Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals
2018
In this article we develop a new sequential Monte Carlo method for multilevel Monte Carlo estimation.
In particular, the method can be used to estimate expectations with respect to a target
probability distribution over an infinite-dimensional and noncompact space—as produced, for example,
by a Bayesian inverse problem with a Gaussian random field prior. Under suitable assumptions
the MLSMC method has the optimal O(e
−2
) bound on the cost to obtain a mean-square error of
O(e
2
). The algorithm is accelerated by dimension-independent likelihood-informed proposals [T. Cui,
K. J. Law, and Y. M. Marzouk, (2016), J. Comput. Phys., 304, pp. 109–137] designed for Gaussian
priors, leveraging a novel variation which uses empirical covariance information in lieu of Hessian
information, hence eliminating the requirement for gradient evaluations. The efficiency of the algorithm
is illustrated on two examples: (i) inversion of noisy pressure measurements in a PDE model
of Darcy flow to recover the posterior distribution of the permeability field and (ii) inversion of noisy
measurements of the solution of an SDE to recover the posterior path measure.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
24
References
26
Citations
NaN
KQI