| Abstract: |
| In this talk we focus on Bayesian inverse problems in which the forward parameter-to-observable map is approximated in a stochastic way, for instance by Monte Carlo (MC) simulations. Such problems 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 likelihood 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 achieving the same error, which is verified theoretically and demonstrated by numerical experiments. |
|