Research Interests and Educational Opportunities
My research interests combine mathematical modeling and statistical analysis using computationally intensive methods and simulation. My research stems from current problems in biology. Interested graduate students, undergraduate students and postdocs are encouraged to contact me directly by e-mail at email@example.com for research opportunities in the areas listed below.
Descriptions of some of the projects, interesting to me, follow:
Statistical methods for the analysis of microbial community composition:
Diseases occur not only due to harmful pathogens that act in isolation but also due to disruption of the balance of the human-microbial ecosystem (the human microbiome). This emerging knowledge requires a revision of the current diagnostic approaches to incorporate information about the “normal” state of these ecosystems and the nature of deviation from this state that can result in disease. It also requires making these revised approaches readily available to the medical community to facilitate diagnosing diseases. The goal for this project is to develop computational approaches to differentiate between normal and abnormal (associated with disease symptoms) microbial communities, taking metadata (such as gender, age, ethnicity, and health history) into consideration.
Experimental Evolution (Plasmid and phage Evolution):
Mathematical models provide predictive power to help explain the evolutionary and ecological mechanisms of plasmids and phage. I am interested in developing stochastic models to describe the mechanics of evolution and the interaction between a parasite (a plasmid or phage) and a host (a bacterial cell) and utilize these models in statistical inference of the factors most important in such ecological and evolutionary structure.
Barcoding of Life (A decision theoretic approach based on the coalescent):
Accurate assignment and clustering are crucial for responding effectively and efficiently to newly detected potential disease carriers or disease causing species. Assignment facilitates prediction of the biology of the classified individual(s). Should we identify an insect to belong to a disease-carrying species/group, for example, we could invoke counter measures to eliminate the environmental conditions that help the spread of these insects. Accurate assignment depends on the accurate and correct characterization of groups/species, and, hence, on the accurate and correct clustering. I am interested in developing new, model-based, statistical methods to use barcode data to quickly and accurately identify (assign) individual organisms and to distinguish and characterize (cluster) different species and groups. Methods I develop utilize the evolutionary history, inferred from the data, and a measure of similarity or difference, in a decision theoretic framework, to make an informed decision of assignment or clustering.
Systematic Biology (A decision theoretic approach to model selection in phylogenetic analysis):
Likelihood and Bayesian methods in phylogenetic analysis rely on choosing a justifiable stochastic model of evolution based on which researchers infer the relationship between different individuals (taxa) that belong to different species. We developed and continue to refine a decision theoretic approach that takes into account performance, as well as fit in choosing an evolutionary model for phylogenetic inference.
The underlying mathematics and statistics disciplines of the above described projects are: Statistical Genetics, Bayesian Statistics, Mathematical Biology, Stochastic Processes and Optimization