Astrostatistical Challenges for the New Astronomy presents a collection of monographs authored by several of the disciplines leading astrostatisticians, i.e. by researchers from the fields of statistics and astronomy-astrophysics, who work in the statistical analysis of astronomical and cosmological data. Eight of the ten monographs are enhancements of presentations given by the authors as invited or special topics in astrostatistics papers at the ISI World Statistics Congress (2011, Dublin, Ireland). The opening chapter, by the editor, was adapted from an invited seminar given at Los Alamos National Laboratory (2011) on the history and current state of the discipline; the second chapter by Thomas Loredo was adapted from his invited presentation at the Statistical Challenges in Modern Astronomy V conference (2011, Pennsylvania State University), presenting insights regarding frequentist and Bayesian methods of estimation in astrostatistical analysis. The remaining monographs are research papers discussing various topics in astrostatistics. The monographs provide the reader with an excellent overview of the current state astrostatistical research, and offer guidelines as to subjects of future research. Lead authors for each chapter respectively include Joseph M. Hilbe (Jet Propulsion Laboratory and Arizona State Univ); Thomas J. Loredo (Dept of Astronomy, Cornell Univ); Stefano Andreon (INAF-Osservatorio Astronomico di Brera, Italy); Martin Kunz ( Institute for Theoretical Physics, Univ of Geneva, Switz); Benjamin Wandel ( Institut d'Astrophysique de Paris, Univ Pierre et Marie Curie, France); Roberto Trotta (Astrophysics Group, Dept of Physics, Imperial College London, UK); Phillip Gregory (Dept of Astronomy, Univ of British Columbia, Canada); Marc Henrion (Dept of Mathematics, Imperial College, London, UK); Asis Kumar Chattopadhyay (Dept of Statistics, Univ of Calcutta, India); Marisa March (Astrophysics Group, Dept of Physics, Imperial College, London, UK)./body
Data analysis lies at the heart of every experimental science. Providing a modern introduction to statistics, this book is ideal for undergraduates in physics. It introduces the necessary tools required to analyse data from experiments across a range of areas, making it a valuable resource for students. In addition to covering the basic topics, the book also takes in advanced and modern subjects, such as neural networks, decision trees, fitting techniques and issues concerning limit or interval setting. Worked examples and case studies illustrate the techniques presented, and end-of-chapter exercises help test the reader's understanding of the material.
Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.
This new text surveys a series of fundamental problems in astrophysics, both analytically and computationally, for advanced students in physics and astrophysics. The contents are supported by more than 110 class-tested Mathematica® notebooks, allowing rigorous solutions to be explored in a visually engaging way. Topics covered include many classical and historically interesting problems, enabling students to appreciate the mathematical and scientific challenges that have been overcome in the subject's development. The text also shows the advantages and disadvantages of using analytical and computational methods. It will serve students, professionals and capable amateurs to master the quantitative details of modern astrophysics and the computational aspects of their research projects. Downloadable Mathematica® resources available at www.cambridge.org/koberlein.
Based around a series of real-life scenarios, this engaging introduction to statistical reasoning will teach you how to apply powerful statistical, qualitative and probabilistic tools in a technical context. From analysis of electricity bills, baseball statistics, and stock market fluctuations, through to profound questions about physics of fermions and bosons, decaying nuclei, and climate change, each chapter introduces relevant physical, statistical and mathematical principles step-by-step in an engaging narrative style, helping to develop practical proficiency in the use of probability and statistical reasoning. With numerous illustrations making it easy to focus on the most important information, this insightful book is perfect for students and researchers of any discipline interested in the interwoven tapestry of probability, statistics, and physics.
Modern astronomical research is beset with a vast range of statistical challenges, ranging from reducing data from megadatasets to characterizing an amazing variety of variable celestial objects or testing astrophysical theory. Linking astronomy to the world of modern statistics, this volume is a unique resource, introducing astronomers to advanced statistics through ready-to-use code in the public domain R statistical software environment. The book presents fundamental results of probability theory and statistical inference, before exploring several fields of applied statistics, such as data smoothing, regression, multivariate analysis and classification, treatment of nondetections, time series analysis, and spatial point processes. It applies the methods discussed to contemporary astronomical research datasets using the R statistical software, making it invaluable for graduate students and researchers facing complex data analysis tasks. A link to the author's website for this book can be found at www.cambridge.org/msma. Material available on their website includes datasets, R code and errata.
This textbook provides advanced undergraduate and graduate students with a complete introduction to modern cosmology. It successfully bridges the gap between undergraduate and advanced graduate texts by discussing topics of current research, starting from first principles. Throughout this authoritative volume, emphasis is given to the simplest, most intuitive explanation for key equations used by researchers. The first third of the book carefully develops the necessary background in general relativity and quantum fields. The rest of the book then provides self-contained accounts of all the key topics in contemporary cosmology, including inflation, topological defects, gravitational lensing, galaxy formation, large-scale structure and the distance scale. To aid understanding, the book is well illustrated with helpful figures and includes outline solutions to nearly 100 problems. All necessary astronomical jargon is clearly explained, ensuring the book is self-contained for any student with undergraduate physics.
Gravitational lensing is a consequence of general relativity, where the gravitational force due to a massive object bends the paths of light originating from distant objects lying behind it. Using very little general relativity and no higher level mathematics, this text presents the basics of gravitational lensing, focusing on the equations needed to understand the phenomena. It then applies them to a diverse set of topics, including multiply imaged objects, time delays, extrasolar planets, microlensing, cluster masses, galaxy shape measurements, cosmic shear, and lensing of the cosmic microwave background. This approach allows undergraduate students and others to get quickly up to speed on the basics and the important issues. The text will be especially relevant as large surveys such as LSST and Euclid begin to dominate the astronomical landscape. Designed for a one semester course, it is accessible to anyone with two years of undergraduate physics background.
This thesis explores advanced Bayesian statistical methods for extracting key information for cosmological model selection, parameter inference and forecasting from astrophysical observations. Bayesian model selection provides a measure of how good models in a set are relative to each other - but what if the best model is missing and not included in the set? Bayesian Doubt is an approach which addresses this problem and seeks to deliver an absolute rather than a relative measure of how good a model is. Supernovae type Ia were the first astrophysical observations to indicate the late time acceleration of the Universe - this work presents a detailed Bayesian Hierarchical Model to infer the cosmological parameters (in particular dark energy) from observations of these supernovae type Ia.
Providing the knowledge and practical experience to begin analysing scientific data, this book is ideal for physical sciences students wishing to improve their data handling skills. The book focuses on explaining and developing the practice and understanding of basic statistical analysis, concentrating on a few core ideas, such as the visual display of information, modelling using the likelihood function, and simulating random data. Key concepts are developed through a combination of graphical explanations, worked examples, example computer code and case studies using real data. Students will develop an understanding of the ideas behind statistical methods and gain experience in applying them in practice. Further resources are available at www.cambridge.org/9781107607590, including data files for the case studies so students can practise analysing data, and exercises to test students' understanding.