A collaborative paper titled Bayesian Parameter Inference for Partially Observed Diffusions using Multilevel Stochastic Runge-Kutta Methods by Professor Pierre Del Moral, Foreign Academic Fellow of the Base, Professor Shulan Hu and Associate Professor Xinyu Wang, both Researchers of the Base, has been published in International Journal for Uncertainty Quantification, a prestigious academic journal.

Abstract: 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.

Keywords: Bayesian inference/ diffusions/ multilevel Monte Carlo/ Runge-Kutta

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

Author profile

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.

Shulan Hu, Professor and Ph.D. Supervisor, Zhongnan University of Economics and Law; Director of the Research Center for Digital Intelligence Development; Researcher at the Base for Introducing Talents in Digital Technology and Modern Finance Discipline Innovation; First Batch of Wenlan Young Scholars; Director of the Resource and Environment Branch of the Chinese Association for Applied Statistics; Director of the Big Data Branch; Director of the Hubei Provincial Association for Applied Statistics; Member of the Hubei Provincial Technical Committee for Data Standardization. "Double-Qualified" Tutor of the Second Batch of Industry-Education Integration Training Bases of CCB College. She once served as Deputy General Manager of the Financial Technology Department and Financial Accounting Department (Digitalization Office) of China Construction Bank Hubei Branch on secondment.Research Interests: Theory of Stochastic Algorithms for Big Data and its Applications; Financial Risk Modeling, Econometrics; Development and Utilization of Data Circulation, Data Asset/Product Evaluation Models, Data Standards.She has presided over and completed multiple projects including the National Natural Science Foundation of China and the National Social Science Foundation of China. She has also presided over more than 20 projects such as those of Central Universities, Graduate Case Bank Projects, Quality Course Projects, All-English Course Construction Projects, MBA Case Bank Projects, and Enterprise Horizontal Projects. She has published more than 30 papers in renowned domestic and foreign journals, published 1 national-level "14th Five-Year Plan" textbook and 1 monograph, guided students to win more than 30 national-level awards in various competitions, and participated in the formulation of multiple data resource-related standards.

Xinyu Wang, Associate Professor and Master's Supervisor, Zhongnan University of Economics and Law.Research Interests: Big Data Statistical Analysis; Theory of Stochastic Algorithms; Applications of Stochastic Processes and Stochastic Analysis in Economics and Finance.He has published more than 20 papers in authoritative domestic and foreign journals such as 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, and Acta Mathematica Sinica.