Very many variables and limited numbers of observations; The p>>n problem in current statistical applications

Summary form only given. Nonlinearity and chaos are ubiquitous and fascinating. Chaotic systems, in particular, are exquisitely sensitive to small perturbations, but their behavior has a fixed and highly characteristic pattern. Understanding this somewhat counterintuitive combination of effects is important to one's ability to model the physical world. I will begin this talk by reviewing of some of the basic ideas of the field of nonlinear dynamics and describe how those ideas can be leveraged to analyze time-series data. Most of these nonlinear time-series analysis techniques were developed for low-dimensional systems, however, and many of them require perfect models — situations that are rare in the geosciences. For practitioners in these fields, then, it is important to understand how and when to use nonlinear time-series analysis, how to interpret the results, and how to recognize when and why these methods fail. I will demonstrate all of this in the context of a specific problem: understanding and predicting processor and memory loads in