| List of contributors | p. ix |
| Preface | p. xi |
| Methods | p. 1 |
| Foundations and algorithms | p. 3 |
| Rational inference | p. 3 |
| Foundations | p. 4 |
| Inference | p. 11 |
| Algorithms | p. 20 |
| Concluding remarks | p. 32 |
| Simple applications of Bayesian methods | p. 36 |
| Introduction | p. 36 |
| Essentials of modern cosmology | p. 37 |
| Theorists and pre-processed data | p. 41 |
| Experimentalists and raw measurements | p. 49 |
| Concluding remarks | p. 54 |
| Parameter estimation using Monte Carlo sampling | p. 57 |
| Why do sampling? | p. 57 |
| How do I get the samples? | p. 59 |
| Have I taken enough samples yet? | p. 69 |
| What do I do with the samples? | p. 70 |
| Conclusions | p. 77 |
| Model selection and multi-model inference | p. 79 |
| Introduction | p. 79 |
| Levels of Bayesian inference | p. 80 |
| The Bayesian framework | p. 82 |
| Computing the Bayesian evidence | p. 87 |
| Interpretational scales | p. 89 |
| Applications | p. 90 |
| Conclusions | p. 96 |
| Bayesian experimental design and model selection forecasting | p. 99 |
| Introduction | p. 99 |
| Predicting the effectiveness of future experiments | p. 100 |
| Experiment optimization for error reduction | p. 106 |
| Experiment optimization for model selection | p. 115 |
| Predicting the outcome of model selection | p. 120 |
| Summary | p. 124 |
| Signal separation in cosmology | p. 126 |
| Model of the data | p. 127 |
| The hidden, visible and data spaces | p. 128 |
| Parameterization of the hidden space | p. 129 |
| Choice of data space | p. 133 |
| Applying Bayes' theorem | p. 137 |
| Non-blind signal separation | p. 140 |
| (Semi-)blind signal separation | p. 151 |
| Applications | p. 165 |
| Bayesian source extraction | p. 167 |
| Traditional approaches | p. 168 |
| The Bayesian approach | p. 170 |
| Variable-source-number models | p. 175 |
| Fixed-source-number models | p. 178 |
| Single-source models | p. 178 |
| Conclusions | p. 191 |
| Flux measurement | p. 193 |
| Introduction | p. 193 |
| Photometric measurements | p. 193 |
| Classical flux estimation | p. 196 |
| The source population | p. 199 |
| Bayesian flux inference | p. 201 |
| The faintest sources | p. 204 |
| Practical flux measurement | p. 209 |
| Gravitational wave astronomy | p. 213 |
| A new spectrum | p. 213 |
| Gravitational wave data analysis | p. 214 |
| The Bayesian approach | p. 220 |
| Bayesian analysis of cosmic microwave background data | p. 229 |
| Introduction | p. 229 |
| The CMB as a hierarchical model | p. 231 |
| Polarization | p. 240 |
| Complications | p. 242 |
| Conclusions | p. 243 |
| Bayesian multilevel modelling of cosmological populations | p. 245 |
| Introduction | p. 245 |
| Galaxy distance indicators | p. 247 |
| Multilevel models | p. 252 |
| Future directions | p. 261 |
| A Bayesian approach to galaxy evolution studies | p. 265 |
| Discovery space | p. 265 |
| Average versus maximum likelihood | p. 266 |
| Priors and Malmquist/Eddington bias | p. 268 |
| Small samples | p. 270 |
| Measuring a width in the presence of a contaminating population | p. 272 |
| Fitting a trend in the presence of outliers | p. 275 |
| What is the number returned by tests such as x2, KS, etc.? | p. 280 |
| Summary | p. 281 |
| Photometric redshift estimation: methods and applications | p. 283 |
| Introduction | p. 283 |
| Template methods | p. 285 |
| Bayesian methods and non-colour priors | p. 286 |
| Training methods and neural networks | p. 287 |
| Errors on photo-z | p. 289 |
| Optimal filters | p. 290 |
| Comparison of photo-z codes | p. 290 |
| The role of spectroscopic datasets | p. 292 |
| Synergy with cosmological probes | p. 294 |
| Discussion | p. 296 |
| Index | p. 299 |
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