Sequential Monte Carlo methods for Bayesian elliptic inverse problems
Sequential Monte Carlo methods for Bayesian elliptic inverse problems
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DOI：
10.1007/s11222-015-9556-7
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发表时间：
2014-12
影响因子：
2.2
通讯作者：
A. Beskos;A. Jasra;Ege A. Muzaffer;A. Stuart
中科院分区：
文献类型：
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作者：
A. Beskos;A. Jasra;Ege A. Muzaffer;A. Stuart
在这篇文章中，我们考虑了一个贝叶斯反问题的椭圆型偏微分方程在二维和三维。这类反问题在水文学等应用中很重要，但未知场与测量值之间的联系函数的复杂性可能使其难以从相关的后验中得出推论。我们证明，对于这个反问题的一个基本的顺序蒙特卡罗（SMC）方法具有Monte Carlo收敛速度与常数是独立的尺寸的离散化的问题，确实收敛的SMC方法建立在一个函数空间设置。我们还开发了在Kantas等人（SIAM/阿萨J Uncertain Quantif 2：464-489，2014）中引入的用于逆问题的SMC方法的增强;该增强被设计用于处理该椭圆逆问题的额外复杂性。该方法的有效性和理想的理论性能，证明了数值例子在两个和三个维度。
In this article, we consider a Bayesian inverse problem associated to elliptic partial differential equations 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 sequential Monte Carlo (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 SMC methods for inverse problems which were introduced in Kantas et al. (SIAM/ASA J Uncertain Quantif 2:464–489, 2014); 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 for numerical examples in both two and three dimensions.