UID:
almafu_9959228385502883
Format:
1 online resource (xviii, 476 pages) :
,
digital, PDF file(s).
ISBN:
1-107-71343-9
,
1-283-52836-3
,
1-139-01565-6
,
9786613840813
,
1-139-52676-6
,
1-139-52556-5
,
1-139-53142-5
,
1-139-53023-2
,
1-139-52795-9
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover; Modern Statistical Methods for Astronomy; Title; Copyright; Dedication; Contents; Preface; Motivation and goals; Audience; Outline and classroom use; Astronomical datasets and R scripts; Acknowledgements; 1: Introduction; 1.1 The role of statistics in astronomy; 1.1.1 Astronomy and astrophysics; 1.1.2 Probability and statistics; 1.1.3 Statistics and science; 1.2 History of statistics in astronomy; 1.2.1 Antiquity through the Renaissance; 1.2.2 Foundations of statistics in celestial mechanics; 1.2.3 Statistics in twentieth-century astronomy; 1.3 Recommended reading; 2: Probability
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2.1 Uncertainty in observational science2.2 Outcome spaces and events; 2.3 Axioms of probability; 2.4 Conditional probabilities; 2.4.1 Bayes' theorem; 2.4.2 Independent events; 2.5 Random variables; 2.5.1 Density and distribution functions; 2.5.2 Independent and identically distributed random variables; 2.6 Quantile function; 2.7 Discrete distributions; 2.8 Continuous distributions; 2.9 Distributions that are neither discrete nor continuous; 2.10 Limit theorems; 2.11 Recommended reading; 2.12 R applications; 3: Statistical inference; 3.1 The astronomical context
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3.2 Concepts of statistical inference3.3 Principles of point estimation; 3.4 Techniques of point estimation; 3.4.1 Method of moments; 3.4.2 Method of least squares; 3.4.3 Maximum likelihood method; 3.4.4 Confidence intervals; 3.4.5 Calculating MLEs with the EM algorithm; 3.5 Hypothesis testing techniques; 3.6 Resampling methods; 3.6.1 Jackknife; 3.6.2 Bootstrap; 3.7 Model selection and goodness-of-fit; 3.7.1 Nonparametric methods for goodness-of-fit; 3.7.2 Likelihood-based methods for model selection; 3.7.3 Information criteria for model selection; 3.7.4 Comparing different model families
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3.8 Bayesian statistical inference3.8.1 Inference for the binomial proportion; 3.8.2 Prior distributions; 3.8.3 Inference for Gaussian distributions; 3.8.4 Hypotheses testing and the Bayes factor; 3.8.5 Model selection and averaging; 3.8.6 Bayesian computation; 3.9 Remarks; 3.10 Recommended reading; 3.11 R applications; 4: Probability distribution functions; 4.1 Binomial and multinomial; 4.1.1 Ratio of binomial random variables; 4.2 Poisson; 4.2.1 Astronomical context; 4.2.2 Mathematical properties; 4.2.3 Poisson processes; 4.3 Normal and lognormal; 4.4 Pareto (power-law)
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4.4.1 Least-squares estimation4.4.2 Maximum likelihood estimation; 4.4.3 Extensions of the power-law; 4.4.4 Multivariate Pareto; 4.4.5 Origins of power-laws; 4.5 Gamma; 4.6 Recommended reading; 4.7 R applications; 4.7.1 Comparing Pareto distribution estimators; 4.7.2 Fitting distributions to data; 4.7.3 Scope of distributions in R and CRAN; 5: Nonparametric statistics; 5.1 The astronomical context; 5.2 Concepts of nonparametric inference; 5.3 Univariate problems; 5.3.1 Kolmogorov-Smirnov and other e.d.f. tests; 5.3.2 Robust statistics of location; 5.3.3 Robust statistics of spread
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5.4 Hypothesis testing
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English
Additional Edition:
ISBN 0-521-76727-X
Language:
English
URL:
https://doi.org/10.1017/CBO9781139015653
