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Explore advanced computational methods for solving Bayesian inverse problems where the forward parameter-to-observable map requires Monte Carlo approximations in this one-hour conference talk. Learn how to address the computational challenges that arise when high-accuracy likelihood approximations demand extensive Monte Carlo simulations with many samples, making posterior distribution sampling computationally expensive. Discover an efficient sampling method based on pseudo-marginal sequential Monte Carlo (SMC) with tempering that incorporates a multilevel approach to accelerate posterior sampling. Examine how this multilevel strategy achieves significant speedup compared to single-level SMC methods using high-fidelity Monte Carlo simulations while maintaining the same posterior target. Understand the practical applications of these techniques in uncertainty quantification problems, particularly in particle transport scenarios where parameter-to-observable maps are defined through Boltzmann equation solutions. Review numerical experiments that demonstrate the effectiveness and computational advantages of the proposed multilevel sequential Monte Carlo approach for Bayesian inverse problems with random likelihoods.
