STATISTICS COLLOQUIUM
Thursday, April 28th, 2011 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)
Speaker: Fushing Hsieh (Dept. of Statistics, UC Davis)
Title: Rank & Odds: NCAA Football and Rhesus Macaque
Abstract: In this talk we discuss a typical issue of inferring a global structure from a collection of local information. Here the global structure is the ranking of all involving football teams or monkeys, and the local information is the dyadic win-or-loss. We illustrate the complex information content through a network representation of the collection of dyadic data. This complexity is shown as a cause of inadequacy and failure of statistical modeling and computing, especially based on linearity ranking assumption and maximum likelihood or Bayesian approaches, even when the number of involving subjects is relatively small. A Beta random field approach is introduced to resolve this issue without making global structural assumption. The ideal behind our proposal is to prune a possibly severely tangled mono-directed dominance sub-graph into a series of primary bundles of parallel dominance paths. Further we employ a conservative directed odds approximation via a device called "information transitivity ", which mimicking a signal transmission through a noisy channel. Upon a realization of Beta random field, the simulated Annealing algorithm is applied to find an optimal upper triangular odds matrix such that its lower triangular matrix has as few entries being larger than 1 as possible. A mean field version of Beta random field ensemble is used a point estimation of the non-linear ranking network, while a confidence band for the ranking structure is also derived. We analyze two real data sets: NCAA 1-A Football league consisting of 120 teams and a cage of Rhesus Macaque consisting of 94 adult monkeys. We show some surprising results on both analyses that validate our computational learning approach via Beta random field.
