Bayesian Methods in Cosmology

Abstract

These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level starts from elementary notions, without assuming any previous knowledge of statistical methods, and then progresses to more advanced, research-level topics. After an introduction to the importance of statistical inference for the physical sciences, elementary notions of probability theory and inference are introduced and explained. Bayesian methods are then presented, starting from the meaning of Bayes Theorem and its use as inferential engine, including a discussion on priors and posterior distributions. Numerical methods for generating samples from arbitrary posteriors (including Markov Chain Monte Carlo and Nested Sampling) are then covered. The last section deals with the topic of Bayesian model selection and how it is used to assess the performance of models, and contrasts it with the classical p-value approach. A series of exercises of various levels of difficulty are designed to further the understanding of the theoretical material, including fully worked out solutions for most of them.

86 pages, 16 figures. Lecture notes for the 44th Saas Fee Advanced Course on Astronomy and Astrophysics, "Cosmology with wide-field surveys" (March 2014), to be published by Springer. Comments welcome

References in corpus (22)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
• Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• First-year Sloan Digital Sky Survey-II (SDSS-II) Supernova Results: Hubble Diagram and Cosmological Parameters
• Statistics: Handle with Care, Detecting Multiple Model Components with the Likelihood Ratio Test
• PolyChord: nested sampling for cosmology
• How many cosmological parameters?
• A Nested Sampling Algorithm for Cosmological Model Selection
• Cosmological Constraints from Measurements of Type Ia Supernovae discovered during the first 1.5 years of the Pan-STARRS1 Survey
• Applications of Bayesian model selection to cosmological parameters
• Fast and reliable MCMC for cosmological parameter estimation
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Measuring D_A and H at z=0.57 from the Baryon Acoustic Peak in the Data Release 9 Spectroscopic Galaxy Sample
• Measuring the effective complexity of cosmological models
• Present and future evidence for evolving dark energy
• Bayesian model selection without evidences: application to the dark energy equation-of-state
• Encyclopaedia Curvatonis
• Applications of Bayesian model averaging to the curvature and size of the Universe
• Should we doubt the cosmological constant?
• Comment on "Bayesian Analysis of Pentaquark Signals from CLAS Data", with Response to the Reply by Ireland and Protopopsecu
• Application of Bayesian model averaging to measurements of the primordial power spectrum

Cited by in corpus (19)

• Dark Matter Annihilation to Neutrinos
• Aurora: A Generalised Retrieval Framework for Exoplanetary Transmission Spectra
• Cosmological parameter inference with Bayesian statistics
• A tale of two sites -- II: Inferring the properties of minihalo-hosted galaxies with upcoming 21-cm interferometers
• The integrated 3-point correlation function of cosmic shear
• Constraints on warm dark matter from UV luminosity functions of high-z galaxies with Bayesian model comparison
• Differentiating Modern and Prebiotic Earth Scenarios for TRAPPIST-1e: High-resolution Transmission Spectra and Predictions for JWST
• BAO from angular clustering: optimization and mitigation of theoretical systematics
• Bayesian evidence for $\alpha$-attractor dark energy models
• Spherical Bayesian mass-mapping with uncertainties: full sky observations on the celestial sphere
• A Cosmological Underdensity Does Not Solve the Hubble Tension
• Search for Lorentz Invariance Violation from stacked Gamma-Ray Burst spectral lag data
• Sparse Bayesian mass-mapping with uncertainties: local credible intervals
• Observational constraints on the oscillating dark energy cosmologies
• A revised density split statistic model for general filters
• Bayesian analysis of Juno/JIRAM's NIR observations of Europa
• Optimal prior for Bayesian inference in a constrained parameter space
• Mass classification of dark matter perturbers of stellar tidal streams
• A Bayesian approach to truncated data sets: An application to Malmquist bias in Supernova Cosmology