On excursion sets, tube formulas and maxima of random fields

By Robert J. Adler. 2000

233 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering, Signal Processing

View Paper: https://www.semanticscholar.org/paper/a569aab8734ff45b1f41b270dfcbf37a664f4046

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Environmental Engineering

In Signal Processing

Citations in the corpus

On Oceanic Rogue Waves (2015, methodology): “In this regime, the statistics of extreme waves can be described with the Tayfun (1980) model coupled with AdlerTaylor (2009) theory on the Euler-characteristics of random fields.”
False Discovery Control for Random Fields (2004, methodology): “Using inequality (1.1.7) of Adler (2000), ( 1 − 1 z2 ) ϕ(z) z ≤ (1 − (z)) ≤ ϕ(z) z , we get the conditions −bz π l2 + √ b π pl + e z ≤ 0 for e ≥ 0, and −bz π l2 + √ b π pl + ( 1 − 1 z2 ) e z ≤ 0 for e 0.”
Topological complexity of smooth random functions (2011, background): “[4,8,9,74,87, 89, 90] with an excellent introductory review in [88]).”
An informational approach to the global optimization of expensive-to-evaluate functions (2006, unknown): “However, no tractable analytical expression for pX∗|fS (x) is available [ 2 ,19].”
Validity of the expected Euler characteristic heuristic (2005, unknown): “Referring to (4), certainly not every smooth Gaussian process of interest is isotropic, nor are the conditions required of M easily interpretable (cf. Definition 4.5.1 in [ 3 ]).”
A gaussian kinematic formula (2006, methodology): “A heuristic justification of the above approximation can be found in [2, 6], with a rigorous justification in [17].”
Random fields of multivariate test statistics, with applications to shape analysis (2008, methodology): “In an unpublished manuscript by Sun (referenced in Adler [ 2 ]), it was generalized to include more general boundary cases.”
Statistical analysis of fNIRS data: A comprehensive review (2014, unknown): “(44) is the so-called " Possion clumping heuristics " saying that, for a large threshold value u, the excursion set usually has one cluster (i.e. EC value becomes one) without holes; so the mean value is a good approximation of the excursion probability (Adler, 2000; Adler and Taylor, 2007).”
Extreme Value Analysis: an Introduction (2013, methodology): “In addition, Adler (2000) and Azaïs and Wschebor (2009) are mainly dedicated to level sets and extrema of Gaussian random ﬁelds.”
Sparse Shape Representation using the Laplace-Beltrami Eigenfunctions and Its Application to Modeling Subcortical Structures (2012, methodology): “For RFT to work, the Gaussianness and smoothness of data are needed [1, 35].”
NIRS-SPM: statistical parametric mapping for near infrared spectroscopy (2008, unknown): “The expected EC approach has been extensively studied by Adler ( Adler, 1981, 2000; Adler and Taylor, 2007), Worsley (Worsley, 1994, 1995; Cao and Worsley, 1999b) and more recently by Taylor et al.”
ON THE EQUIVALENCE OF THE TUBE AND EULER CHARACTERISTIC METHODS FOR THE DISTRIBUTION OF THE MAXIMUM OF GAUSSIAN FIELDS OVER PIECEWISE SMOOTH DOMAINS (2002, methodology): “General discussion on this equivalence was given in a recent paper by Adler (2000) .”