## Practical Statistics for AstronomersAstronomy, like any experimental subject, needs statistical methods to interpret data reliably. This practical handbook presents the most relevant statistical and probabilistic machinery for use in observational astronomy. Classical parametric and non-parametric methods are covered, but there is a strong emphasis on Bayesian solutions and the importance of probability in experimental inference. Chapters cover basic probability, correlation analysis, hypothesis testing, Bayesian modelling, time series analysis, luminosity functions, and clustering. The book avoids the technical language of statistics in favour of demonstrating astronomical relevance and applicability. It contains many worked examples, and problems that make use of databases which are available on the Web. It is suitable for self-study at advanced undergraduate or graduate level, as a reference for professional astronomers, and as a textbook basis for courses in statistical methods in astronomy. |

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### Contents

III | 1 |

IV | 3 |

V | 4 |

VI | 6 |

VII | 7 |

VIII | 8 |

IX | 9 |

X | 10 |

XXXVII | 123 |

XXXVIII | 126 |

XXXIX | 130 |

XL | 133 |

XLI | 139 |

XLII | 142 |

XLIII | 143 |

XLIV | 148 |

XI | 11 |

XII | 15 |

XIII | 17 |

XIV | 24 |

XV | 32 |

XVI | 34 |

XVII | 37 |

XVIII | 41 |

XIX | 43 |

XX | 51 |

XXI | 52 |

XXII | 54 |

XXIII | 57 |

XXIV | 66 |

XXV | 67 |

XXVI | 69 |

XXVII | 74 |

XXVIII | 76 |

XXIX | 77 |

XXX | 79 |

XXXI | 86 |

XXXII | 92 |

XXXIII | 103 |

XXXIV | 105 |

XXXV | 107 |

XXXVI | 118 |

### Common terms and phrases

analysis angular correlation function assumed astronomers asymptotic average Avni baseline Bayes Bayesian bins bivariate bootstrap calculate cell chi-square test classical clustering coefficient compute contours correlation function covariance matrix datasets degrees of freedom depends derived described detection distance equation error estimate example expected Feigelson filter flux density flux limit flux-limited Fourier transform frequency galaxy Gaussian distribution given independent inference integration intervals Kolmogorov-Smirnov Kolmogorov-Smirnov test likelihood function luminosity function Malmquist bias maximum maximum-likelihood mean measurement method Monte Carlo multivariate noise non-parametric tests normalized objects observations offset parameters peak points Poisson distribution posterior distribution posterior probability power law power spectrum prior prob(a probability distribution quantity radio sources random numbers sample scale scan Schechter function Section signal significance simple simulation skewness source count spectra standard deviation supernova surface density survey Table technique test statistic theorem tion upper limits values variables variance Vmax zero