Quasi-Monte Carlo method in population genetics parameter estimation

The computations of likelihood or posterior distribution of parameters of complex population genetics models are common tasks in computational biology. The numerical results of these approaches are often found by Monte Carlo simulations. Much of the recent work of Monte Carlo approaches to population genetics problems has used pseudorandom sequences. This paper explores alternatives to these standard pseudorandom numbers and considers the use of uniform random sequences, more specifically, uniformly distributed sequences (quasi-random numbers) to calculate the likelihood. We demonstrate by examples that quasi-Monte Carlo can be a viable alternative to the Monte Carlo methods in population genetics. Analysis of a simple two-population problem in this paper shows that parallel quasi-Monte Carlo methods achieve the same or better parameter estimates as standard Monte Carlo and have the potential to converge faster and so reduce the computational burden.