Text S1 Modeling mutual exclusivity of cancer mutations

Here, for convenience, the mutually mutated gene is specified by a vector of binary random variables H = (H1, . . . ,Hn), only one of which can be assigned value 1 at a time: P (Hg = 1) = 1 n , and Hg = 1 implies that Hg′ = 0 for all g ′ 6= g. To obtain P (y|θ), the observed likelihood for observation y (equation 1 in the main text), we need to marginalize the hidden variables out. This likelihood depends only on the number k of values 1 in this observation, its length n, and on the parameters θ, and will be shortly denoted fθ(k, n). Let d = δ(1− β) + (1− δ)α.