标题： 通过受控序贯蒙特卡罗和分裂方案对扩散过程的推断 显示英文标题

标题： Inference for Diffusion Processes via Controlled Sequential Monte Carlo and Splitting Schemes

摘要： 我们引入了一个适用于广泛类别的半线性随机微分方程（SDEs）的推断框架。最近的研究表明，数值分裂方案可以保持这类SDEs的关键特性，产生显式的伪似然函数，从而允许对完全观测过程进行参数推断。在此基础上，在多种离散时间观测制度下（特别是部分和完全观测，以及有噪声和无噪声的情况），我们将隐含的伪似然表示为Feynman--Kac流的归一化常数，从而可以通过受控序贯蒙特卡洛方法高效估计，并适应基于似然的方法以利用此伪似然进行推断。本文开发的策略使我们能够在各种问题上获得良好的推断结果。通过扩散桥，我们能够在不使用通常需要大量特定应用努力的复杂数值方案的情况下，计算上减少来自时间离散化的偏差。模拟结果显示，在假设椭圆性条件下，我们的方法在计算效率和准确性之间提供了出色的权衡，适用于点估计和后验估计。应用于神经科学示例显示了该方法在具有挑战性环境中的良好性能。 显示英文摘要

摘要： We introduce an inferential framework for a wide class of semi-linear stochastic differential equations (SDEs). Recent work has shown that numerical splitting schemes can preserve critical properties of such types of SDEs, give rise to explicit pseudolikelihoods, and hence allow for parameter inference for fully observed processes. Here, under several discrete time observation regimes (particularly, partially and fully observed with and without noise), we represent the implied pseudolikelihood as the normalising constant of a Feynman--Kac flow, allowing its efficient estimation via controlled sequential Monte Carlo and adapt likelihood-based methods to exploit this pseudolikelihood for inference. The strategy developed herein allows us to obtain good inferential results across a range of problems. Using diffusion bridges, we are able to computationally reduce bias coming from time-discretisation without recourse to more complex numerical schemes which typically require considerable application-specific efforts. Simulations illustrate that our method provides an excellent trade-off between computational efficiency and accuracy, under hypoellipticity, for both point and posterior estimation. Application to a neuroscience example shows the good performance of the method in challenging settings.