Random fields of multivariate test statistics, with applications to shape analysis

By Jonathan E. Taylor, Keith J. Worsley. 2008

100 citations recorded by the source corpus.

Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are nonzero using classical multivariate statistics evaluated at each point. The problem is to find the P-value of the maximum of such a random field of test statistics. We approximate this by the expected Euler characteristic of the excursion set. Our main result is a very simple method for calculating this, which not only gives us the previous result of Cao and Worsley [Ann. Statist. 27 (1999) 925-942] for Hotelling's T 2 , but also random fields of Roy's maximum root, maximum canonical correlations [Ann. Appl. Probab. 9 (1999) 1021-1057], multilinear forms [Ann. Statist. 29 (2001) 328-371], x 2 [Statist. Probab. Lett 32 (1997) 367-376, Ann. Statist. 25 (1997) 2368-2387] and x 2 scale space [Adv. in Appl. Probab. 33 (2001) 773-793]. The trick involves approaching the problem from the point of view of Roy's union-intersection principle. The results are applied to a problem in shape analysis where we look for brain damage due to nonmissile trauma.

Subfields: Applied Mathematics, Environmental Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fcefb3439887b7df64260498c391bec97f960086

How researchers see this paper

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

In Applied Mathematics

1. Tommaso Cai
2. Weidong Liu
3. Sayan Mukherjee
4. Omer Bobrowski

In Environmental Engineering

1. Sayan Mukherjee
2. Omer Bobrowski

In Geometry and Topology

1. Omer Bobrowski

Citations in the corpus

• The topology of probability distributions on manifolds (2013, background): “In topological data analysis, topological summaries of data are used to infer or extract underlying structure in the data [19, 22, 40, 49, 52].”
• SurfStat: A Matlab toolbox for the statistical analysis of univariate and multivariate surface and volumetric data using linear mixed effects models and random field theory (2009, unknown): “References: Adler, R (2007), '', Random fields and geometry, vol.”
• Two‐sample test of high dimensional means under dependence (2014, background): “See Cao and Worsley (1999) and Taylor and Worsley (2008).”