Biometrika Advance Access published online on February 6, 2007
Biometrika, doi:10.1093/biomet/asm004
| ||||||||||||||||||||||||||||||||||||||||||||||||||||
Maxima of discretely sampled random fields, with an application to ‘bubbles’
Department of Statistics, Stanford University, Stanford, California 94305-4065, U.S.A
Department of Mathematics & Statistics, McGill University, Montréal, Québec, Canada H3A 2K6
Département de Psychologie, Université de Montréal, Montréal, Québec, Canada H3 C 3 J7
jonathan.taylor{at}stanford.edu
keith.worsley{at}mcgill.ca
frederic.gosselin{at}umontreal.ca
Received for publication 1 March 2005.
Revision received 1 June 2006.
 |
Abstract |
|---|
A smooth Gaussian random field with zero mean and unit variance is sampled on a discrete lattice, and we are interested in the exceedance probability or P-value of the maximum in a finite region. If the random field is smooth relative to the mesh size, then the P-value can be well approximated by results for the continuously sampled smooth random field (Adler, 1981; Worsley, 1995a; Taylor & Adler, 2003; Adler & Taylor, 2007). If the random field is not smooth, so that adjacent lattice values are nearly independent, then the usual Bonferroni bound is very accurate. The purpose of this paper is to bridge the gap between the two, and derive a simple, accurate upper bound for intermediate mesh sizes. The result uses a new improved Bonferroni-type bound based on discrete local maxima. We give an application to the ‘bubbles’ technique for detecting areas of the face used to discriminate fear from happiness.
Key Words: Bonferroni • Bubbles • Euler characteristic • Random field
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  D. D. Cox and J. S. Lee Pointwise testing with functional data using the Westfall-Young randomization method Biometrika, September 1, 2008; 95(3): 621 - 634. [Abstract] [PDF]
|
|