Probabilistic and Statistical Analysis of Population Evoluation Data

University Of Georgia Research Foundation Inc, Athens GA

Investigators

Abstract

proposal: 0307057 PI: Anand Vidyashankar title: Probabilistic and Statistical Analysis of Population Evolution Data Abstract: This project is aimed at developing probabilistic and statistical theory for population evolution data. These data possess features that can broadly be described as variants of the branching phenomenon. Specific scientific questions that drive this project are motivated towards understanding the PCR (Polymerase Chain Reaction) dynamics. Specifically, this project develops statistical models (linear and generalized linear models) after initially modeling the amplification process as a variant of a general branching process. Due to the non-standard nature of the problem, novel methodologies and techniques are necessary to understand the inferential aspects stemming from these statistical models. These in turn lead to interesting probabilistic questions about large deviations, conditional limit laws, and central limit theorems. The last two decades have seen an explosion of novel ideas in the areas of biotechnology and information technology. These discoveries are being felt in such diverse areas as finance, e-commerce, biology, and network traffic. The scientific experiments carried out using these modern technologies are yielding data that possess various intricacies and complexities. This research is aimed at providing concrete solutions to some of these complexities. An immediate application of the results of this project would be in accurately quantifying the HIV-1 viral load in HIV-1 infected patients. Other areas of applications include cancer biology, Internet congestion and its impact on e-commerce.