| Abstract: |
| In this talk, we introduce a sequential Monte Carlo (SMC-GM) algorithm equipped with a Gaussian mixture transition kernel. This algorithm is designed to improve the efficiency of sampling from the posterior measure in infinite-dimensional Bayesian inverse problems. We establish the denseness of Gaussian mixture measures with respect to the total variation distance in separable Hilbert spaces, which serves as the foundation for our convergence theory. Additionally, we propose a well-defined preconditioned Crank-Nicolson method with a Gaussian mixture prior (pCN-GM) for use in infinite-dimensional function spaces. By leveraging the denseness of Gaussian mixture measures and the invariance of the pCN-GM transition kernel, we provide a convergence theorem for SMC-GM. In our numerical experiments, we apply this method to a nonlinear Darcy flow statistical inverse problem, confirming its high sampling efficiency, low error, capability to sample complex posteriors, and dimension-independence. |
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