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Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations

Scargle, J. D. and Norris, J. P. and Jackson, Brad and Chiang, James (2013) Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations. Astrophysical Journal, 764 (2). Art No 167. ISSN 0004-637X. doi:10.1088/0004-637X/764/2/167.

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This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it—an improved and generalized version of Bayesian Blocks [Scargle 1998]—that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piecewise linear and piecewise exponential representations, multi-variate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by [Arias-Castro, Donoho and Huo 2003]. In the spirit of Reproducible Research [Donoho et al. (2008)] all of the code and data necessary to reproduce all of the figures in this paper are included as auxiliary material.

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Additional Information:C 2013. The American Astronomical Society. All rights reserved. Printed in the U.S.A. This work was supported by Joe Bredekamp and the NASA Applied Information Systems Research Program. We especially recognize the Center for Applied Mathematics, Computation and Statistics (CAMCOS) in the Department of Mathematics, San Jose State University for support through the Henry Woodward Fund. J.D.S. is grateful for the hospitality of the following institutions during various phases of this work: the Institute for Pure and Applied Mathematics at the University of California at Los Angeles, the Banff International Research Station, the Keck Institute for Space Studies at Caltech, the Kavli Institute for Particle Astrophysics at Stanford University and the Statistical and Mathematical Sciences Institute at Duke University. We are grateful to Tom Loredo, Glen MacLachlan, Erik Petigura, Jake Vanderplas, Zeljko Ivezic, Ery Arias-Castro, Sam Kou, Lin Lin, Talvikki Hovatta, and Marc Coram for helpful comments, and to Alice Allen for help with the posting at “The Engineering Deck: Astrophysics Source Code Library” on the Starship Asterisk Web site: We are also grateful to the anonymous referee for useful suggestions.
Group:Keck Institute for Space Studies
Issue or Number:2
Record Number:CaltechAUTHORS:20160201-095750497
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64118
Deposited By: Colette Connor
Deposited On:04 Feb 2016 18:35
Last Modified:10 Nov 2021 23:26

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