Event data are ubiquitous in astronomy and space sciences, since a majority of astronomical data begin with the collection of individual events, typically photons. Mathematicians and statisticians have developed several methods for the characterization of event data, which can be generally divided into methods for unbinned data that record individual events, and for data collected into pre–determined bins. Methods for individual events include sequential analysis and other tests for variability, spatial point processes for spatial characterization, Poisson processes, and maximum–likelihood estimation for model fitting. For example, these methods are used in the Bayesian blocks model and in autoregressive and other models for temporal phenomena. It is common to analyze event data after binning the events according to energy or time, thus leading to spectra and light curves that are the basis of many, if not a majority of, astronomical studies. Methods for binned data include the analysis of count data, weighted least squares and maximum–likelihood model fitting, local regression smoothing, autocorrelation functions, autoregressive models and models for spectral analysis.
This Research Topic is a collection of papers presented at
iid2022: Statistical Methods for Event Data – Illuminating the Dynamic Universe, a Workshop and Winter School on Statistics to be held at the Lake Guntersville State Park Lodge (AL) on Nov. 15-19, 2022. It aims to bring together students, professional astronomers and statisticians of different backgrounds to further disseminate the use of statistical methods for astronomy, space sciences and related fields. This workshop has a two–fold motivation: (a) the training and engagement of young scientists in proper statistical methods for the analysis and interpretation of data; and (b) the gathering of scientists – both astronomers and in other related fields – to exchange recent advances in the statistics and analysis of event data. The gathering will be in the form of a workshop, whereby each session will feature an introductory lecture that aims primarily at explaining the current state of the subject, followed by contributed talks and discussion of the methods with emphasis on recent progress and applications, and hands–on collaborative analysis of sample problems with advanced software.
Topics of relevance include:
- General methods of statistical estimation: Maximum-likelihood (ML), likelihood ratio, random processes and associated distributions for event data.
- Statistics for spatial analysis in astronomy, including examination of clustering and other spatial structures
- Statistics for spectral data, including Poisson--based likelihood--ratio methods such as the Cash statistic.
- Methods for various source sizes, or by type (e.g., i diffuse, structured, compact sources, etc.), or messenger type (e.g., ground--based observations, space--based, in-situ, particles)
- Statistics to identify sources in low count-rate data: Poisson probabilities, Li-Ma and Feldman-Cousins criteria, Bayesian approaches.
- Statistics for temporal analysis of low count-rate data: tests for variability, Bayesian Block models, autoregressive models
- Linear and non linear methods of regression: weighted least--squares, ML, parameter estimation and goodness-of-fit, error estimation and characterization
- Specialized methods in the low count-rate regime and biases from the use of Gaussian approximations for event data
- Point processes, Markov chains and other stochastic processes
- Binomial and multinomial models, contingency tables and logistic regression
- Upper and lower limits, censored and truncated data
- Statistics for numerical methods (e.g., Monte Carlo, MCMC, machine learning, resampling methods like jackknife and bootstrap)
- Software development in support of statistical data analysis for astronomy and beyond
