The field of AstroStatistics is at the intersection of observational Astronomy, Statistics, and data science. In recent years, there has been a massive increase in the development and, application of new statistical methods to problems in high energy astrophysics. In particular Bayesian methods using Markov Chain Monte Carlo have been implemented in both XSPEC and Sherpa. Such, Bayesian methods allow researchers to fit multi-level models that, for example, account for complexities, and uncertainties in instrumental effects, realistic representations of physical processes, selection effects, and/or distributions of and relationships among parameters, all in a principled statistical manner. Although recent tools, such as those deploying MCMC in XSPEC and Sherpa, are making it much easier for astronomers to access the power of modern Bayesian methods, using them involves a range of statistical and computation subtleties, and a variety of more sophisticated, next generation tools are becoming available. The goal of our session is to review advances in statistical methods, to present applications to data, and ,to discuss current issues and future perspectives. The session includes talks from both, astronomers and statisticians and a time for discussion.
Chair: Aneta Siemiginowska (CfA/CHASC)
Abstract: Statistical discovery questions in physics and astrophysics often involve mathematical subtleties that mean standard methods (e.g., chi-square) are inappropriate and can lead to misleading results. At the same time Bayesian and classical statistical techniques can lead researchers to differing conclusions. Moreover modern computational strategies are typically infeasible under extreme discovery criteria (4 sigma or more). This talk explores the statistical challenges that arise in the quantification of discovery and suggests a strategy that combines Bayesian and classical statistical techniques to tackle these challenges.
Abstract: Calibration data for instruments used for astrophysical measurements are often obtained by observing different astronomical objects (a.k.a. sources) with well-understood characteristics simultaneously with different instruments. The proper concordance among different instruments is a vital issue in such calibration data sets. This requires a careful modeling of the mean signals, the intrinsic source differences, and measurement errors. Although in high-energy astronomy the data are Poisson photon counts, they are large enough (typically >>30) to justify an approximate log-normal model, or a more general log-t model. This has the advantage of permitting imperfection in the multiplicative mean modeling to be captured by the residual variance. The estimator then takes an analytically tractable form of power shrinkage, with a half-variance adjustment to ensure an unbiased multiplicative mean model on the original scale. We apply our method to several data sets, from a combination of observations of active galactic nuclei (AGN) and spectral line emission from the supernova remnant E0102, obtained with a variety of X-ray telescopes such as Chandra, XMM-Newton, Suzaku, and Swift. We demonstrate that the proposed model gives important guidance for astrophysicists to adjust for disagreements between different instruments and various sources. The data are compiled by the International Astronomical Consortium for High Energy Calibration (IACHEC) researchers.
Abstract: I wil describe the current MCMC implementation in XSPEC and its use for Bayesian analysis, discuss some of the challenges, and consider future enhancements.
Abstract:In high-energy astrophysics, a single spectrum or light curve rarely tells the whole story. Instead, we learn about the physics of black holes by observing how their spectra change with time, or we aim to draw conclusions about dense matter physics from a population of neutron stars and their light curves. Traditionally, however, much more thought is devoted to modeling individual spectra or light curves independently than to sample inference methods. If the sample is governed by a single underlying physical process, this approach ignores important information, and makes us less confident in our results than we ought to be. Here Bayesian hierarchical models offer a principled, self-consistent solution: they allow us to combine multiple observations to explicitly infer properties of the whole sample, often with more precision than modeling each observation separately would have yielded. In this talk, I will give an overview of the state-of-the-art in Bayesian hierarchical modeling and associated sampling methods in high-energy astrophysics, as well as show some recent advances in using this approach in both X-ray spectroscopy and timing.
Abstract: Choosing between several models is an everyday problem in the analysis of X-ray spectra. Is it justified to add a spectral line? Is physical effect A present? Do I need to replace this component with a more detailed physical model? Until now, the methods commonly applied in practice have been limited. BXA allows practical Bayesian model comparison for spectral models, by connecting the Multinest algorithm to xspec/sherpa. I will demonstrate how to use BXA for model selection between different obscurer geometries of AGN, show that this approach is more sensitive than likelihood ratio thresholds and present how to calibrate false selection rates. BXA also allows robust parameter estimation, because contrary to MCMC approaches, BXA easily deals with multiple solutions and automatically converges to a well-defined end point. Finally, I will briefly discuss how to infer about the populations behind limited samples with Hierarchical Bayesian inference.
Aneta Siemiginowska (asiemiginowska @ cfa . harvard . edu) Vinay Kashyap (vkashyap @ cfa . harvard . edu)