Dr Robb Muirhead
Part 1: Consider a random rotation of a fixed point on a unit sphere in p-dimensions, where p is at least 3. For example, regard the earth as a unit sphere in 3 dimensions. You are standing near the Sydney Opera House, and the next thing you know you find yourself in Tahiti. A move to Tahiti from Sydney may be viewed as an orthogonal transformation, represented by a 3 × 3 orthogonal matrix. If this orthogonal matrix is random and uniformly distributed (I will explain what I mean by this), you could have ended up anywhere in the sense that your location is uniformly distributed on the surface of the unit sphere. Now, suppose that the same orthogonal matrix is used to move you again to a new place on the unit sphere. What can you say about where you are now? Have you moved back closer to Sydney, or further away, or could you still be anywhere? And what if this keeps happening to you, again and again?
Part 2: Here is a simply worded statistical problem, but one for which a really satisfactory solution seems elusive. Given a random sample from a k-variate normal distribution with unknown mean vector and unknown covariance matrix, produce a confidence interval for the maximum component of the mean vector. I will motivate this problem by describing what a regulatory pharmaceutical guidance says should be done when analyzing data collected in a thorough “QT study”, and describe an approach which works well in some circumstances. Q and T are two points on an electrocardiogram (ECG or EKG, depending on where you live), and the duration of the interval between them, the ‘QT interval’, represents the working phase of the heart – when the heart is contracting. In the pharmaceutical industry, studies that indicate significant QT prolongation are often sufficient for a company to discontinue development of a compound.
About the speaker: Dr Robb Muirhead is Senior Director, Statistical Research and Consulting Center, Pfizer Global R&D (leading health products company), in New London, Connecticut (USA). He was previously a Professor at The University of Michigan and at Yale University. His main research interests are multivariate statistical analysis, statistical modeling, Bayesian statistics, and pharmaceutical statistics.
Dr Robb Muirhead
Pfizer Global R&D (USA)
Thu, 14/10/2010 - 3:00pm