Approximations for weighted Kolmogorov-Smirnov distributions via boundary crossing probabilities

A statistical application to Gene Set Enrichment Analysis implies calculating the distribution of themaximum of a certain Gaussian process, which is a modification of the standard Brownian bridge. Using the transformation into a boundary crossing problem for the Brownian motion and a piecewise linear boundary, it is proved that the desired distribution can be approximated by an n-dimensional Gaussian integral. Fast approximations are defined and validated by Monte Carlo simulation. The performance of the method for the genomics application is discussed.