University of Washington - Department of Statistics
What is Phase II of the Human Genome Project? How many Paleo-Amerindians crossed the Bering land bridge? Where did the salmon in Lake Washington come from? How many different genes control the onset of Alzheimer's disease? Why is Statistical Genetics relevant to these and many other questions? What are the opportunities in Statistical Genetics? -- as a student, and beyond -- at UW, and beyond.
Maximum Likelihood Estimation For Parametric Dispersal Models
The direction and distance that an individual travels between its birth and the time it reproduces is an important demographic parameter. Estimates of the distribution characterizing this movement are important in understanding the fine scale genetic structure of a population and the ecological factors that are relevant to its persistence. In addition to conservation of populations, understanding these factors can aid in gauging the impact of the release of genetically engineered or non-native organisms. I present a method for inferring the maximum likelihood estimate of a parametric distribution for the dispersal distance using genetic data and spatial information at two consecutive generations. Likelihood ratios are estimated by using Monte Carlo methods to approximate a sum over a large number of discrete latent variables.
Trend Estimation using Wavelets
A common problem in the analysis of environmental time series is how to deal with a possible trend component, which is usually thought of as large scale (or low frequency) variations or patterns in the series that might be best modelled separately from the rest of the series. Trend is often confounded with low frequency stochastic fluctuations, particularly in the case of models such as fractionally differenced processes (FDPs), which can account for long memory dependence (slowly decaying auto-correlation) and can be extended to encompass non-stationary processes exhibiting quite significant low frequency components. In this talk we assume a model of polynomial trend plus fractionally differenced noise and apply the discrete wavelet transform (DWT) to separate a time series into pieces that can be used to estimate both the FDP parameters and the trend. The estimation of the FDP parameters is based on an approximation maximum likelihood approach that is made possible by the fact that the DWT decorrelates FDPs approximately. Once the FDP parameters have been estimated, we can then test for a non-zero trend. After outlining the work that we have done to date on testing for non-zero trends, we demonstrate our methodology by applying it to a popular climate dataset.
Wine and Cheese reception to follow in the Statistics lounge, 3rd floor, Padelford.