J. Martínek: Multilevel Sequential Monte Carlo for Bayesian Inverse Problems with Random Likelihoods скачать в хорошем качестве

J. Martínek: Multilevel Sequential Monte Carlo for Bayesian Inverse Problems with Random Likelihoods

In this talk we focus on Bayesian inverse problems in which the forward parameter-to-observable map is approximated by Monte Carlo (MC) simulations. Such problems often arise, for example, in uncertainty quantification of particle transport, where the parameter-to-observable map is defined through the solution of the Boltzmann equation. Approximating the likelihood with high accuracy requires MC simulations with many samples, which makes sampling from the posterior distribution expensive. We present an efficient method for sampling from the posterior based on pseudo-marginal sequential Monte Carlo (SMC) using tempering. To accelerate sampling from the posterior the method adopts a multilevel approach. A significant speedup is achieved compared to a single-level SMC using high-fidelity MC simulations while targeting the same posterior, which is demonstrated by numerical experiments.