A1227
Title: Statistics and structures: Examples from oceanography
Authors: Jonathan Lilly - Planetary Science Institute (United States) [presenting]
Abstract: In seeking to extract information from large oceanographic datasets, advances have come when a model for the structure of a particular type of phenomenon is combined with relevant statistical considerations. Three examples are given: (i) isolated, bumplike anomalies in sea surface height profiles observed by satellites, associated with coherent oceanic vortices; (ii) quasi-oscillatory features in data from freely-drifting instruments, associated with fluid trapping within these vortices; and (iii) random motions of large-scale fluid turbulence observed by freely-drifting instruments. In the first two cases, a structural model is created for isolated events and for modulated oscillations, respectively; both types of features are then detected using the continuous wavelet transform, and statistical significance is assessed by comparing two key feature properties with the distributions expected under a null hypothesis of unstructured red noise. The 2D survival function or complementary cumulative distribution function emerges as a useful statistical quantity. In the third example, a three-parameter stochastic model essentially mimicking real-world trajectory behavior is created using the Matern process, shown to be rightly thought of as a damped version of fractional Brownian motion. A general lesson from these efforts is the central importance of a suitable structural model as a basis for framing statistical questions.
