| Statistical Programs |
| College of Agriculture | University of Idaho |
| Seminar Announcement |
|
"Applied Statistics in Agriculture" |
|
No BLUE Among Phylogenetic
Estimators
Presented By |
| Dr. Paul Joyce |
|
Deptartment of Mathematics University of Idaho |
|
Tuesday, 3:30 P. M. Ag. Science 204 |
|
Multivariate analysis is a branch of statistics that
successfully exploits the powerful tools of linear algebra
to obtain a fairly comprehensive theory of estimation. The
purpose of this talk is to explore to what extent a linear
theory of estimation can be developed in the context of
coalescent models used in the analysis of DNA polymorphism.
We consider a large class of coalescent models. In the
process we discover several limitations to linear estimators
that are quite distinct from the classical theory. In
particular, there does not exist a BLUE (best linear unbiased
estimator) for the mutation rate, under the assumptions of
the neutral model of evolution. In fact, no linear estimator
performs uniformly better than the Watterson (1975) method
based on a simple statistic that requires no information on
the genealogy of the sample. For certain coalescent models,
the Watterson estimator is actually optimal. The general conclusion is the following. If genealogical information is useful for estimating the rate of evolution, then there is no optimal linear method. If there is an optimal linear method, then no genealogical information is needed. |
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