2014/12/15 by Alex Beskos, Beskos, Alex, Ajay Jasra +5 · 3 citations
Decision Sciences · Earth and Planetary Sciences · Environmental Science · #Computation (stat.CO) #FOS: Computer and information sciences #Groundwater flow and contamination studies #Probabilistic and Robust Engineering Design #Seismic Imaging and Inversion Techniques
paper · doi:10.48550/arxiv.1412.4459
openalex publication_date 2014/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we consider a Bayesian inverse problem associated to elliptic partial differential equations (PDEs) in two and three dimensions. This class of inverse problems is important in applications such as hydrology, but the complexity of the link function between unknown field and measurements can make it difficult to draw inference from the associated posterior. We prove that for this inverse problem a basic SMC method has a Monte Carlo rate of convergence with constants which are independent of the dimension of the discretization of the problem; indeed convergence of the SMC method is established in a function space setting. We also develop an enhancement of the sequential Monte Carlo (SMC) methods for inverse problems which were introduced in \citekantas; the enhancement is designed to deal with the additional complexity of this elliptic inverse problem. The efficacy of the methodology, and its desirable theoretical properties, are demonstrated on numerical examples in both two and three dimensions.