  We present the first application of a Nested Sampling algorithm to explore
the high-dimensional phase space of particle collision events. We describe the
adaptation of the algorithm, designed to perform Bayesian inference
computations, to the integration of partonic scattering cross sections and the
generation of individual events distributed according to the corresponding
squared matrix element. As a first concrete example we consider gluon
scattering processes into 3-, 4- and 5-gluon final states and compare the
performance with established sampling techniques. Starting from a flat prior
distribution Nested Sampling outperforms the Vegas algorithm and achieves
results comparable to a dedicated multi-channel importance sampler. We outline
possible approaches to combine Nested Sampling with non-flat prior
distributions to further reduce the variance of integral estimates and to
increase unweighting efficiencies.
