Bayesian Inference for Partially Observed Continuous-Time Processes
This thesis develops Bayesian inference methods for partially observed stochastic differential equations (SDEs) with unknown parameters, focusing on the stochastic Volterra equation (SVE), non-synchronous diffusions, and McKean-Vlasov SDEs. Employing Euler-Maruyama discretization.
Overview
We introduce a novel approach combining Particle Markov Chain Monte Carlo (MCMC) within the Multilevel Monte Carlo (MLMC) framework. Our method constructs approximate posterior couplings for joint parameter and hidden variable distributions at adjacent discretization levels, corrected via importance sampling. The proposed multilevel MCMC demonstrates superior computational efficiency over single-level methods, achieving specified mean square error (MSE) at significantly lower cost. Contributions span theoretical analysis, algorithmic innovation, and applications.
Presenters
Brief Biography
Amin Wu is an Ph.D. candidate in Statistics at the King Abdullah University of Science and Technology (KAUST), working in Stochastic Numerics Research Group under the supervision of Professor Raul Tempone. Before joining KAUST, Wu obtained a bachelor's degree from the Communication University of China.
