Fast and accurate calculation of a computationally intensive statistic for mapping disease genes

Many statistical methods in biology utilize numerical integration in order to deal with moderately high-dimensional parameter spaces without closed form integrals. One such method is the PPL, a class of models for mapping and modeling genes for complex human disorders. While the most common approach to numerical integration in statistics is MCMC, this is not a good option for the PPL for a variety of reasons, leading us to develop an alternative integration method for this application. We utilize an established sub-region adaptive integration method, but adapt it to specific features of our application. These include division of the multi-dimensional integrals into three separate layers, implementing internal constraints on the parameter space, and calibrating the approximation to ensure adequate precision of results for our application. The proposed approach is compared with an empirically driven fixed grid scheme as well as other numerical integration methods. The new method is shown to require far fewer function evaluations compared to the alternatives while matching or exceeding the best of them in terms of accuracy. The savings in evaluations is sufficiently large that previously intractable problems are now feasible in real time.