Amin Wu successfully defended her PhD Thesis

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Abstract:

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, we introduce a novel approach combining Markov Chain Monte Carlo (MCMC) Andrieu et al. (2010) 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.

Advisors:

Prof. Ajay Jasra, and Prof. Raúl Tempone

Committee Members:

Prof. Hernando Ombao (KAUST), Prof. Diogo Gomes (KAUST), and Prof. David Nott (National University of Singapore)