Department of Mathematics & Statistics, McGill University
Room I1.09 (I block, 1st floor), University of Waikato
The analysis of heritability, through the intraclass correlation coefficient, has a long history in statistics, dating back over 100 years. We have recently acquired data from MRI images of the brains of identical and non-identical twins and we want to know what parts of the brain are heritable. In other words, we wish to calculate the old-fashioned heritability coefficient at every point in a 3D image. The challenge is how to deal with this new type of data - the heritability random field. We use some new results on the geometry of random fields to set a threshold for these fields that allows us to detect those parts of the brain that are inherited, and those that are not. Along the way, I'll look at generalised linear models for image data, local multidimensional scaling, and the Nash Embedding Theorem.