Application of Bayesian model averaging to measurements of the primordial power spectrum

Parkinson, David; Liddle, Andrew R.

doi:10.1103/physrevd.82.103533

Cited by 17 publications

(15 citation statements)

References 54 publications

(42 reference statements)

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“…The notion of Bayesian doubt, introduced in [ 624 ], can also be used to extend the power of Bayesian model selection to the space of unknown models in order to test our paradigm of a ΛCDM cosmological model. Bayesian model averaging [ 571 , 709 ] can also be used to obtain final inferences parameters which take into account the residual model uncertainty. Due to the concentration of probability mass onto simpler models (as a consequence of Occam’s razor), Bayesian model averaging can lead to tighter parameter constraints than non-averaged procedures, for example on the curvature parameter [ 917 ].…”

Section: Statistical Methods For Performance Forecastsmentioning

confidence: 99%

“…Bayesian model averaging [ 571 , 709 ] can also be used to obtain final inferences parameters which take into account the residual model uncertainty. Due to the concentration of probability mass onto simpler models (as a consequence of Occam’s razor), Bayesian model averaging can lead to tighter parameter constraints than non-averaged procedures, for example on the curvature parameter [ 917 ].…”

Section: Statistical Methods For Performance Forecastsmentioning

confidence: 99%

See 1 more Smart Citation

Cosmology and Fundamental Physics with the Euclid Satellite

Amendola¹,

Appleby²,

Bacon³

et al. 2013

Living Rev. Relativ.

800

665

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Euclid is a European Space Agency medium-class mission selected for launch in 2019 within the Cosmic Vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky.Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis.This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

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Section: Statistical Methods For Performance Forecastsmentioning

confidence: 99%

Section: Statistical Methods For Performance Forecastsmentioning

confidence: 99%

Cosmology and Fundamental Physics with the Euclid Satellite

Amendola¹,

Appleby²,

Bacon³

et al. 2013

Living Rev. Relativ.

800

665

View full text Add to dashboard Cite

show abstract

“…Parkinson and Liddle [53] applied Bayesian model averaging to measurements of the parameters of the primordial power spectrum of density fluctuations. They considered five different models.…”

Section: Applications In Astrophysicsmentioning

confidence: 99%

On the identifiability of copulas in bivariate competing risks models

2013

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Abstract. In competing risks models, the joint distribution of the event times is not identifiable even when the margins are fully known, which has been referred to as the "identifiability crisis in competing risks analysis" (Crowder, 1991). We model the dependence between the event times by an unknown copula and show that identification is actually possible within many frequently used families of copulas. The result is then extended to the case where one margin is unknown.MSC 2010 subject classifications: Primary 62N01, secondary 62N99

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“…The top label denotes the Bayes factor of the n run -model compared to the power-law n s -model, using current observations. as used by [24]. Figure 4 shows the 1D and 2D marginalised posterior distributions for the inflationary parameters, using current experiments (black line): n s = 0.985 ± 0.017, n run = −0.043 ± 0.018 and r run < 0.324; and Planck (red line) and CMBPol (green line) realisations.…”

Section: Running Scalar Spectral-indexmentioning

confidence: 99%

“…with WMAP7+QUaD [4]. It has also been shown that the existence of a turn-over in P R (k), by using model-independent techniques, is preferred [14,15,24,32].…”

Section: Introductionmentioning

confidence: 99%

Constraints on the tensor-to-scalar ratio for non-power-law models

Vázquez

Bridges

et al. 2013

J. Cosmol. Astropart. Phys.

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Abstract. Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby & Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: r LD = 0.11 ± 0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys.

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Application of Bayesian model averaging to measurements of the primordial power spectrum

Cited by 17 publications

References 54 publications

Cosmology and Fundamental Physics with the Euclid Satellite

Cosmology and Fundamental Physics with the Euclid Satellite

On the identifiability of copulas in bivariate competing risks models

Constraints on the tensor-to-scalar ratio for non-power-law models

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