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Trajectory Data Analyses for Pedestrian Space-time Activity Study
Published on: February 25, 2013
Signals as departures from random walks
Glenn Ierley1, Alex Kostinski2
1Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, Michigan 49931, USA and Scripps Institution of Oceanography, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0225, USA.
Abstract:
We study statistics of data ranking, focusing on the recently discovered distribution-invariant discrete eigenvalue spectrum for an independent and identically distributed (IID) process. We employ a variant of a cumulative distribution function in rank and time that maps the sampling variability for an IID process onto a set of random walks. This mapping admits confidence bounds on whether the residual (data with signal removed) arises solely from IID sampling variability. Any deviations judged significant are regarded as signals, whether deterministic, chaotic, or random. Unlike our recent work on extracting unknown signals in arbitrary noise, here we focus on aspects that are easily combined with any other methods of signal extraction. The ubiquitous case of a single trace receives particular attention. The approach is illustrated on dark current and gamma-ray arrival datasets where we examine the residual for consistency with the expected sampling variability of IID noise.
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