Practical statistics for astronomers /
"Astronomy needs statistical methods to interpret data, but statistics is a many-faceted subject which is difficult for non-specialists to access. This handbook helps astronomers analyze the complex data and models of modern astronomy. This second edition has been revised to feature many more e...
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| Main Author: | |
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| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge [England] ; New York :
Cambridge University Press,
2012.
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| Edition: | 2nd ed. |
| Series: | Cambridge observing handbooks for research astronomers ;
8. |
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- Cover; Practical Statistics for Astronomers, Second Edition; Cover insets; Cambridge Observing Handbooks for Research Astronomers; Title; Copyright; Contents; Foreword to first edition; Foreword to second edition; Note on notation; 1 Decision; 1.1 How is science done?; 1.2 Probability; probability distributions; 1.3 Bolt-on statistics?; 1.4 Probability and statistics in inference: an overview of this book; 1.5 How to use this book; Exercises; 2 Probability; 2.1 What is probability?; 2.2 Conditionality and independence; 2.3 ... and Bayes' theorem; 2.4 Probability distributions; 2.4.1 Concept.
- 2.4.2 Some common distributions2.5 Bayesian inferences with probability; 2.6 Monte Carlo generators; Exercises; 3 Statistics and expectations; 3.1 Statistics; 3.2 What should we expect of our statistics?; 3.3 Simple error analysis; 3.3.1 Random or systematic?; 3.3.2 Error propagation; 3.3.3 Combining distributions; 3.4 Some useful statistics, and their distributions; 3.5 Uses of statistics; Exercises; 4 Correlation and association; 4.1 The fishing trip; 4.2 Testing for correlation; 4.2.1 Bayesian correlation-testing; 4.2.2 The classical approach to correlation-testing.
- 4.2.3 Correlation-testing: classical, non-parametric4.2.4 Correlation-testing: Bayesian versus non-Bayesian tests; 4.3 Partial correlation; 4.4 But what next?; 4.5 Principal component analysis; Exercises; 5 Hypothesis testing; 5.1 Methodology of classical hypothesis testing; 5.2 Parametric tests: means and variances, t and F tests; 5.2.1 The Behrens-Fisher Test; 5.2.2 Non-Gaussian parametric testing; 5.2.3 Which model is better? The Bayes factor; 5.3 Non-parametric tests: single samples; 5.3.1 Chi-square test; 5.3.2 Kolmogorov-Smirnov one-sample test; 5.3.3 One-sample runs test of randomness.
- 5.4 Non-parametric tests: two independent samples5.4.1 Fisher exact test; 5.4.2 Chi-square two-sample (or k-sample) test; 5.4.3 Wilcoxon-Mann-Whitney U test; 5.4.4 Kolmogorov-Smirnov two-sample test; 5.5 Summary, one- and two-sample non-parametric tests; 5.6 Statistical ritual; Exercises; 6 Data modelling and parameter estimation: basics; 6.1 The maximum-likelihood method; 6.2 The method of least squares: regression analysis; 6.3 The minimum chi-square method; 6.4 Weighting combinations of data; 6.5 Bayesian likelihood analysis; 6.6 Bootstrap and jackknife; Exercises.
- 7 Data modelling and parameter estimation: advanced topics7.1 Model choice and Bayesian evidence; 7.2 Model simplicity and the Ockham factor; 7.3 The integration problem; 7.4 Pitfalls in model choice; 7.5 The Akaike and Bayesian information criteria; 7.6 Monte Carlo integration: doing the Bayesian integrals; 7.7 The Metropolis-Hastings algorithm; 7.8 Computation of the evidence by MCMC; 7.9 Models of models, and the combination of data sets; 7.10 Broadening the range of models, and weights; 7.11 Press and Kochanek's method; 7.12 Median statistics; Exercises; 8 Detection and surveys.
