In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we focus upon the case of neuroscience. The data are assumed to be observed regularly in time and driven by the SDE model with unknown parameters. In practice the SDE may not have an analytically tractable solution and this leads naturally to a time-discretization. We adapt the multilevel Markov chain Monte Carlo method of [11], which works with a hierarchy of time discretizations and show empirically and theoretically that this is preferable to using one single time discretization. The improvement is in terms of the computational cost needed to obtain a pre-specified numerical error. Our approach is illustrated on models that are found in neuroscience.

翻译：本文研究了由跳跃过程驱动的一类部分观测随机微分方程（SDE）的贝叶斯参数推断问题。这类模型在各类应用中普遍存在，本文重点关注神经科学领域。假设观测数据在时间上具有规则采样间隔，并由含未知参数的SDE模型驱动。实际应用中，该SDE可能不存在解析解，因此自然需要引入时间离散化方法。我们改进了文献[11]中的多层马尔可夫链蒙特卡洛方法，该方法利用不同时间离散化层级构建分层结构，并通过实证与理论分析证明，相较于单一时间离散化策略更具优势。改进效果体现在达到预设数值误差所需的计算成本方面。本文在神经科学领域的典型模型上验证了所提方法。