An Anchor Placement Approach in the Method of Anchored Distributions

• Activity Number: 363
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Yarong Yang*+ and Matt Over and Haruko Murakami and Yoram Rubin
• Companies: University of California at Berkeley and University of California at Berkeley and University of California at Berkeley and University of California at Berkeley
• Keywords: inversion ; Singular Value Decomposition ; likelihood ; Bayesian ; sensitivity

Abstract

The method of anchored distributions (MAD) is a general Bayesian inversion technique aimed at estimating the parameters in distributed-parameter fields. Anchors, the central element of MAD, are statistical distributions of the target parameters at specific locations, which are used to localize large-scale, indirect data. They are intended to capture the information contained in multi-type, multi-scale data that is relevant for the inversion and express it in terms of the dependent variables. It is important to work with a small number of anchors in order to reduce the dimensionality of the likelihood function, and to achieve that, anchors must be placed strategically. In this study we employ Singular Value Decomposition (SVD) of the sensitivity matrix, elements of which express the sensitivity of each data location to each potential anchor location, to identify such strategic locations. The locations selected by our proposed method are tested in synthetic studies. Comparison studies between inversion based on anchors placed at strategic locations vs. anchors placed at locations deemed less beneficial are discussed, showing the advantage of our proposed approach.