Statistics for Astrophysics

Jean-Baptiste Marquette

Description

This book includes the lectures given during the third session of the School of Statistics for Astrophysics that took place at Autrans, near Grenoble, in France, in October 2017. The subject is Bayesian Methodology.

The interest of this statistical approach in astrophysics probably comes from its necessity and its success in determining the cosmological parameters from observations, especially from the cosmic background luctuations. The cosmological community has thus been very active in this field for many years. But the Bayesian methodology, complementary to the more classical frequentist one, has many applications in physics in general due to its ability to incorporate a priori knowledge into inference, such as uncertainty brought by the observational processes. The Bayesian approach becomes more and more widespread in the astrophysical literature.

This book contains statistics courses on basic to advanced methods with practical exercises using the R environment, by leading experts in their field. This covers the foundations of Bayesian inference, Markov chain Monte Carlo technique, model building, Approximate Bayesian Computation (ABC) and Bayesian nonparametric inference and clustering.

Sujets

• Sciences expérimentales
• Astronomie et astrophysique
• Sciences et techniques
• Astrophysics
• Bayesian inference
• Physics
• Astrophysique
• Science

Informations

• Publié par: EDP Sciences
• Date de parution: 01 décembre 2018
• Nombre de lectures: 0
• EAN13: 9782759822751
• Langue: English
• Poids de l'ouvrage: 14 Mo

Extrait

Stascs for Astrophysics Bayesian Methodology

Didier Fraix‐Burnet, Stéphane Girard, Julyan Arbel and Jean‐Bapste Marquee, Eds

Stascs for Astrophysics Bayesian Methodology

Didier Fraix‐Burnet, Stéphane Girard, Julyan Arbel and Jean‐Bapste Marquee, Eds

This book includes the lectures given during the third session of the School of Sta‐ scs for Astrophysics that took place at Autrans, near Grenoble, in France, in Oc‐ tober 2017. The subject is Bayesian Methodology.

The interest of this stascal approach in astrophysics probably comes from its necessity and its success in determining the cosmological parameters from obser‐ vaons, especially from the cosmic background fluctuaons. The cosmological community has thus been very acve in this field for many years. But the Bayesian methodology, complementary to the more classical frequenst one, has many ap‐ plicaons in physics in general due to its ability to incorporate a priori knowledge into inference, such as uncertainty brought by the observaonal processes. The Bayesian approach becomes more and more widespread in the astrophysical lite‐ rature.

This book contains stascs courses on basic to advanced methods with praccal exercises using the R environment, by leading experts in their field. This covers the foundaons of Bayesian inference, Markov chain Monte Carlo technique, model building, Approximate Bayesian Computaon (ABC) and Bayesian nonpa‐ rametric inference and clustering.

ISBN : 978‐2‐7598‐2274‐4

9 782759 822744

www.edpsciences.org

Stascs for Astrophysics Bayesian Methodology

Didier Fraix‐Burnet, Stéphane Girard, Julyan Arbel and Jean‐Bapste Marquee, Eds

Printed in France

ISBN(print): 978-2-7598-2274-4 – ISBN(ebook): 978-2-7598-2275-1

All rights relative to translation, adaptation and reproduction by any means whatsoever are reserved, worldwide. In accordance with the terms of paragraphs 2 and 3 of Article 41 of the French Act dated March 11, 1957, “copies or reproductions reserved strictly for private use and not intended for collective use” and, on the other hand, analyses and short quotations for example or illustrative purposes, are allowed. Otherwise, “any representation or reproduction – whether in full or in part – without the consent of the author or of his successors or assigns, is unlawful” (Article 40, paragraph 1). Any representation or reproduction, by any means whatsoever, will therefore be deemed an infringement of copyright punishable under Articles 425 and following of the French Penal Code.

© EDP Sciences, 2018

Organisers

Fraix-Burnet Didier, Univ. Grenoble Alpes, CNRS, IPAG, France Girard Stéphane, Univ. Grenoble Alpes, Inria, CNRS, LJK, Grenoble, France Arbel Julyan, Univ. Grenoble Alpes, Inria, CNRS, LJK, Grenoble, France Marquette Jean-Baptistede Bordeaux, France, LAB, CNRS, Univ.

Lecturers

van Dyk David, Imperial College London, UK Robert ChristianWarwick, France/UKParis-Dauphine, Univ. , Univ. Stennig David, Imperial College London, UK Xixi Yu, Imperial College London, UK Arbel JulyanGrenoble Alpes, Inria, CNRS, LJK, Grenoble, France, Univ.

