various methods imputing missing data. problems are challenging irreducible diffusions, our correspondingly mo...