Studies in Astronomical Time Series Analysis. V. Bayesian Blocks, a New Method to Analyze Structure in Photon Counting Data

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Abstract
I describe a new time-domain algorithm for detecting localized structures (bursts), revealing pulse shapes, and generally characterizing intensity variations. The input is raw counting data, in any of three forms: time-tagged photon events (TTE), binned counts, or time-to-spill (TTS) data. The output is the most probable segmentation of the observation into time intervals during which the photon arrival rate is perceptibly constant, i.e., has no statistically significant variations. The idea is not that the source is deemed to have this discontinuous, piecewise constant form, rather that such an approximate and generic model is often useful. Since the analysis is based on Bayesian statistics, I call the resulting structures Bayesian blocks. Unlike most, this method does not stipulate time bins—instead the data determine a piecewise constant representation. Therefore the analysis procedure itself does not impose a lower limit to the timescale on which variability can be detected. Locations, amplitudes, and rise and decay times of pulses within a time series can be estimated independent of any pulse-shape model—but only if they do not overlap too much, as deconvolution is not incorporated. The Bayesian blocks method is demonstrated by analyzing pulse structure in BATSE γ-ray data.