Bayesian Methods in Cosmology

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In recent years cosmologists have advanced from largely qualitative models of the Universe to precision modelling using Bayesian methods, in order to determine the properties of the Universe to high accuracy. This timely book is the only comprehensive introduction to the use of Bayesian methods in cosmological studies, and is an essential reference for graduate students and researchers in cosmology, astrophysics and applied statistics. The first part of the book focuses on methodology, setting the basic foundations and giving a detailed description of techniques. It covers topics including the estimation of parameters, Bayesian model comparison, and separation of signals. The second part explores a diverse range of applications, from the detection of astronomical sources (including through gravitational waves), to cosmic microwave background analysis and the quantification and classification of galaxy properties. Contributions from 24 highly regarded cosmologists and statisticians make this an authoritative guide to the subject.

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Product Details

  • ISBN-13: 9780521887946
  • Publisher: Cambridge University Press
  • Publication date: 1/31/2010
  • Pages: 316
  • Product dimensions: 7.00 (w) x 9.70 (h) x 0.80 (d)

Meet the Author

M. P. Hobson is Reader in Astrophysics and Cosmology at the Cavendish Laboratory, University of Cambridge, where he researches theoretical and observational cosmology, Bayesian statistical methods, gravitation and theoretical optics.

Andrew H. Jaffe is Professor of Astrophysics and Cosmology at Imperial College and a member of the Planck Surveyor Satellite collaboration, which will create the highest-resolution and most sensitive maps of the CMB ever produced.

Andrew R. Liddle is Professor of Astrophysics at the University of Sussex. He is the author of over 150 journal articles and four books on cosmology, covering topics from early Universe theory to modelling astrophysical data.

Pia Mukherjee is a Postdoctoral Researcher in the Astronomy Centre at the University of Sussex, specialising in constraining cosmological models, including dark energy models, from observational data.

David Parkinson is a Postdoctoral Research Fellow in the Astronomy Centre at the University of Sussex, working in the areas of cosmology and the early Universe.

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Table of Contents

List of contributors ix

Preface xi

Part I Methods 1

1 Foundations and algorithms John Skilling 3

1.1 Rational inference 3

1.2 Foundations 4

1.3 Inference 11

1.4 Algorithms 20

1.5 Concluding remarks 32

2 Simple applications of Bayesian methods D. S. Sivia S. G. Rowlings 36

2.1 Introduction 36

2.2 Essentials of modern cosmology 37

2.3 Theorists and pre-processed data 41

2.4 Experimentalists and raw measurements 49

2.5 Concluding remarks 54

3 Parameter estimation using Monte Carlo sampling Antony Lewis Sarah Bridle 57

3.1 Why do sampling? 57

3.2 How do I get the samples? 59

3.3 Have I taken enough samples yet? 69

3.4 What do I do with the samples? 70

3.5 Conclusions 77

4 Model selection and multi-model inference Andrew R. Liddle Pia Mukherjee David Parkinson 79

4.1 Introduction 79

4.2 Levels of Bayesian inference 80

4.3 The Bayesian framework 82

4.4 Computing the Bayesian evidence 87

4.5 Interpretational scales 89

4.6 Applications 90

4.7 Conclusions 96

5 Bayesian experimental design and model selection forecasting Roberto Trotta Martin Kunz Pia Mukherjee David Parkinson 99

5.1 Introduction 99

5.2 Predicting the effectiveness of future experiments 100

5.3 Experiment optimization for error reduction 106

5.4 Experiment optimization for model selection 115

5.5 Predicting the outcome of model selection 120

5.6 Summary 124

6 Signal separation in cosmology M. P. Hobson M. A. J. Ashdown V. Stolyarov 126

6.1 Model of the data 127

6.2 The hidden, visible and data spaces 128

6.3 Parameterization of the hidden space 129

6.4 Choice of data space 133

6.5 Applying Bayes' theorem 137

6.6 Non-blind signal separation 140

6.7 (Semi-)blind signal separation 151

Part II Applications 165

7 Bayesian source extraction M. P. Hobson Gra?a Rocha Richard S. Savage 167

7.1 Traditional approaches 168

7.2 The Bayesian approach 170

7.3 Variable-source-number models 175

7.4 Fixed-source-number models 178

7.5 Single-source models 178

7.6 Conclusions 191

8 Flux measurement Daniel Mortlock 193

8.1 Introduction 193

8.2 Photometric measurements 193

8.3 Classical flux estimation 196

8.4 The source population 199

8.5 Bayesian flux inference 201

8.6 The faintest sources 204

8.7 Practical flux measurement 209

9 Gravitational wave astronomy Neil Cornish 213

9.1 A new spectrum 213

9.2 Gravitational wave data analysis 214

9.3 The Bayesian approach 220

10 Bayesian analysis of cosmic microwave background data Andrew H. Jaffe 229

10.1 Introduction 229

10.2 The CMB as a hierarchical model 231

10.3 Polarization 240

10.4 Complications 242

10.5 Conclusions 243

11 Bayesian multilevel modelling of cosmological populations Thomas J. Loredo Martin A. Hendry 245

11.1 Introduction 245

11.2 Galaxy distance indicators 247

11.3 Multilevel models 252

11.4 Future directions 261

12 A Bayesian approach to galaxy evolution studies Stefano Andreon 265

12.1 Discovery space 265

12.2 Average versus maximum likelihood 266

12.3 Priors and Malmquist/Eddington bias 268

12.4 Small samples 270

12.5 Measuring a width in the presence of a contaminating population 272

12.6 Fitting a trend in the presence of outliers 275

12.7 What is the number returned by tests such as x2, KS, etc.? 280

12.8 Summary 281

13 Photometric redshift estimation: methods and applications Ofer Lahav Filipe B. Abdalla Manda Banerji 283

13.1 Introduction 283

13.2 Template methods 285

13.3 Bayesian methods and non-colour priors 286

13.4 Training methods and neural networks 287

13.5 Errors on photo-z 289

13.6 Optimal filters 290

13.7 Comparison of photo-z codes 290

13.8 The role of spectroscopic datasets 292

13.9 Synergy with cosmological probes 294

13.10 Discussion 296

Index 299

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