A Nested Sampling Algorithm for Cosmological Model Selection

@article{Mukherjee2006ANS,
  title={A Nested Sampling Algorithm for Cosmological Model Selection},
  author={Pia Mukherjee and David Parkinson and Andrew R. Liddle},
  journal={The Astrophysical Journal Letters},
  year={2006},
  volume={638},
  pages={L51 - L54}
}
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… 

Model selection in cosmology

TLDR
The CosmoNest code is described, the first computationally efficient implementation of Bayesian model selection in a cosmological context, and it is applied to recent WMAP satellite data, examining the need for a perturbation spectral index differing from the scale-invariant (Harrison-Zel'dovich) case.

Applications of Bayesian model selection to cosmological parameters

Bayesian model selection is a tool to decide whether the introduction of a new parameter is warranted by data. I argue that the usual sampling statistic significance tests for a null hypothesis can

Cosmological Bayesian Model Selection: Recent Advances and Open Challenges

TLDR
The conceptual underpinnings and the algorithmic implementations of Bayesian model comparison in cosmological problems: determining whether the Universe is infinite and selecting the “best” model of inflation are summarized.

Information criteria for astrophysical model selection

TLDR
The Deviance Information Criterion combines ideas from both heritages; it is readily computed from Monte Carlo posterior samples and, unlike the AIC and BIC, allows for parameter degeneracy.

Cosmological model selection

TLDR
The results of applying model selection methods to new cosmological data such as the CMB measurements by WMAP are described and the methods of computing the evidence are described, and particular on Nested Sampling.

Parameter Fitting of Cosmological Models using Evolutionary Strategies

TLDR
This project proposes Evolutionary Strategies as a better sampling method and examines what theories in Cosmology do generated posterior samples support or reject, by analysing parameter fits, confidence intervals and the importance and correlations of parameters in Cosmological models.

Bayesian analysis of cosmological models.

TLDR
This thesis first reviews the cosmological model and the formation and distribution of galaxy clusters before formulating a statistic within the Bayesian framework, namely theBayesian razor, that allows model testing of probability distributions.

Including parameter dependence in the data and covariance for cosmological inference

The final step of most large-scale structure analyses involves the comparison of power spectra or correlation functions to theoretical models. It is clear that the theoretical models have parameter

Bayesian model comparison in cosmology with Population Monte Carlo

We use Bayesian model selection techniques to test extensions of the standard flat Λ cold dark matter (ΛCDM) paradigm. Dark-energy and curvature scenarios, and primordial perturbation models are

Bayesian Evidence for a cosmological constant using new high-redshift supernova data

We carry out a Bayesian model selection analysis of different dark energy parametrizations using the recent luminosity distance data of high redshift supernovae from Riess et al. 2007 and from the
...

References

SHOWING 1-10 OF 26 REFERENCES

Bayesian model selection and isocurvature perturbations

Present cosmological data are well explained assuming purely adiabatic perturbations, but an admixture of isocurvature perturbations is also permitted. We use a Bayesian framework to compare the

Bayesian joint analysis of cluster weak lensing and Sunyaev–Zel'dovich effect data

As the quality of the available galaxy cluster data improves, the models fitted to these data might be expected to become increasingly complex. Here we present the Bayesian approach to the problem of

Cosmological parameters from CMB and other data: A Monte Carlo approach

We present a fast Markov chain Monte Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent cosmic microwave background ~CMB! experiments and provide

First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters

WMAP precision data enable accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat Λ-dominated universe seeded by a nearly scale-invariant adiabatic

The Essence of Quintessence and the Cost of Compression

Standard two-parameter compressions of the infinite dimensional dark energy model space show crippling limitations even with current Type Ia supernova (SN Ia) data unless strong priors are imposed.

Nested sampling for general Bayesian computation

Nested sampling estimates directly how the likelihood function relates to prior mass. The evidence (alternatively the marginal likelihood, marginal den- sity of the data, or the prior predictive) is

Revealing the Nature of Dark Energy Using Bayesian Evidence

We apply the Bayesian concept of ‘evidence’ to reveal systematically the nature of dark energy from present and future supernova luminosity distance measurements. We express the unknown dark energy

Large-scale power in the CMB and new physics: An analysis using Bayesian model comparison

TLDR
This work discusses possible alternate models that give better fits on large scales and applies a model-comparison technique to select amongst them and finds that models with a cutoff in the power spectrum at large scales are indeed preferred by data, but only by a factor of 3.6.

Parameter constraints for flat cosmologies from cosmic microwave background and 2dFGRS power spectra

We constrain flat cosmological models with a joint likelihood analysis of a new compilation of data from the cosmic microwave background (CMB) and from the 2dF Galaxy Redshift Survey (2dFGRS).

The 2dF Galaxy Redshift Survey: the power spectrum and the matter content of the Universe

The 2dF Galaxy Redshift Survey has now measured in excess of 160 000 galaxy redshifts. This paper presents the power spectrum of the galaxy distribution, calculated using a direct Fourier transform