Abstract #301466

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JSM 2002 Abstract #301466
Activity Number: 385
Type: Contributed
Date/Time: Thursday, August 15, 2002 : 8:30 AM to 10:20 AM
Sponsor: Section on Physical & Engineering Sciences*
Abstract - #301466
Title: Projection Pursuit for k-Dimensional Instabilities
Author(s): Woollcott Smith*+ and Andrew Solow
Affiliation(s): Temple University and Woods Hole Oceanographic Institution
Address: North Broad Street, Philadelphia, Pennsylvania, 19122,
Keywords: multivariate normal ; mixtures ; dynamic systems ; density estimation
Abstract:

In physical, financial, and biological systems, sometimes there are unstable points in state space where, even under random perturbation, the system is unlikely to be observed. In this note, we assume that one-dimensional independent observations of the system are made, and we wish to find k linear combinations of the data, k< l, that are most indicative of these instabilities. That is, we seek a k-dimensional data cloud containing a hole. The hole may indicate a point of instability or other mechanisms that create an anomalous lack of observations in k-dimensional space. The computational techniques and the theory developed are closely related to estimating mixtures of multivariate normal densities via maximum likelihood.

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