The Hardy-Weinberg law is of basic importance in studying biological systems, and it is important to be able to determine if a population is in Hardy-Weinberg equilibrium. For finite populations, this means testing if they are a draw from a distribution known as Hardy-Weinberg proportions. Because the state space is exponentially large in the population size, the only efficient means for doing this is Monte Carlo simulation. Here we explore three different Monte Carlo techniques for this problem. To begin, we give the first linear time algorithm for generating random variates exactly from the desired distribution in the absence of extra constraints such as structural zeros. Second, we build and test Markov chains for this problem that work in the presence of structural zeros. Finally, we design and explore the behavior of a sequential importance sampling technique.

Keywords: Hardy-Weinberg; Monte Carlo; Direct Sampling; Exact p-value; Sequential Importance Sampling; Grobner Basis

The manuscript is available in PDF format.