Bayesian Models for Astrophysical Data

Bayesian Models for Astrophysical Data

Author: Joseph M. Hilbe

Publisher: Cambridge University Press

Published: 2017-04-27

Total Pages: 429

ISBN-13: 1108210740

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This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.


Bayesian Methods in Cosmology

Bayesian Methods in Cosmology

Author: Michael P. Hobson

Publisher: Cambridge University Press

Published: 2010

Total Pages: 317

ISBN-13: 0521887941

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Comprehensive introduction to Bayesian methods in cosmological studies, for graduate students and researchers in cosmology, astrophysics and applied statistics.


Bayesian Models for Astrophysical Data

Bayesian Models for Astrophysical Data

Author: Joseph M. Hilbe

Publisher: Cambridge University Press

Published: 2017-04-27

Total Pages: 429

ISBN-13: 1107133084

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A hands-on guide to Bayesian models with R, JAGS, Python, and Stan code, for a wide range of astronomical data types.


Modeling Count Data

Modeling Count Data

Author: Joseph M. Hilbe

Publisher: Cambridge University Press

Published: 2014-07-21

Total Pages: 301

ISBN-13: 1107028337

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This book provides guidelines and fully worked examples of how to select, construct, interpret and evaluate the full range of count models.


Statistical Methods for Astronomical Data Analysis

Statistical Methods for Astronomical Data Analysis

Author: Asis Kumar Chattopadhyay

Publisher: Springer

Published: 2014-10-01

Total Pages: 356

ISBN-13: 149391507X

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This book introduces “Astrostatistics” as a subject in its own right with rewarding examples, including work by the authors with galaxy and Gamma Ray Burst data to engage the reader. This includes a comprehensive blending of Astrophysics and Statistics. The first chapter’s coverage of preliminary concepts and terminologies for astronomical phenomenon will appeal to both Statistics and Astrophysics readers as helpful context. Statistics concepts covered in the book provide a methodological framework. A unique feature is the inclusion of different possible sources of astronomical data, as well as software packages for converting the raw data into appropriate forms for data analysis. Readers can then use the appropriate statistical packages for their particular data analysis needs. The ideas of statistical inference discussed in the book help readers determine how to apply statistical tests. The authors cover different applications of statistical techniques already developed or specifically introduced for astronomical problems, including regression techniques, along with their usefulness for data set problems related to size and dimension. Analysis of missing data is an important part of the book because of its significance for work with astronomical data. Both existing and new techniques related to dimension reduction and clustering are illustrated through examples. There is detailed coverage of applications useful for classification, discrimination, data mining and time series analysis. Later chapters explain simulation techniques useful for the development of physical models where it is difficult or impossible to collect data. Finally, coverage of the many R programs for techniques discussed makes this book a fantastic practical reference. Readers may apply what they learn directly to their data sets in addition to the data sets included by the authors.


Astrostatistics

Astrostatistics

Author: Gutti Jogesh Babu

Publisher: CRC Press

Published: 1996-08-01

Total Pages: 242

ISBN-13: 9780412983917

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Modern astronomers encounter a vast range of challenging statistical problems, yet few are familiar with the wealth of techniques developed by statisticians. Conversely, few statisticians deal with the compelling problems confronted in astronomy. Astrostatistics bridges this gap. Authored by a statistician-astronomer team, it provides professionals and advanced students in both fields with exposure to issues of mutual interest. In the first half of the book the authors introduce statisticians to stellar, galactic, and cosmological astronomy and discuss the complex character of astronomical data. For astronomers, they introduce the statistical principles of nonparametrics, multivariate analysis, time series analysis, density estimation, and resampling methods. The second half of the book is organized by statistical topic. Each chapter contains examples of problems encountered astronomical research and highlights methodological issues. The final chapter explores some controversial issues in astronomy that have a strong statistical component. The authors provide an extensive bibliography and references to software for implementing statistical methods. The "marriage" of astronomy and statistics is a natural one and benefits both disciplines. Astronomers need the tools and methods of statistics to interpret the vast amount of data they generate, and the issues related to astronomical data pose intriguing challenges for statisticians. Astrostatistics paves the way to improved statistical analysis of astronomical data and provides a common ground for future collaboration between the two fields.


Numerical Analysis Using R

Numerical Analysis Using R

Author: Graham W. Griffiths

Publisher: Cambridge University Press

Published: 2016-04-26

Total Pages: 637

ISBN-13: 131665415X

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This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.


Bayesian Logical Data Analysis for the Physical Sciences

Bayesian Logical Data Analysis for the Physical Sciences

Author: Phil Gregory

Publisher: Cambridge University Press

Published: 2005-04-14

Total Pages: 498

ISBN-13: 113944428X

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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.


Model-Based Clustering and Classification for Data Science

Model-Based Clustering and Classification for Data Science

Author: Charles Bouveyron

Publisher: Cambridge University Press

Published: 2019-07-25

Total Pages: 447

ISBN-13: 1108640591

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Cluster analysis finds groups in data automatically. Most methods have been heuristic and leave open such central questions as: how many clusters are there? Which method should I use? How should I handle outliers? Classification assigns new observations to groups given previously classified observations, and also has open questions about parameter tuning, robustness and uncertainty assessment. This book frames cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions. It builds the basic ideas in an accessible but rigorous way, with extensive data examples and R code; describes modern approaches to high-dimensional data and networks; and explains such recent advances as Bayesian regularization, non-Gaussian model-based clustering, cluster merging, variable selection, semi-supervised and robust classification, clustering of functional data, text and images, and co-clustering. Written for advanced undergraduates in data science, as well as researchers and practitioners, it assumes basic knowledge of multivariate calculus, linear algebra, probability and statistics.