On the web


All packages below implement RFT-based inference, and while they target primarily 3D field analysis, can also be applied to 1D/2D field analysis.


  1. Adler R, Hasofer A (1976). Level crossings for random fields. The Annals of Probability 4(1), 1–12.

  2. Adler RJ (1981). The Geometry of Random Fields. Wiley, New York.

  3. Adler RJ, Taylor JE (2007). Random Fields and Geometry. Springer, New York.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. Friston KJ, Ashburner JT, Kiebel SJ, Nichols TE, Penny WD (Eds.) (2007) Statistical Parametric Mapping: The Analysis of Functional Brain Images. Elsevier, London.

  9. Hasofer A (1978). Upcrossings of random fields. Advances in Applied Probability 10, 14–21.

  10. Nichols T, Holmes A (2002). Nonparametric permutation tests for functional neuroimaging: a primer with examples. Human Brain Mapping 15(1), 1–25.

  11. Pataky TC (2015) RFT1D: Smooth One-Dimensional Random Field Upcrossing Probabilities in Python. Journal of Statistical Software (accepted for publication 18 April 2015).

  12. Taylor JE, Worsley KJ (2008). Random fields of multivariate test statistics, with applications to shape analysis. Annals of Statistics 36(1), 1–27.

  13. Worsley K, Taylor J, Tomaiuolo F, Lerch J. (2004). Unified univariate and multivariate random field theory. NeuroImage 23, S189–S195.

  14. 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.