This lecture is concerned with probability models for distance matrices, which are non-negative symmetric matrices of negative type. Several families of distributions are considered, including Wishart distance matrices and Mahalanobis distance matrices, all derived ultimately from Gaussian matrices by marginalization. The likelihood functions are obtained in a relatively straightforward manner without an explicit representation of the joint density. Some elementary applications are described, including maximum-likelihood estimation of phylogenetic trees, and maximum likelihood estimation of genealogical trees. If time permits, I will discuss various ways in which distance models may be used for the analysis of exchangeable arrays, such as micro-arrays, with rows indexed by individuals and columns by genes or sites.
- This lecture is part of the Department of Statistics Annual Bradley Lecture Series. Please see the Bradley Lecture webpage for more details.