Acknowledgments

We thank our sponsors:

Labex OSUG@2020, Grenoble

Maison de la Modélisation et de la Simulation, Nanosciences et Envi- ronnement (Maimosine, Grenoble)

Institut de Planétologie et d’Astrophysique de Grenoble (IPAG)

Idex - Comue Université Grenoble Alpes

Inria Grenoble Rhône-Alpes

Laboratoire Jean Kuntzmann (LJK)

Université Grenoble Alpes

Grenoble INP

Programme National de Cosmologie et Galaxies (PNCG), Institut Na- tional des Sciences de l’Univers (INSU), CNRS

and the support from the GdR MaDICS (CNRS)

International Society for Bayesian Analysis (ISBA).

4

Statistics for Astrophysics - Bayesian Methodology

List of Participants

Berihuete Angel, Universidad de Cadiz, Spain Bernard Edouard, Observatoire de la Côte d’Azur, France Bernus Léo, IMCCE, France Bilton Lawrence, The University of Hull, UK Bontemps Sylvain, Laboratoire d’Astrophysique de Bordeaux, France Boux Fabien, University Grenoble Alpes, France Buss Claudia, Laboratoire d’Astrophysique de Marseille, France Cai Yongzhi, University of Padova, Italy Cornu David, UTINAM, France Dauvergne Frédéric, Paris-Meudon Observatory, France Forbes Florence, Inria, France Galli Phillip, University of Sao Paulo, Brazil Hackstein Stefan, Sternwarte Bergedorf, Germany Harrison Ian, University of Manchester, UK Hestroffer Daniel, IMCCE/Paris Observatory, France Hottier Clément, Observatoire de Paris, France Khalaj Pouria, Inst. of Planetology and Astrophysics of Grenoble, France Khusanova Yana, Laboratoire d’Astrophysique de Marseille, France Kovlakas Konstantinos, University of Crete IESL/FORTH, Greece Kruuse Maarja, Tartu Observatory, Estony Lalande Florian, ENSAI / ERC COSMIC DANCE, France Law Chi Yan, Chinese university of Hong kong, Hong Kong Lescinskaité Alina, Center for Physical Sciences and Technology, Lituany Lestrade Jean-Francois, LERMA Observatoire de Paris, France Lu Hongliang, Inria, France Marshall Douglas, Université Paris Diderot, France Miret Roig Nuria, Université de Bordeaux, France Munoz Ramirez Veronica, INSERM, France Osborn Hugh, Laboratoire d’Astrophysique de Marseille, France Pagani Laurent, CNRS Observatoire de Paris, France Pascale Raffaele, University of Bologna, Italy Pilia Maura, INAF - Osservatorio di Cagliari, Italy Piron Frédéric, CNRS/IN2P3/LUPM, France Ramos Ramirez Pau, Barcelona University, Spain Sagredo Bryan, Universidad de Chile, Chile Setyawati Yoshinta, AEI Hannover, Germany Slezak É ric, Observatoire de la Côte d’Azur, France Spoto Federica, Observatoire de la Côte d’Azur, France Terrazas Vargas Juan Carlos, Universidad de Chile, Chile Thiel Vivien, Max Planck Institut fuer Radioastronomie, Germany Vega Garcia Laura, Max Planck Institut fuer Radioastronomie, Germany Vono Maxime, IRIT, France

Table of Contents

Foreword BAYESIAN STATISTICAL METHODS FOR ASTRONOMY PART I: FOUNDATIONS  David C. Stenning and David A. van Dyk

1 Foundations of Bayesian Data Analysis 2 Further Topics with Univariate Parameter Models 3 Final Comments References

BAYESIAN STATISTICAL METHODS FOR ASTRONOMY PART II: MARKOV CHAIN MONTE CARLO  David C. Stenning and David A. van Dyk 1 Introduction 2 Rejection Sampling 3 Markov Chain Monte Carlo 4 Practical Challenges and Advice 5 Overview of Recommended Strategy References BAYESIAN STATISTICAL METHODS FOR ASTRONOMY PART III: MODEL BUILDING  David C. Stenning and David A. van Dyk 1 Introduction to Multi-Level Models 2 A Multilevel Model for Selection Effects 3 James-Stein Estimators and Shrinkage 4 Hierarchical Models and the Bayesian Perspective 5 Concluding Remarks References

9

11 11 22 26 27

29 29 30 34 42 55 56

59 59 60 66 70 73 75

8

Statistics for Astrophysics - Bayesian Methodology

APPROXIMATE BAYESIAN COMPUTATION, AN INTRODUCTION  Christian P. Robert 1 Mudmap: ABC at a glance 2 ABC Basics 3 ABC Consistency 4 Summary Statistics, the ABC Conundrum 5 ABC Model Choice 6 Conclusion References CLUSTERING MILKY WAY’S GLOBULAR CLUSTERS: A BAYESIAN NONPARAMETRIC APPROACH  Julyan Arbel 1 R requirements 2 Introduction and motivation 3 Model-based clustering 4 Bayesian nonparametrics around the Dirichlet process 5 Application to clustering of globulars of our galaxy References

77 77 80 93 96 98 107 107

113 113 114 117 119 130 137