Approximate Bayesian inference and model selection for stochastic differential equations (SDEs) (A06)

本课题主要研究随机微分方程组和动态点过程模型中漂移函数的贝叶斯半参数和完全非参数估计方法。我们将发展有效的序列蒙特卡罗方法和变分贝叶斯方法来解决这一问题，并研究它们的收敛速度和逼近性质。我们还将推导出贝叶斯模型选择的新方法，以根据可用的数据来决定给定集合中的哪个先验可以有效地用于手头的SDE问题。

This project is concerned with Bayesian semi-parametric and fully nonparametric approaches for estimating drift functions in systems of stochastic differential equations (SDE) and dynamical point process models. We will develop efficient sequential Monte Carlo approaches and variational Bayesian methods for this problem and study their convergence rates and approximation properties. We will also derive new methods for Bayesian model selection to decide - on the basis of available data - which prior from a given collection can be efficiently used for the SDE problem at hand.