References¶
On the web¶
Software¶
All packages below implement RFT-based inference, and while they target primarily 3D field analysis, can also be applied to 1D/2D field analysis.
Literature¶
- Adler R, Hasofer A (1976). Level crossings for random fields. The Annals of Probability 4(1), 1–12.
- Adler RJ (1981). The Geometry of Random Fields. Wiley, New York.
- Adler RJ, Taylor JE (2007). Random Fields and Geometry. Springer, New York.
- Cao J (1999). The size of the connected components of excursion sets of X2, t and F fields. Advances in Applied Probability 31(3), 579–595.
- Cao J, Worsley KJ (1999). The detection of local shape changes via the geometry of Hotelling’s T2 fields. Annals of Statistics 27(3), 925–942.
- Carbonell F, Worsley KJ, Galan L (2011). The geometry of the Wilks’s Lambda random field. Annals of the Institute of Statistical Mathematics 63(1), 1–27.
- Friston K, Worsley K, Frackowiak R, Mazziotta J, Evans A (1994). Assessing the significance of focal activations using their spatial extent. Human Brain Mapping 1(3), 210–220.
- Friston KJ, Ashburner JT, Kiebel SJ, Nichols TE, Penny WD (Eds.) (2007) Statistical Parametric Mapping: The Analysis of Functional Brain Images. Elsevier, London.
- Hasofer A (1978). Upcrossings of random fields. Advances in Applied Probability 10, 14–21.
- Nichols T, Holmes A (2002). Nonparametric permutation tests for functional neuroimaging: a primer with examples. Human Brain Mapping 15(1), 1–25.
- Pataky TC (2015) RFT1D: Smooth One-Dimensional Random Field Upcrossing Probabilities in Python. Journal of Statistical Software (accepted for publication 18 April 2015).
- Taylor JE, Worsley KJ (2008). Random fields of multivariate test statistics, with applications to shape analysis. Annals of Statistics 36(1), 1–27.
- Worsley K, Taylor J, Tomaiuolo F, Lerch J. (2004). Unified univariate and multivariate random field theory. NeuroImage 23, S189–S195.
- Worsley K. (1994). Local maxima and the expected Euler characteristic of excursion sets of X2, F and t fields. Advances in Applied Probability 26(1), 13–42.