# Methodology books for astronomy

**Statistics for Astrophysics: Bayesian Methodology**

Didier Fraix-Burnet, Stephane Girard, Julyan Arbel, Jean-Baptiste Marquette (editors, 2018) This book includes the lectures given during the third session of the School of Statistics for Astrophysics that took place at Autrans, near Grenoble, in France, in October 2017, covering basic to advanced methods with practical exercises using the R environment, by leading experts in their field. This covers the foundations of Bayesian inference, Markov chain Monte Carlo technique, model building, Approximate Bayesian Computation (ABC) and Bayesian nonparametric inference and clustering.

- by Imad Pasha & Christopher Agostino (2016) An on-line textbook with tutorials and other resources (e.g. guides to UNIX, Vi, SSH) developing for a course at University of California, Berkeley. Topics include basic Python, libraries, loops, classes, LaTeX and HTML.

- by Stefano Cavuoti (2015) In the last decade a new generation of telescopes and sensors has allowed the production of a very large amount of data and astronomy has become, a data-rich science; this transition is often labeled as: "data revolution" and "data tsunami". This new age of Astronomy calls for a new generation of tools and, for a new methodological approach to many problems, and for the acquisition of new skills. The attempts to find a solution to this problems falls under the umbrella of a new discipline which originated by the intersection of astronomy, statistics and computer science: Astroinformatics.

**Statistical Methods for Astronomical Data Analysis**

**Statistics for Astrophysics: Methods and Application of the Regression**

**Astronomy and Big Data: A Data Clustering Approach to Identifying Uncertain Galaxy Morphology**

- by Zeljko Ivezic, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray (2014). This volume presents a wealth of practical analysis problems, evaluates techniques for solving them, and explains how to use various approaches for different types and sizes of data sets. For all applications described in the book, Python code and example data sets are provided. The supporting data sets have been carefully selected from contemporary astronomical surveys (for example, the Sloan Digital Sky Survey) and are easy to download and use.

**Astrostatistics and Data Mining**

- edited by Luis Manuel Sarro, Laurent Eyer, William O'Mullane, and Joris De Ridder. Review talks on Bayesian model selection for cosmology, mining massive astronomical data sets and astroinformatics. Contributed talks on galaxy clustering, Solar System modeling, Gaia mission planning, variable star classification, irregularly spaced time series, strong gravitational lensing, and stellar property estimation.

**Astrostatistical Challenges for the New Astronomy**

- edited by Joseph M. Hilbe (2013). Review talks on Bayesian astrostatistics, statistical cosmology with the cosmic microwave background and supernovae, extrasolar planet modeling, subspace methods for data mining, and Independent Component Analysis.

**Advanced Statistical Methods for Astrophysical Probes of Cosmology**

- by Marisa Cristina March (2013). A volume in Springer Theses series recognizing outstanding Ph.D. research, it concentrates Bayesian and other techniques for analyzing supernova SN 1a data.

**Statistical Challenges in Modern Astronomy V**

- edited by Eric D. Feigelson & G. Jogesh Babu (2012). These are the proceedings of the latest SCMA conference held every 5 years at Penn State with research-level presentations on statistics in cosmology, data mining, image and time series analysis. Each talk is accompanied by a cross-disciplinary Commentary.

**Modern Statistical Methods for Astronomy with R Applications **

- by Eric D. Feigelson & G. Jogesh Babu (2012). Classroom and reference book on statistical methodology covering: probability, statistical inference, nonparametrics, density estimation, regression, multivariate analysis and classification, censoring and truncation, time series and spatial point processes. Provides R and CRAN scripts for 19 astronomical datasets.

**Practical Statistics for Astronomers**

- by Jasper V. Wall & C. R. Jenkins (2012, 2nd ed). Textbook on methods relevant for observational astronomy with emphasis on Bayesian approaches and worked problems. Covers probability, correlation, hypothesis testing, Bayesian models, Markov chain Monte Carlo integration, time series analysis, luminosity functions and clustering. Data tables and solutions are provided.

**Advances in Machine Learning and Data Mining for Astronomy**

- edited by Michael J. Way, Jeffrey D. Scargle, Kamal M. Ali & Ashok N. Srivastava (2012), Reviews of topics such as: data analysis for gamma-ray and cosmic microwave background astronomy; catalog cross-identification; Poisson images; classification of galaxies, light curves, and high energy sources; weak gravitational lensing; photometric redshifts; galaxy clustering; transiting planet detection; gravitational wave detection; Virtual Observatory and distributed computing applications; ensemble classification; and more.

- edited by Michael P. Hobson, Andrew H. Jaffe, Andrew R. Liddle, Pia Mukherjee and David Parkinson (2010). The volume reviews: Bayesian parameter estimation, model selection, Monte Carlo sampling, and experimental design; signal separation; source extraction; flux measurement; gravitational wave detection; cosmic microwave background modeling; modeling cosmological populations and galaxy evolution; photometric redshifts.

**Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity**

by J. L. Starck, F. Murtagh & J. Fadili (2010). This book presents the state of the art in sparse and multiscale image and signal processing, covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Recent concepts of sparsity and morphological diversity are described and exploited for various problems such as denoising, inverse problem regularization, sparse signal decomposition, blind source separation, and compressed sensing. This book weds theory and practice in examining applications in areas such as astronomy, biology, physics, digital media, and forensics. Matlab and IDL code are included.

**Astronomical Image and Data Analysis**

by J. L. Starck & F. Murtagh (2nd ed., 2006). This volume explains how to handle real problems in astronomical data analysis using a modern arsenal of powerful techniques. It treats those innovative methods of image, signal, and data processing that are proving to be both effective and widely relevant. Methods include: detection and filtering; image compression; multichannel, multiscale, and catalog data analytical methods; wavelets transforms, Picard iteration, and software tools.

