## Practical Statistics for AstronomersAstronomy needs statistical methods to interpret data, but statistics is a many-faceted subject that 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 examples using Monte Carlo simulations, and now also includes Bayesian inference, Bayes factors and Markov chain Monte Carlo integration. Chapters cover basic probability, correlation analysis, hypothesis testing, Bayesian modelling, time series analysis, luminosity functions and clustering. Exercises at the end of each chapter guide readers through the techniques and tests necessary for most observational investigations. The data tables, solutions to problems, and other resources are available online at www.cambridge.org/9780521732499. Bringing together the most relevant statistical and probabilistic techniques for use in observational astronomy, this handbook is a practical manual for advanced undergraduate and graduate students and professional astronomers. |

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### Contents

1 Decision | 1 |

2 Probability | 20 |

3 Statistics and expectations | 55 |

4 Correlation and association | 71 |

5 Hypothesis testing | 92 |

basics | 126 |

advanced topics | 151 |

8 Detection and surveys | 182 |

9 Sequential data 1D statistics | 230 |

10 Statistics of largescale structure | 262 |

statistics and our Universe | 291 |

The literature | 316 |

Statistical tables | 321 |

335 | |

347 | |

### Common terms and phrases

1/f noise algorithm analysis angular power spectrum assuming astronomers average baseline Bayes factor bias bins bivariate bootstrap calculate cell cent Chapter classical clustering coefficient components compute contours correlation function cosmology covariance matrix data sets degrees of freedom depends derived described detection Equation error estimate example Figure filtering fluctuations flux density frequency frequentist galaxy Gaussian distribution independent inference integration Kolmogorov–Smirnov likelihood function limit luminosity distribution luminosity function mean measurement Monte Carlo noise non-parametric tests Normal null hypothesis objects observations parameters peak plot Poisson distribution posterior distribution posterior probability power law power spectrum prior probability distribution quasars radio random numbers ratio redshift sample scale scan Section shows signal significance simple simulation source count spectra standard deviation supernova surface density survey Table technique test statistic theorem tion variables variance WMAP zero