Marginal Likelihoods from Monte Carlo Markov Chains

Heavens, Alan; Fantaye, Y.; Mootoovaloo, Arrykrishna; Eggers, Hans J.; Hosenie, Zafiirah; Kroon, Steve; Sellentin, Elena

doi:10.48550/arxiv.1704.03472

Cited by 73 publications

(92 citation statements)

References 19 publications

(27 reference statements)

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“…2). In Heavens et al (2017) an approach based on kth nearest-neighbour distances is proposed to compute the marginal likelihood from posterior samples, although the technique is limited to low-dimensional settings.…”

Section: Introductionmentioning

confidence: 99%

Machine learning assisted Bayesian model comparison: learnt harmonic mean estimator

McEwen¹,

Wallis²,

Price³

et al. 2021

Preprint

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Section: Introductionmentioning

confidence: 99%

Machine learning assisted Bayesian model comparison: learnt harmonic mean estimator

McEwen¹,

Wallis²,

Price³

et al. 2021

Preprint

View full text Add to dashboard Cite

“…To compare the two phenomenological models under consideration with the ΛCDM model, we calculate the values of Bayesian evidence for each model, where the code MCEvidence [59] which is a popular python package to compute the Bayesian evidence is adopted here, and the observational data correspond to the joint sample of SNe, BAO and CMB data. In Table 3, we present the natural logarithm of the Bayesian evidence for each model, ln B i , as well as the natural logarithm of the Bayes factor, ln B i0 , where the subscript "0" denotes the ΛCDM model.…”

Section: Model Selection Statisticsmentioning

confidence: 99%

Investigating the dynamical models of cosmology with recent observations and upcoming gravitational-wave data

Zheng,

Chen,

et al. 2022

Preprint

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We explore and compare the capabilities of the recent observations of standard cosmological probes and the future observations of gravitational-wave (GW) standard sirens on constraining cosmological parameters. It is carried out in the frameworks of two typical dynamical models of cosmology, i.e., the ω 0 ω a CDM model with ω(z) = ω 0 + ω a * z/(1 + z), and the ξindex model with ρ X ∝ ρ m a ξ , where ω(z) is the dark energy equation of state, and ρ X and ρ m are the energy densities of dark energy and matter, respectively. In the cosmological analysis, the employed data sets include the recent observations of the standard cosmological probes, i.e., Type Ia supernovae (SNe Ia), baryon acoustic oscillation (BAO) and cosmic microwave background (CMB), and the mock GW standard siren sample with 1000 merging neutron star events anticipated from the third-generation detectors. In the scenarios of both ω 0 ω a CDM and ξ-index models, it turns out that the mock GW sample can reduce the uncertainty of the Hubble constant H 0 by about 50% relative to that from the joint SNe+BAO+CMB sample; nevertheless, the SNe+BAO+CMB sample demonstrates better performance on limiting other parameters. Furthermore, the Bayesian evidence is applied to compare the dynamical models with the ΛCDM model. The Bayesian evidences computed from the SNe+BAO+CMB sample reveal that the ΛCDM model is the most supported one; moreover, the ω 0 ω a CDM model is more competitive than the ξ-index model.

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“…[18]), or we could follow the Bayesian evidence analysis. Since the latter can lead to more accurate results (since it is not based on point estimation), in this subsection we will apply it using the publicly available cosmological code MCEvidence [19,20] which computationally incorporates directly the MCMC chains (for more details we refer to [21]). In Table IV we show the revised Jeffreys scale by Kass and Raftery [22], which uses the value of the Bayes factor ln B ij in order to quantify the strength of evidence of an underlying cosmological model M i with respect to the reference model M j (typically ΛCDM) [23].…”

Section: B Bayesian Comparison With λCdm Scenariomentioning

confidence: 99%

Observational constraints on soft dark energy and soft dark matter: challenging $Λ$CDM

Saridakis¹,

Yang²,

Pan³

et al. 2021

Preprint

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Soft cosmology is an extension of standard cosmology allowing for a scale-dependent equationof-state (EoS) parameter in the dark sectors, which is one of the properties of soft materials in condensed-matter physics, that may arise either intrinsically or effectively. We use data from Supernovae Type Ia (SNIa), Baryonic Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB) probes, in order to impose observational constraints on soft dark energy and soft dark matter. We examine three simple models, corresponding to the minimum extensions of ΛCDM scenario, namely we consider that at large scales the dark sectors have the EoS's of ΛCDM model (dust dark matter and cosmological constant respectively), while at intermediate scales either dark energy or dark matter or both, may have a different EoS according to constant "softness" parameters s de and s dm . The observational confrontation shows that for almost all datasets the softness parameters deviate from their ΛCDM values (at 2σ confidence level for one of the models, and at 1σ for the other two), and thus the data favor soft cosmology. Finally, performing a Bayesian evidence analysis we find that the examined models are preferred over ΛCDM cosmology.

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Marginal Likelihoods from Monte Carlo Markov Chains

Cited by 73 publications

References 19 publications

Machine learning assisted Bayesian model comparison: learnt harmonic mean estimator

Machine learning assisted Bayesian model comparison: learnt harmonic mean estimator

Investigating the dynamical models of cosmology with recent observations and upcoming gravitational-wave data

Observational constraints on soft dark energy and soft dark matter: challenging $Λ$CDM

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