Exact Computation of Coalescent Likelihood under the Infinite Sites Model

Coalescent likelihood is the probability of observing the given population sequences under the coalescent model. Computation of coalescent likelihood under the infinite sites model is a classic problem in coalescent theory. Existing methods are based on either importance sampling or Markov chain Monte Carlo. In this paper, we develop a simple method that can compute the exact coalescent likelihood for many datasets of moderate size, including a real biological data whose likelihood was previously thought to be difficult to compute exactly. Simulations demonstrate that the practical range of exact coalescent likelihood computation is significantly larger than what was previously believed.