**Bayesian Logical Data Analysis for the Physical Sciences**

- by P. C. Gregory (2005). After introduction to probabilities, Bayesian and frequentist inference, this monograph presents Bayesian applications to data with Gaussian and Poisson errors, linear and nonlinear modelling, maximum entropy, Markov chain Monte Carlo integration, and spectral analysis of time series. Provides worked examples with astronomical data, problem sets, and codes associated with Mathematica.

**Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity**

- by Jean-Luc Starck, Fionn Murtagh and Jalal M. Fadili. Monograph on multiscale image and signal processing for astronomy with Matlab and IDL codes. Topics include statistical denoising, inverse problem regularization, sparse signal decomposition, blind source separation, and compressed sensing.

**Multivariate Data Analysis for Astrophysics**

**by Fionn Murtagh (c. 2005). Unpublished lecture notes for a graduate course for astronomers with astronomical applications emphasizing clustering (hierarchical, minimal spanning tree, Voronoi tesselation, partitioning, mixture models, self-organizing maps, ultrametric spaces, P-adic coding), and discriminant analysis (Bayes and nonparametric discrimination, multilayer perceptron). An update of his 1987 monograph appears **

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**Data Reduction and Error Analysis for the Physical Sciences**

- by Philip Bevington & D. Keith Robinson (2003, 2nd ed.). Popular text with code covering error analysis, Monte Carlo techniques, least-squares fitting, maximum-likelihood, and goodness-of-fit.

**Statistical Challenges in Astronomy**

- edited by Eric D. Feigelson and G. Jogesh Babu. Research conference covering large astronomical surveys, statistical cosmology, nonparametric inference, clustering and classification, harmonic times series analysis, and wavelet analysis. Talks with cross-disciplinary commentaries.

**Astronomical Image and Data Analysis**

- by Jean-Luc Starck and Fionn Murtagh (2002). Advanced techniques for treating astronomical data including data filtering & storage, image processing (edge detection, segmentation, pattern recognition), image compression, source detectcion, multiscale analysis using wavelet transforms, deconvolution, multivariate data, entropies, catalogs and Virtual Observatories.

**Statistics of the Galaxy Distribution**

- by Vicent J. Martinez and Enn Saar (2002). Comprehensive monograph on the large-scale galaxy of the universe traced by galaxy redshift surveys. It reviews the astronomical observations, statistical techniques and cosmological inferences.

- by Prasenjit Saha. Brief introductory book covering Gaussian & Poisson distributions, Monte Carlo methods, least squares, nonlinear regression, and entropy. Available free on the Web.

**Probability and Statistics in Experimental Physics**

- by Byron P. Roe (2001, 2nd edition) Textbook covering basic comcepts, statistical distributions, Monte Carlo methods, central limit theorem, correlation coefficients, curve fitting with constraints andconfidence belts, likelihood ratios, least-squares and robust estimation (including errors in x and y), Poisson problems. Problem sets with solutions.

- by Glen Cowan (1998). Guide to practical applications of statistics in expermental physical science with examples from particle physics. Includes Monte Carlo methods; parameter estimation (maximum likelihood, least squares, moments); errors, limits and confidence intervals; and characteristic functions.

**Image processing and Data Analysis: The Multiscale Approach**

- by J.-L. Starck, F. Murtagh & A. Bijaoui (1998). Technical monograph on the use of wavelets for multiscale analysis of astronomical, engineering, remote sensing, and medical images.

- by G. Jogesh Babu & Eric D. Feigelson (1996). A review of research topics on the methodology of astronomical data analysis including resampling methods, spatial point processes, symmetrical linear regressions, multivariate classification, time series analysis, censoring and truncation. Introduces astronomical problems to statisticians.

**Data Analysis: A Bayesian Tutorial**

- by Devinder Sivia (1996). A clear introduction by a physicist covering parameter estimation, model selection, assigning probabilities, nonparametric estimation, and experimental design.

**Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences**

- by Roger J. Barlow (1993). Introductory treatment of parameter estimation (least squares, maximum likelihood), hypothesis testing, Bayesian statistics and non-parametric methods.

**Statistics in Theory and Practice**

- by Robert Lupton (1993). Intermediate-level monograph aimed at physical scientists explaining probability distributions, sampling statistics, confidence intervale, hypothesis testing, maximum likelihood estimation, goodness-of-fit, and nonparametric rank tests. Includes problems with answers.

**A Practical Guide to Data Analysis for Physical Science Students**

- by Louis Lyons (1991). Undergraduate text for interpretation of experiments including distributions and moments, Gaussian errors, combining results, least-squares fitting, weighting and confidence intervals, parameter testing.

**Some older volumes of interest include:** Statistics for nuclear and particle physicists (Louis Lyons, 1986)

E. T. Jaynes: Papers on probability, statistics and statistical physics (E. T. Jaynes, 1989)

Multivariate Data Analysis (Fionn Murtagh, 1987)

The History of Statistics: The Measurement of Uncertainty Before 1900 (Stephen M. Stigler, 1986)

Statistical Methods in Experimental Physics (W. A. Eadie et al., 1971)

Method of least squares and principles of the theory of observations (I. V. Linnik, 1961)

Combination of Observations (William M. Smart, 1958)

Statistical Astronomy (Robert J. Trumpler & Harold F. Weaver, 1953)

Introduction to Physical Statistics (Robert B. Lindsay, 1941)

Scientific Inference (Harold Jeffreys, 1937)

On the algebraical and numerical theory of errors of observations and the combination of observations (George B. Airy, 1861)

Theory of the combination of observations least subject to error (Carl F. Gauss, 1823, English ed 1995)