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Modern statistical methods for astronomy : with R applications /
"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. Yet most astronomers still use a narrow suite of traditional stati...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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.
- 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).
- 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.