Statistics Colloquia, 2007

## Department of Mathematics and Statistics, Dalhousie University

Statistics Colloquium Chair: Hong Gu

Unless otherwise indicated, the following location and time apply to all colloquium talks.

Location: Colloquium Room (Chase Building, Room 319)

Time: Thursday 3:30 to 4:30pm.

Date: Apr. 16, 2:30 to 3:30pm
Speaker: Prof. Rolf Turner, Department of Mathematics and Statistics, University of New Brunswick
Title: Direct Maximization of the Likelihood of a Hidden Markov Model.

Abstract: Hidden Markov models form a popular and versatile means of handling serial dependence in data. Ever since these models were introduced by Baum and his co-workers in about 1970, the method of choice for fitting them has been the EM (expectation/maximization) algorithm. This is due to the fact that the likelihood of a hidden Markov model is a bit hard to handle. Recently however a couple of authors have noticed that it is actually possible to calculate the Hessian of the log likelihood of a hidden Markov model, which suggests that one might simply maximize the likelihood by applying Newton's method.

I have implemented the calculations in R and tested out the idea on a couple of fairly complicated examples. Newton's method turns out to be insufficiently stable. However the Levenberg-Marquardt algorithm (which essentially interpolates between Newton's method and the method of steepest ascent) seems to work like a charm. A seven-fold increase in speed over the EM algorithm was achieved.

This talk will be aimed at non-specialists, so I will explain a bit about maximum likelihood, hidden Markov models, the EM algorithm, Levenberg-Marquardt, the two complicated models that I have fitted using this technique, and possibly Life, the Universe and Everything.

Date: March 29 3:30 to 4:30pm
Speaker: Grover, VK,
Title: Hardy-Weinberg Disequilibrium and its application in testing disease association
Authors: Grover, VK1, Cole, DEC2, Hamilton DC1

1 Department of Mathematics & Statistics, Dalhousie University

2 Departments of Laboratory Medicine & Pathobiology, Medicine, and Genetics (Paediatrics), University of Toronto

Abstract:

Hardy-Weinberg equilibrium (HWE) describes the relationship between gametic or allele frequencies, and the resulting genotypic frequencies. It holds under the assumptions of random mating, large population size, no mutation, migration or selection. There are several possible explanations for deviations from HWE including genotyping error, population stratification, selection bias, and admixture. Nielsen et al. (AJHG 1999;63:1531) showed that Hardy-Weinberg disequilibrium (HWD) at a marker locus is evidence for linkage disequilibrium (LD) between marker and disease-susceptibility loci as well as for heterogeneity of disease. They also found that the power to detect HWD was greater than the power to detect LD. Wittke-Thompson et al. (AJHG 2005;76:967) noted that HWD is expected at or near disease-susceptibility loci in the affected sub-population. Lee (Am J Epi 2003;158:397) proposed using HWD as a convenient tool for gene-searching. He found that fewer subjects were needed by the test for HWD than for the TDT and the LR test. In HWD tests, a problem arises if a multiplicative gene-dose effect is present because the HWD coefficient is then zero in the affecteds. In this talk we investigate the information resident in genotyping first and second degree relatives (sibs, parents and grand-parents) to determine if the additional data contained a tractable solution.

Link to the 2006 statistical colloquia

Link to the 2005 statistical colloquia