Abstract
This thesis focuses on the use of multilevel Monte Carlo methods to achieve optimal error versus cost performance for statistical computations in hidden Markov models as well as for unbiased estimation under four cases: nonlinear filtering, unbiased filtering, unbiased estimation of hessian, continuous linear Gaussian filtering.
Brief Biography
Fangyuan Yu is a Ph.D. student in the Statistics program at KAUST, his research focuses on Stochastic methods for filtering, Monte Carlo methodology, and Particle Filtering method, his supervisor is Professor Ajay Jasra. Before joining KAUST, he holds a master's degree from the National University of Singapore and a bachelor's degree from Shandong University.