Some new random field tools for spatial analysis
By Robert J. Adler. 2008
55 citations recorded by the source corpus.
This is a brief review, in relatively non-technical terms, of recent rather technical advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric characteristics of excursion sets of random fields, such as their volume, surface area and Euler characteristics. What is particularly important in these formulae is that whereas the previous theory covered only stationary, Gaussian random fields, the new theory requires neither stationarity nor, a fortiori, isotropy. Furthermore, it covers a wide class of non-Gaussian random fields. The formulae provided by these advances have a wide range of potential applications, including new techniques of parameter estimation, model testing, and thresholding for spatial and space-time functions. The paper reviews this theory, and provides brief descriptions of some of the applications.
Subfields: Building and Construction, Environmental Engineering
View Paper: https://www.semanticscholar.org/paper/b79e65ff0c4770f7b4c5b2dacb54cdce6d9ee90e
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In Building and Construction
In Environmental Engineering
Citations in the corpus
- Spatio-temporal exceedance locations and confidence regions (2013, methodology): “…approach to determining this threshold utilizes the theory of random fields [Adler (2010), Adler and Taylor (2007)] and the expected Euler characteristic [Taylor, Worsley and Gosselin (2007), Adler (2008)] to determine the probability that the maximum test statistic is greater than some threshold.”