Statistical Machine Learning for Astronomy -- A Textbook

TL;DR

This textbook systematically introduces Bayesian statistical machine learning techniques tailored for astronomy, emphasizing uncertainty quantification, theoretical foundations, and applications to large-scale astronomical data analysis.

Contribution

It provides a comprehensive, theory-driven framework connecting classical statistical methods with modern machine learning within an astronomical context.

Findings

Unified Bayesian framework for astronomical data analysis

Derivation of methods from first principles with mathematical rigor

Application of techniques to large astronomical surveys

Abstract

This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques and traditional statistical methods. We show how these techniques emerge from familiar statistical foundations. The consistently Bayesian perspective prioritizes uncertainty quantification and statistical rigor essential for scientific inference in astronomy. The textbook progresses from probability theory and Bayesian inference through supervised learning including linear regression with measurement uncertainties, logistic regression, and classification. Unsupervised learning topics cover Principal Component Analysis and clustering methods. We then introduce computational techniques through sampling and Markov Chain Monte Carlo, followed by Gaussian Processes as probabilistic nonparametric methods and neural networks within the broader statistical context. Our theory-focused pedagogical approach derives each method from first principles with complete mathematical development, emphasizing statistical insight and complementing with astronomical applications. We prioritize understanding why algorithms work, when they are appropriate, and how they connect to broader statistical principles. The treatment builds toward modern techniques including neural networks through a solid foundation in classical methods and their theoretical underpinnings. This foundation enables thoughtful application of these methods to astronomical research, ensuring proper consideration of assumptions, limitations, and uncertainty propagation essential for advancing astronomical knowledge in the era of large astronomical surveys.