My research interests span a variety of areas ranging from problems motivated by current developments in science and technology to problems in probability and statistics that do not have immediate real-life applications. My thesis was in the area of Large Deviations for Branching Processes in Fixed and Random Environments. It turned out that the tail bounds for multitype branching processes that I obtained in my thesis had interesting applications in studying the execution times of algorithms computer science. I have developed interests in other areas of probability and statistics while still maintaining an active research interest in branching processes.
My continued interest in branching processes is motivated mainly by applications in the area of biotechnology, internet traffic, clinical trials, and population genetics. In the problems encountered in these areas, there is an underlying branching process that governs the dynamics of the physical process. However, to answer questions of scientific interest and understand the relationships between various measurements further modelling becomes crucial. I have developed Branching Regression Models to model results of PCR experiments and internet traffic. I am also working on methodologies to obtain empirical likelihood based inference for the regression parameters of branching regression models Empirical Likelihood Inference for Branching Regression Models.
Statitical models that capture dependece in Multicast Traffic is important in understanding the performance of Internet. In a current work on Autoregressive models on Trees, I have developed statistical procedures for analysis of data from internet measurements.