Multilevel Sequential Monte Carlo Samplers

Understand

In this article we consider the approximation of expectations w.r.t.

• probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems.
• In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with the step-size level $h_L$.
• In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods.