Generalizing the host galaxy dispersion measure distribution in FRB cosmology with 125 events produces Hubble constant estimates consistent with Planck 2018 and SH0ES while strongly favoring these models over narrow-prior alternatives on feedback strength.
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Marginal Likelihoods from Monte Carlo Markov Chains
12 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one needs to be able to estimate the density of points in parameter space, and this can be challenging in high numbers of dimensions. Here we present a Bayesian analysis, where we obtain the posterior for the marginal likelihood, using $k$th nearest-neighbour distances in parameter space, using the Mahalanobis distance metric, under the assumption that the points in the chain (thinned if required) are independent. We generalise the algorithm to apply to importance-sampled chains, where each point is assigned a weight. We illustrate this with an idealised posterior of known form with an analytic marginal likelihood, and show that for chains of length $\sim 10^5$ points, the technique is effective for parameter spaces with up to $\sim 20$ dimensions. We also argue that $k=1$ is the optimal choice, and discuss failure modes for the algorithm. In a companion paper (Heavens et al. 2017) we apply the technique to the main MCMC chains from the 2015 Planck analysis of cosmic background radiation data, to infer that quantitatively the simplest 6-parameter flat $\Lambda$CDM standard model of cosmology is preferred over all extensions considered.
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A sign-switching dark energy model (Λ_s CDM) recovers positive effective neutrino masses (0.055 ± 0.050 eV) consistent with oscillation data, unlike ΛCDM which prefers negative values (-0.075 eV), for DESI DR2 + CMB + supernova fits with z_† > 2.4.
Alpha-attractor quintessential inflation models are disfavored by DESI observations and Delta Neff limits from gravitational waves, as they predict an inconsistent scalar spectral index when the gravitational-wave abundance is constrained.
The QDEE model fits combined cosmological datasets better than Lambda CDM, shifts the Hubble constant higher, and shows strong Bayesian evidence in its favor.
Late-time datasets yield 1-2.74σ preference for dynamical dark energy over ΛCDM, with consistent signs of Quintom-B behavior (ω0 > -1, ωa < 0) that strengthen when DES-Dovekie or Union3 supernovae are added.
DESI DR2 BAO combined with Pantheon+, DES-Dovekie and Union3 supernovae yields 1.1-2.3 sigma preference for Quintom-B type evolving dark energy (w0 > -1, wa < 0) with phantom crossing near z ~ 0.5, but no model reaches robust statistical significance.
Cosmic string networks are constrained to less than ~1% of the energy density using CMB+BAO+SN data, with some models preferring mildly negative densities but no Bayesian evidence favoring them over LambdaCDM.
The Little Rip model reduces the Hubble tension below 3σ with CMB plus BAO data but only improves the statistical fit to CMB data alone per Bayes factors, and shifts toward quintessence behavior when DESI-DR2 is included.
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Generalizing the host galaxy dispersion measure distribution in FRB cosmology with 125 events produces Hubble constant estimates consistent with Planck 2018 and SH0ES while strongly favoring these models over narrow-prior alternatives on feedback strength.
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