This one-day workshop will introduce participants to a range of standard and state-of-the-art methods and tools for exploratory and statistical analysis of time series data arising in astronomy. Three sessions will cover:
- Periodograms and related Fourier methods,
- New methods for irregularly sampled time series and individual-event data, and
- New tools for spectro-temporal analysis of photon counting and event data.
The sessions will include tutorial introductions to the motivating astronomy and key statistical and signal processing ideas, and software demonstrations, including hands-on exercises using Python packages developed for astronomical time series analysis.
Brief descriptions of the three planned sessions are as follows.
Time series exploration using periodograms: Periodograms---data-derived functions resembling a Fourier power spectrum---arise in multiple contexts in time series data analysis. This session will cover three such contexts: detecting and characterizing periodic signals, estimating the power spectrum for a signal with a continuous power spectrum, and approximate modeling of time series with Gaussian process models. Each context uses periodograms, but each requires different post-processing of a periodogram to quantify evidence in the data. Failing to distinguish different use cases has led to persistant misunderstandings about periodograms. The session will address these topics analytically and with Python exercises. Presenter: Tom Loredo, Cornell Center for Astrophysics and Planetary Science, Cornell University.
New methods for analyzing irregularly sampled time series and point data: This session will present: (1) An algorithm for computing the complex Fourier transform of unevenly sampled time series; its magnitude is the well-known Lomb-Scargle periodogram, but its phase gives the useful but rarely studied phase spectrum. (2) Various uses of the discrete correlation function for unevenly sampled time series. (3) Recent developments in Scargle's popular Bayes Blocks framework, including applications with high-energy data, and LIGO data. Software demonstrations will use MATLAB, though several algorithms are also being ported to Python. Presenter: Jeffrey Scargle, NASA Ames Research Center.
New tools for spectro-temporal analysis of X ray time series data: This session will describe methods for modeling photon counting and individual-photon event data from sources with time-evolving energy spectra in high-energy astrophysics ("spectral-timing data"). Methods covered will include dynamic power spectra, cross spectra, covariance spectra, spectral lag estimation, and related methods. The session will demonstrate methods using the Python Stingray package, including demonstrations of tools for simulating light curves and time-tagged event data with diverse types of variability. Presenter: Daniela Huppenkothen, Center for Data-Intensive Research in Astronomy and Cosmology (DIRAC), University of Washington.