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

TL;DR

This paper introduces an improved Bayesian Blocks algorithm for detecting and characterizing local variability in time series data, effectively handling observational errors, data gaps, and various data modes, with applications in astronomical data analysis.

Contribution

The paper presents a generalized, nonparametric Bayesian Blocks method capable of real-time and retrospective analysis, extending previous work to handle diverse data types and complexities.

Findings

High detection efficiency for weak signals close to theoretical limits

Effective handling of data gaps and variable exposure

Versatile application to different data modes and representations

Abstract

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.