Signals as departures from random walks

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Department of Mathematical Sciences; Department of Physics


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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Physical Review E