We develop a method to analyse the effect of an asymmetric supernova on hierarchical multiple star systems and present analytical formulas to calculate orbital parameters for surviving binaries or hierarchical triples and runaway velocities for their dissociating equivalents. The effect of an asymmetric supernova on the orbital parameters of a binary system has been studied to a great extent, but this effect on higher multiplicity hierarchical systems has not been explored before. With our method, the supernova effect can be computed by reducing the hierarchical multiple to an effective binary by means of recursively replacing the inner binary by an effective star at the centre of mass of that binary. We apply our method to a hierarchical triple system similar to the progenitor of PSR J1903+0327 suggested by Portegies Zwart et al. We confirm their earlier finding that PSR J1903+0327 could have evolved from a hierarchical triple that became unstable and ejected the secondary star of the inner binary. Furthermore, if such a system did evolve via this mechanism the most probable configuration would be a small supernova kick velocity, an inner binary with a large semi-major axis, and the fraction of mass accreted on to the neutron star to the mass lost by the secondary most likely be between 0.35 and 0.5.

We have coupled a fast, parametrized star cluster evolution code to a Markov Chain Monte Carlo code to determine the distribution of probable initial conditions of observed star clusters, which may serve as a starting point for future N -body calculations. In this paper we validate our method by applying it to a set of star clusters which have been studied in detail numerically with N -body simulations and Monte Carlo methods: the Galactic globular clusters M4, 47 Tucanae, NGC 6397, M22, ω Centauri, Palomar 14 and Palomar 4, the Galactic open cluster M67, and the M31 globular cluster G1. For each cluster we derive a distribution of initial conditions that, after evolution up to the cluster's current age, evolves to the currently observed conditions. We find that there is a connection between the morphology of the distribution of initial conditions and the dynamical age of a cluster and that a degeneracy in the initial half-mass radius towards small radii is present for clusters which have undergone a core collapse during their evolution. We find that the results of our method are in agreement with N -body and Monte Carlo studies for the majority of clusters. We conclude that our method is able to find reliable posteriors for the determined initial mass and half-mass radius for observed star clusters, and thus forms an suitable starting point for modeling an observed cluster's evolution.