Bases: nipy.algorithms.statistics.rft.ChiSquared
Bases: nipy.algorithms.statistics.rft.ECcone
EC densities for a Chi-Squared(n) random field.
Bases: nipy.algorithms.statistics.rft.IntrinsicVolumes
A class that takes the intrinsic volumes of a set and gives the EC approximation to the supremum distribution of a unit variance Gaussian process with these intrinsic volumes. This is the basic building block of all of the EC densities.
If product is not None, then this product (an instance of IntrinsicVolumes) will effectively be prepended to the search region in any call, but it will also affect the (quasi-)polynomial part of the EC density. For instance, Hotelling’s T^2 random field has a sphere as product, as does Roy’s maximum root.
Bases: numpy.lib.polynomial.poly1d
A subclass of poly1d consisting of polynomials with a premultiplier of the form
(1 + x^2/m)^-exponent
where m is a non-negative float (possibly infinity, in which case the function is a polynomial) and exponent is a non-negative multiple of 1/2.
These arise often in the EC densities.
Bases: nipy.algorithms.statistics.rft.ECcone
EC densities for a F random field.
Bases: nipy.algorithms.statistics.rft.ECcone
Hotelling’s T^2: maximize an F_{1,dfd}=T_dfd^2 statistic over a sphere of dimension k.
Bases: nipy.algorithms.statistics.rft.ECcone
Maximize a multivariate Gaussian form, maximized over spheres of dimension dims. See
Kuri, S. & Takemura, A. (2001). ‘Tail probabilities of the maxima of multilinear forms and their applications.’ Ann, Statist. 29(2): 328-371.
Bases: nipy.algorithms.statistics.rft.ECcone
EC densities for one-sided F statistic in
Worsley, K.J. & Taylor, J.E. (2005). ‘Detecting fMRI activation allowing for unknown latency of the hemodynamic response.’ Neuroimage, 29,649-654.
Bases: nipy.algorithms.statistics.rft.ECcone
Roy’s maximum root: maximize an F_{dfd,dfn} statistic over a sphere of dimension k.
Bases: nipy.algorithms.statistics.rft.ECcone
EC densities for a t random field.
If dfd == inf (the default), then Q(dim) is the (dim-1)-st Hermite polynomial
H_j(x) = (-1)^j * e^{x^2/2} * (d^j/dx^j e^{-x^2/2})
If dfd != inf, then it is the polynomial Q defined in
Worsley, K.J. (1994). ‘Local maxima and the expected Euler characteristic of excursion sets of chi^2, F and t fields.’ Advances in Applied Probability, 26:13-42.
Return mu_j(S_r(R^n)), the j-th Lipschitz Killing curvature of the sphere of radius r in R^n.
From Chapter 6 of
Adler & Taylor, ‘Random Fields and Geometry’. 2006.
Work out intrinsic volumes of region x interval in the scale space model. See
Siegmund, D.O and Worsley, K.J. (1995). ‘Testing for a signal with unknown location and scale in a stationary Gaussian random field.’ Annals of Statistics, 23:608-639.
and
Taylor, J.E. & Worsley, K.J. (2005). ‘Random fields of multivariate test statistics, with applications to shape analysis and fMRI.’
(available on http://www.math.mcgill.ca/keith