Approximations for weighted Kolmogorov-Smirnov distribution via boundary crossing probabilities.

Abstract: 

A statistical application to Gene Set Enrichment Analysis implies calculating the distribution of the maximum of a Gaussian process, which is a modification of the standard Brownian bridge. It is proved that the distribution of interest can be approximated by multi-dimensional Gaussian integrals using the transformation into a boundary crossing problem for Brownian motion and piecewise linear boundaries.  The results of Monte Carlo simulation validating the approximations will be discussed.