The statistical challenges posed by discrete-valued matrix data (such as contingency tables, co-occurrence tables, adjacency matrices of graphs and networks, and multivariate binary time series) can often be greatly reduced by focusing on the conditional distribution of the pattern of entries in the matrix, given the margins of the matrix. Although this conditioning simplifies the statistical challenges, it greatly increases the computational challenges of any associated statistical procedures. This project has two principle aims: (1) to design practical methods and algorithms for statistical inference about the conditional distribution of a matrix given its margins, and (2) to specialize these methods and algorithms to the scientific needs of a variety of disciplines, including neuroscience, ecology, network analysis, educational testing, and combinatorial approximation.
With the advent of new technologies for gathering and storing large amounts of complex data, statistics is playing an increasingly central role in science, technology, engineering, medicine and commerce. These new data sources require new types of statistical thinking and improved statistical algorithms. This project develops new algorithms for the statistical analysis of networks, such as social networks, ecological networks, and brain networks. Preliminary results are already being used by neuroscience collaborators to better understand the structure of human seizures. This project also funds the training of graduate students who will become the next generation of innovators in science and engineering.