Title
Evolutionary Spectral Envelope
Speaker
David Stoffer, Department of Statistics, University of Pittsburgh
Abstract
The theories and methodologies associated with the analysis of correlated data observed at different points in time is commonly referred to as time series analysis. Within the field, there are two separate, but not mutually exclusive, approaches commonly identified as the time domain approach and the spectral (or frequency) domain approach. The time domain approach presumes that correlation between adjacent points in time is best explained by regression. For example, we may propose a regression model to predict the price of gold tomorrow from the price of gold today. Conversely, the spectral domain approach assumes the primary characteristics of interest in a time series relate to periodic or systematic variations found naturally in most data. These periodic variations may be caused by physical or biological phenomena of interest such as the repetitive nature of recorded speech.
After a brief discussion of these fundamentals, I will introduce the spectral envelope. The concept of the spectral envelope was recently introduced as a general statistical technique for the frequency domain analysis of qualitative-valued time series. The methodology was motivated by a problem in neurology involving the analysis of infant sleep-state cycling as part of the assessment of central nervous system complications due to prenatal maternal substance abuse. The technique has also proven to be a useful procedure for the analysis of long DNA sequences. I will introduce the general methodology at a basic level and illustrate the technique with examples of analyses of a human Y-chromosomal DNA fragment and a gene from the Epstein-Barr virus.
If time permits, I will discuss my current research focus on evolutionary spectral envelope for the analysis of locally stationary processes. For example, a common problem in analyzing long DNA sequence data is to identify coding sequences (genes) that are dispersed throughout the DNA and separated by regions of non-coding. Even within short subsequences of DNA, one encounters local behavior. To address this problem, we are exploring adaptive dyadic tree-based segmentation methods.
