ABSTRACT

Continuous-time models generally imply a stochastic differential equation for latent processes, coupled to a measurement model. Various computational issues can arise, and there are different estimation approaches, with different trade-offs. It has been claimed that a SEM style continuous-time model can reduce run times for Bayesian estimations of continuous-time models from hours to minutes. However this claim is not true in the general case, but requires that individuals are characterized by the same covariance and means structure, and that the number of time points is not large. While such simplifications can be valuable, and indeed are in use in existing software when appropriate, they are in general quite restrictive. The hierarchical Bayesian form of ctsem was, for instance, developed precisely to estimate models where these restrictions do not hold. To try to shed some more light on these aspects, I discuss the related issues herein.

摘要

连续时间模型通常意味着潜在过程的随机微分方程，耦合到测量模型。可能会出现各种计算问题，并且有不同的估计方法，需要进行不同的权衡。据称，SEM 风格的连续时间模型可以将连续时间模型的贝叶斯估计的运行时间从几小时减少到几分钟。然而这种说法在一般情况下并不成立，而是要求个体具有相同的协方差和均值结构特征，并且时间点的数量不多。虽然这种简化可能很有价值，并且确实在适当的时候在现有软件中使用，但它们通常具有很大的限制性。例如，ctsem 的分层贝叶斯形式是 开发精确地估计这些限制不成立的模型。为了更深入地了解这些方面，我将在此讨论相关问题。