基地国外学术骨干Pierre Del Moral教授、基地研究员胡淑兰教授、基地研究员王新宇副教授的合作论文“Bayesian Parameter Inference for Partially Observed Diffusions using Multilevel Stochastic Runge-Kutta Methods”在重要学术期刊International Journal for Uncertainty Quantification发表。

摘要：We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up to an unbiased estimator and that one must time-discretize the diffusion process. In such scenarios it has been shown how one can introduce the multilevel Monte Carlo method to reduce the cost to compute posterior expected values of the parameters for a prespecified mean square error (MSE). These aforementioned methods rely on the Euler-Maruyama discretization scheme which is well known in numerical analysis to have slow convergence properties. We adapt stochastic Runge-Kutta (SRK) methods for Bayesian parameter estimation of static parameters for diffusions. This can be implemented in high dimensions of the diffusion and is seemingly underappreciated in the uncertainty quantification and statistics fields. For a class of diffusions and SRK methods, we consider the estimation of the posterior expectation of the parameters. We prove that to achieve a MSE of O(ε2), for ε>0 given, the associated work is O(ε-2). While the latter is achievable for the Milstein scheme, this method is often not applicable for diffusions in dimension larger than two. We also illustrate our methodology in several numerical examples.

关键词：Bayesian inference, diffusions, multilevel Monte Carlo, Runge-Kutta

论文链接：https://www.dl.begellhouse.com/journals/52034eb04b657aea,7d756a8451ff2381,147a39c80f960173.html

教师简介

Pierre Del Moral is INRIA Research Director and Professor at the University of Bordeaux and at the Ecole Polytechnique in Paris. He obtained the Master of Science in Pure Mathematics and Ph.D. in signal processing at the LAAS-CNRS of Toulouse, France. He is one of the principal designers of the modern theory on particle methods in filtering, rare-event estimation and financial modeling. He has been visiting professor at Purdue University and Princeton University.

胡淑兰，中南财经政法大学教授、博士生导师，数智发展研究中心主任，数字技术与现代金融学科创新引智基地研究员，首届文澜青年学者，中国现场统计学会资源与环境分会理事，大数据分会理事，湖北省现场统计学会理事，湖北省数据标准化技术委员。建行学院第二批产教融合实训基地“双师型”导师。曾挂职于建设银行湖北省分行金融科技部、财务会计部（数字化办）副总经理。研究方向：大数据随机算法理论及其应用；金融风险建模、经济计量学；数据流通开发利用、数据资产/产品评估模型、数据标准。主持完成多项国家自然科学基金、国家社会科学基金等。主持完成中央高校、研究生案例库项目、精品课程项目、全英文课程建设项目、MBA 案例库、企业横向课题等二十多项课题。在国内外知名期刊发表论文30多篇，出版全国“十四五”规划教材1部、著作1部，指导获国家级各类竞赛奖项30余项，参与多项数据资源相关标准制定。

王新宇，中南财经政法大学副教授、硕士生导师。研究方向：大数据统计分析、随机算法理论、随机过程与随机分析在经济金融中的应用。在《Bernoulli》《Mathematics of Computation》《Discrete and Continuous Dynamical Systems》《International Journal for Uncertainty Quantification》《Stochastic and Dynamics》《Acta Applicandae Mathematicae》《Acta Mathematica Scientia》《 Statistics & Probability Letters》《数学学报》等国内外权威期刊发表论文20余篇。