Bayesian Methods in Cosmology

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2010-01-18
  • Publisher: Cambridge University Press
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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.

Author Biography

Michael 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, London, and a member of the Planck Surveyor Satellite collaboration, which will create the highest-resolution and most sensitive maps of the cosmic microwave background 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 Research Fellow in the Astronomy Centre at the University of Sussex, specializing 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.

Table of Contents

List of contributorsp. ix
Prefacep. xi
Methodsp. 1
Foundations and algorithmsp. 3
Rational inferencep. 3
Foundationsp. 4
Inferencep. 11
Algorithmsp. 20
Concluding remarksp. 32
Simple applications of Bayesian methodsp. 36
Introductionp. 36
Essentials of modern cosmologyp. 37
Theorists and pre-processed datap. 41
Experimentalists and raw measurementsp. 49
Concluding remarksp. 54
Parameter estimation using Monte Carlo samplingp. 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
Conclusionsp. 77
Model selection and multi-model inferencep. 79
Introductionp. 79
Levels of Bayesian inferencep. 80
The Bayesian frameworkp. 82
Computing the Bayesian evidencep. 87
Interpretational scalesp. 89
Applicationsp. 90
Conclusionsp. 96
Bayesian experimental design and model selection forecastingp. 99
Introductionp. 99
Predicting the effectiveness of future experimentsp. 100
Experiment optimization for error reductionp. 106
Experiment optimization for model selectionp. 115
Predicting the outcome of model selectionp. 120
Summaryp. 124
Signal separation in cosmologyp. 126
Model of the datap. 127
The hidden, visible and data spacesp. 128
Parameterization of the hidden spacep. 129
Choice of data spacep. 133
Applying Bayes' theoremp. 137
Non-blind signal separationp. 140
(Semi-)blind signal separationp. 151
Applicationsp. 165
Bayesian source extractionp. 167
Traditional approachesp. 168
The Bayesian approachp. 170
Variable-source-number modelsp. 175
Fixed-source-number modelsp. 178
Single-source modelsp. 178
Conclusionsp. 191
Flux measurementp. 193
Introductionp. 193
Photometric measurementsp. 193
Classical flux estimationp. 196
The source populationp. 199
Bayesian flux inferencep. 201
The faintest sourcesp. 204
Practical flux measurementp. 209
Gravitational wave astronomyp. 213
A new spectrump. 213
Gravitational wave data analysisp. 214
The Bayesian approachp. 220
Bayesian analysis of cosmic microwave background datap. 229
Introductionp. 229
The CMB as a hierarchical modelp. 231
Polarizationp. 240
Complicationsp. 242
Conclusionsp. 243
Bayesian multilevel modelling of cosmological populationsp. 245
Introductionp. 245
Galaxy distance indicatorsp. 247
Multilevel modelsp. 252
Future directionsp. 261
A Bayesian approach to galaxy evolution studiesp. 265
Discovery spacep. 265
Average versus maximum likelihoodp. 266
Priors and Malmquist/Eddington biasp. 268
Small samplesp. 270
Measuring a width in the presence of a contaminating populationp. 272
Fitting a trend in the presence of outliersp. 275
What is the number returned by tests such as x2, KS, etc.?p. 280
Summaryp. 281
Photometric redshift estimation: methods and applicationsp. 283
Introductionp. 283
Template methodsp. 285
Bayesian methods and non-colour priorsp. 286
Training methods and neural networksp. 287
Errors on photo-zp. 289
Optimal filtersp. 290
Comparison of photo-z codesp. 290
The role of spectroscopic datasetsp. 292
Synergy with cosmological probesp. 294
Discussionp. 296
Indexp. 299
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