We present nonparametric techniques for constructing and verifying density estimates from high-dimensional data whose irregular dependence structure cannot be modelled by parametric multivariate distributions. A low-dimensional representation of the data is critical in such situations because of the curse of dimensionality. Our proposed methodology consists of three main parts: (1) data reparameterization via dimensionality reduction, wherein the data are mapped into a space where standard techniques can be used for density estimation and simulation; (2) inverse mapping, in which simulated points are mapped back to the high-dimensional input space; and (3) verification, in which the quality of the estimate is assessed by comparing simulated samples with the observed data. These approaches are illustrated via an exploration of the spatial variability of tropical cyclones in the North Atlantic; each datum in this case is an entire hurricane trajectory. We conclude the paper with a discussion of extending the methods to model the relationship between TC variability and climatic variables.

The majority of statistical work on college football's Bowl Championship Series (BCS) has involved proposing or categorizing computer ratings of teams. Computer algorithms, a coaches' poll, and a media poll make up the three ratings systems that are currently equally weighted to produce an overall BCS rating, which ultimately determines which schools will compete in lucrative post-season BCS bowls. We focus on investigating the performance of the BCS as implemented for the 2004, 2005, and 2006 seasons to determine whether equal weights are appropriate. Our Bayesian analysis shows that while the posterior mode places more than half the weight on the media poll, the 95% HPD credible interval contains the equally-weighted scheme. We relate our work to the ongoing controversies over the BCS.