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This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
In astronomical and cosmological studies one often wishes to infer some properties of an infinite-dimensional field indexed within a finite-dimensional metric space given only a finite collection of noisy observational data. Bayesian…
With the volume and availability of astronomical data growing rapidly, astronomers will soon rely on the use of machine learning algorithms in their daily work. This proceeding aims to give an overview of what machine learning is and delve…
Despite centuries of close association, statistics and astronomy are surprisingly distant today. Most observational astronomical research relies on an inadequate toolbox of methodological tools. Yet the needs are substantial: astronomy…
This project outlines the complete development of a variable star classification algorithm methodology. With the advent of Big-Data in astronomy, professional astronomers are left with the problem of how to manage large amounts of data, and…
We are pleased to present a Special Section on Statistics and Astronomy in this issue of the The Annals of Applied Statistics. Astronomy is an observational rather than experimental science; as a result, astronomical data sets both small…
Astroinformatics is a new impact area in the world of astronomy, occasionally called the final frontier, where several astrophysicists, statisticians and computer scientists work together to tackle various data intensive astronomical…
A persistent challenge in astronomical machine learning is a systematic bias where predictions compress the dynamic range of true values-high values are consistently predicted too low while low values are predicted too high. Understanding…
This article is based on the tutorial we gave at the hands-on workshop of the ICRANet-ISFAHAN Astronomy Meeting. We first introduce the basic theory of machine learning and sort out the whole process of training a neural network. We then…
Astronomy has entered the multi-messenger data era and Machine Learning has found widespread use in a large variety of applications. The exploitation of synoptic (multi-band and multi-epoch) surveys, like LSST (Legacy Survey of Space and…
This is an introduction to Bayesian inference with a focus on hierarchical models and hyper-parameters. We write primarily for an audience of Bayesian novices, but we hope to provide useful insights for seasoned veterans as well. Examples…
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In…
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
We present a Bayesian machine learning architecture that combines a physically motivated parametrization and an analytic error model for the likelihood with a deep generative model providing a powerful data-driven prior for complex signals.…
This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used…
Image segmentation plays a critical role in unlocking the mysteries of the universe, providing astronomers with a clearer perspective on celestial objects within complex astronomical images and data cubes. Manual segmentation, while…
Astronomy is entering an era of data-driven discovery, due in part to modern machine learning (ML) techniques enabling powerful new ways to interpret observations. This shift in our scientific approach requires us to consider whether we can…
We present a unified framework to derive fundamental stellar parameters by combining all available observational and theoretical information for a star. The algorithm relies on the method of Bayesian inference, which for the first time…
An array of large observational programs using ground-based and space-borne telescopes is planned in the next decade. The forthcoming wide-field sky surveys are expected to deliver a sheer volume of data exceeding an exabyte. Processing the…
This is a summary of the `Astronomy Perspective' of the 4th meeting on 'Statistical Challenges in Modern Astronomy' held at Penn State University in June 2006. We comment on trends in the Astronomy community towards Bayesian methods and…