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
