A Nested Sampling Algorithm for Cosmological Model Selection

By P. Mukherjee, David Parkinson, Andrew R. Liddle. 2005

316 citations recorded by the source corpus.

The abundance of cosmological data becoming available means that a wider range of cosmological models are testable than ever before. However, an important distinction must be made between parameter fitting and model selection. While parameter fitting simply determines how well a model fits the data, model selection statistics, such as the Bayesian evidence, are now necessary to choose between these different models, and in particular to assess the need for new parameters. We implement a new evidence algorithm known as nested sampling, which combines accuracy, generality of application, and computational feasibility, and we apply it to some cosmological data sets and models. We find that a five-parameter model with a Harrison-Zel'dovich initial spectrum is currently preferred.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c70bf3f8058a5f5c5c7237b58f0560bb1acd537c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. S. Vagnozzi
2. T. Treu
3. A. Banday
4. K. G'orski
5. H. Eriksen
6. Leon V. E. Koopmans
7. D. Baumann
8. Will Handley

In Statistical and Nonlinear Physics

1. Will Handley
2. Jesús Torrado
3. M. Hobson
4. Farhan Feroz
5. V. Poulin
6. A. Lewis
7. L. Verde
8. Julien Lesgourgues

Citations in the corpus

• TAU-REX I: A NEXT GENERATION RETRIEVAL CODE FOR EXOPLANETARY ATMOSPHERES (2014, background): “Nested sampling (NS) algorithms (Skilling 2004, 2006; Mukherjee et al. 2006; Chopin & Robert 2010; Keeton 2011; Jasa & Xiang 2005) are becoming increasing popular in extrasolar planets (e.g. Kipping et al. 2012; Placek et al. 2013).”
• Information criteria for astrophysical model selection (2007, unknown): “Nevertheless, many methods exist (e.g. Gregory 2005; Trotta 2005), and the nested sampling algorithm (Skilling 2006) has proven feasible for many cosmology applications (Mukherjee et al. 2006; Parkinson et al. 2006; Liddle et al. 2006b).”
• On model selection forecasting, Dark Energy and modified gravity (2007, methodology): “…that deviates from a cosmological constant with equation of state parameter w = −1?” etc. (e.g. Liddle et al. (2006); Bridges, Lasenby & Hobson (2006); Mukherjee et al. (2006); Parkinson, Mukherjee & Liddle (2006); Saini et al. (2004); Bridges, Lasenby & Hobson (2007); Trotta (2007) and references…”
• Model selection in finite element model updating using the Bayesian evidence statistic (2011, methodology): “The algorithm has been successfully applied and further modified in a number of recent astronomy and cosmology papers [11,25,26,34].”
• Applications of Bayesian model selection to cosmological parameters (2005, methodology): “While nested sampling reduces the number of likelihood evaluations to the same order of magnitude as for parameter estimation, in the cosmological context this does not necessarily imply that the computing time can be reduced accordingly, see Mukherjee et al. (2006) for details.”
• Hemispherical Power Asymmetry in the Third-Year Wilkinson Microwave Anisotropy Probe Sky Maps (2007, methodology): “The errors on the evidence are estimated by performing eight independent analyses for each case, and computing the standard deviation (Mukherjee et al. 2006).”
• The impact of priors and observables on parameter inferences in the constrained MSSM (2008, background): “Ellipsoidal nested sampling [55] tries to overcome the above problem by approximating the iso-likelihood contour of the point to be replaced by an D–dimensional ellipsoid determined from the covariance matrix of the current set of live points.”
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology (2006, unknown): “These results should be confirmed by Bayesian model comparison techniques (Beltrán et al. 2005; Trotta 2007; Mukherjee et al. 2006; Bridges et al. 2006).”
• Detection of a dark substructure through gravitational imaging (2009, background): “Chopin & Robert (2008), for example, proposed an extension of the nested sampling, based on the principle of importance sampling, while Mukherjee et al. (2006) developedan ellipsoidal nested sampling by approximating the iso-likelihood contours by D-dimensional ellipsoids.”
• INCREASING EVIDENCE FOR HEMISPHERICAL POWER ASYMMETRY IN THE FIVE-YEAR WMAP DATA (2009, methodology): “The Bayesian evidence, E = 3 P (d|H) is computed with the “nested sampling” algorithm (Skilling 2004; Mukherjee et al. 2006).”
• Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses (2007, methodology): “Ellipsoidal sampling (Mukherjee et al. (2006)) partially overcomes the above problem by approximating the iso-likelihood contour of the point to be replaced by anD-dimensional ellipsoid determined from the covariance matrix of the current set of live points.”
• CONSTRAINTS ON COSMIC-RAY PROPAGATION MODELS FROM A GLOBAL BAYESIAN ANALYSIS (2010, background): “(4), the recent development of the MultiNest algorithm (Feroz & Hobson 2008; Feroz et al. 2009) has delivered an extremely powerful and versatile algorithm that has been demonstrated to be able to deal with extremely complex likelihood surfaces in hundreds of dimensions exhibiting multiple peaks.”
• Exploring cosmic origins with CORE: Inflation (2016, methodology): “All evidences have then been derived using the MULTINEST nested sampling algorithm [180, 181, 239] with a target accuracy of 10−4 and the number of live points equal to 30000.”