Rice University logoGeorge R. Brown School of Engineering

Thomas Lumley
University of Auckland

Hypothesis tests based on large quadratic forms 

When a set of n component tests is combined using a weight matrix other than the inverse of their covariance matrix, the natural large-sample approximation to the distribution is a quadratic form in Gaussian variables.  There are three classes of existing ways to evaluate tail probabilities for this distribution: approximations based on matching moments, a saddlepoint approximation, and essentially exact methods based on infinite series. For many purposes all of these are satisfactory. However, when extreme tail probabilities are required, as in DNA resequencing studies, all the existing methods that are sufficiently accurate take n^3 time.  With modern DNA resequencing projects reaching 10,000 participants and interest in tests combining as many as 10,000-100,000 variants, these methods are prohibitively slow.  I will present a new approximation based on a low-rank approximate SVD, and explain why it is both fast and accurate.  

*Join us for light refreshments and meet our guest from 3:45 to 4:00 in the lobby of Duncan Hall. The colloquium begins at 4:00 and ends at 5:00. Open to the general public.  

Monday, September 26, 2016
4:00 PM to 5:00 PM 
Duncan Hall, RM1070