Statistical Aspects of X-ray Spectral Analysis

TL;DR

This chapter provides a comprehensive overview of statistical methods for analyzing X-ray spectra from celestial sources, covering modeling, statistical frameworks, and practical exercises.

Contribution

It introduces modern statistical techniques and practical exercises for spectral analysis, integrating Bayesian and frequentist approaches with real data examples.

Findings

Effective data re-binning improves spectral analysis accuracy.

Bayesian and frequentist methods offer complementary insights.

Hands-on exercises facilitate practical understanding of complex concepts.

Abstract

This handbook chapter gives a modern introduction to spectral analysis of celestial X-ray sources. Concepts presented include the instrumentation response, the linear modelling approximation, Poisson count statistics and the Gaussian approximation, data re-binning, visualisation techniques, handling backgrounds, Bayesian and frequentist viewpoints, uncertainty quantification of model parameters, model checking, model comparison, and inferring population distributions. Realistic hands-on example exercises with accompanying data files and code are included to apply the theoretical concepts in practice.