Supporting Text: Probabilistic Inference of Mutational Pro- cesses and their Localisation in the Cancer Genome

1 Derivation of the EM algorithm for mutation spectra 1.1 The generative model The EM algorithm presented in this work is an application of the method first described in [1]. The starting point of the derivation is the conditional data likelihood, i.e. the probability of observed data (the mutation countsX), conditional on both hidden data (the process activities x) and the model parameters (the mutation spectra μ). The mutations are produced jointly by n independent Poisson processes, such that the Poisson rate for the joint process is the sum of the individual rates.