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Statistics for Astrophysics

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Statistics for Astrophysics 1
Statistics for Astrophysics - Bayesian Methodology 3
List of Participants 7
Table of Contents 9
Foreword 11
BAYESIAN STATISTICAL METHODS FOR ASTRONOMY PART I: FOUNDATIONS 13
1 Foundations of Bayesian Data Analysis 13
2 Further Topics with Univariate Parameter Models 24
3 Final Comments 28
References 29
1 Introduction 31
BAYESIAN STATISTICAL METHODS FOR ASTRONOMY PART II: MARKOV CHAIN MONTE CARLO 31
2 Rejection Sampling 32
3 Markov Chain Monte Carlo 36
4 Practical Challenges and Advice 44
5 Overview of Recommended Strategy 57
References 58
BAYESIAN STATISTICAL METHODS FOR ASTRONOMY PART III: MODEL BUILDING 61
1 Introduction to Multi-Level Models 61
2 A Multilevel Model for Selection Effects 62
3 James-Stein Estimators and Shrinkage 68
4 Hierarchical Models and the Bayesian Perspective 72
5 Concluding Remarks 75
Acknowledgements 77
References 77
APPROXIMATE BAYESIAN COMPUTATION, AN INTRODUCTION 79
1 Mudmap: ABC at a glance 79
2 ABC Basics 82
3 ABC Consistency 95
4 Summary Statistics, the ABC Conundrum 98
5 ABC Model Choice 100
6 Conclusion 109
References 109
CLUSTERING MILKY WAY’S GLOBULAR CLUSTERS: A BAYESIAN NONPARAMETRIC APPROACH 115
1 R requirements 115
2 Introduction and motivation 116
3 Model-based clustering 119
4 Bayesian nonparametrics around the Dirichlet process 121
5 Application to clustering of globulars of our galaxy 132
Acknowledgements 139
References 139

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