Understanding the process of rapid molecular adaptation is important for many key challenges humanity faces today, such as the evolution of pesticide and drug resistance. Our standard population genetic model for describing rapid molecular adaption is the selective sweep, in which a previously rare or absent allele is quickly driven to fixation by positive selection. Selective sweeps can be distinguished into hard sweeps, where a single adaptive mutation arises in the population and then goes to fixation, and soft sweeps, where several adaptive mutations at the same locus rise in the population simultaneously. These soft sweeps can occur either because the adaptive alleles were already present as standing genetic variation (SGV) at the onset of positive selection, or because they arose independently from recurrent de novo mutation (RDN). In this thesis, I develop an Approximate Bayesian Computation (ABC) approach to study whether we can distinguish these different sweep types and infer their evolutionary parameters from the shape of the local coalescence tree at the sweep locus. I demonstrate that my method can reliably infer the selection coefficient and softness of a sweep under various parameter settings. I further show how my method can be used with Bayes factors for differentiating between soft sweeps from SGV and those from RDN, as well as from neutral selection. These findings demonstrate that the local coalescence tree at a sweep locus contains valuable information on the parameters of the sweep and motivates further studies that aim to infer such trees from real population genomic data through reconstruction of ancestral recombination graphs.