Can sector-resolved Bayesian model averaging clarify DESI-era cosmological tensions?

From family Bayes factors to sector activation events

Bayesian model averaging and selection are established tools in astrophysics, with Parkinson and Liddle reviewing the statistical basis and applications across dark energy, primordial power spectra, and cluster data [7]. Paradiso et al. applied this machinery to cosmological extensions, finding that CMB data alone preferred ΛCDM over K-ΛCDM at 86.6% versus 13.4%, strengthening to 99.3% versus 0.7% when CMB was combined with lensing, BAO, and Bicep-KECK 2018 [2]. Their framework also reported a near 50-50 split between ΛCDM and Neff-ΛCDM under a flat model prior, illustrating how model posterior probabilities depend on which families enter the catalog [2]. The anchor paper argues that these family-level comparisons answer a different question from sector-level inference: a prespecified ΛCDM versus w0waCDM test remains an ordinary Bayes factor, but asking whether the late-time background sector is activated requires summing posterior support over all catalog elements realizing that event [1].

The quotient construction formalizes this by treating the catalog as a disjoint union of model-specific parameter spaces, assigning each element to exactly one binary activation pattern A = (AE(z), Ard, ASN, Apert, AGW), and deriving pattern posteriors, sector inclusion probabilities Pα, co-activation probabilities Pαβ, and grouped Bayes factors Bα(D) [1]. A prior-preserving refinement invariance proposition shows these quantities are unchanged when a catalog element is split into sector-preserving sub-elements, removing the combinatorial log-odds bias Δln O(J) = ln J that naive model-index inference suffers under catalog duplication [1]. This is the paper's central methodological contribution: it makes the inferential target the physical activation event rather than the model label.

BAO decomposition and the limits of ruler identification

The anchor paper derives a sector-resolved DESI-CMB-SN likelihood specification in which anisotropic BAO measurements are decomposed into an Alcock-Paczynski shape variable y = ln(DM/DH) and an isotropic-scale variable v = ln(DV/rd) − (1/3)ln z [1]. This split is presented as a decomposition of information content rather than an assumption of independence, since the joint covariance Cyv retains off-diagonal structure unless it is negligible [1]. The sensitivity analysis shows that y is exactly ruler-free, ∂yth/∂ln rd = 0, whereas v is ruler-sensitive but not ruler-exclusive, ∂vth/∂ln rd = −1 with additional dependence on late-time expansion [1]. The practical consequence is that BAO alone cannot identify the early-time ruler sector without external anchors constraining the late-time background, a limitation the paper states explicitly rather than resolving [1].

The paper's minimal eight-pattern geometry analysis for the current DESI-CMB-SN comparison defines required localization diagnostics and failure flags for each open sector: the E(z) sector requires structured residuals not removed by calibration modes, the rd sector requires gain localized in the sound horizon with stable AP and orthogonal scale residuals, and the SN sector requires gain carried by calibration modes with acceptable posterior-predictive checks [1]. These criteria are validation requirements, not results; the paper does not report a sector-level detection on DESI data. Earlier work by Santos et al. used Bayesian model selection on SNe Ia and BAO to argue for non-trivial spatial curvature in a two-scale backreaction model [9], and Coley et al. found that phenomenological backreaction models were not favoured over ΛCDM despite preference for unequal curvature parameters [8]. The anchor paper's framework would recast such claims as questions about which sector—late-time background or ruler—carries the support, but it does not itself adjudicate those earlier debates.

Supernova calibration as a sector, not a nuisance

The anchor paper treats low-rank supernova calibration and selection modes as a distinct sector ΘSN with detection amplitudes ΔmB and qa modes, marginalized analytically through a design matrix M and calibration coefficients q [1]. The validation criteria require that a calibration interpretation show posterior mass moving primarily into patterns with ASN = 1, with improvement carried by the calibration mode q̂ and without SN-block posterior-predictive failure [1]. Data-block replacement tests are specified for Pantheon+ ↔ Union3, Pantheon+ ↔ DES-SN5YR, and DES-SN5YR ↔ Dovekie-like recalibrations at fixed DESI BAO and CMB inputs, with a late-time sector claim requiring stable AE(z) = 1 support under these replacements [1]. This directly addresses the concern that apparent dynamical dark energy support can be absorbed by calibration structure, a possibility raised in recent supernova recalibration studies cited by the anchor paper [1].

The foundational supernova work by Hinton et al. developed Steve, a Bayesian hierarchical model that fits cosmology, SN Ia populations, and systematic uncertainties simultaneously, including Malmquist bias and selection effects characterized through Monte Carlo simulations [5]. Steve demonstrated that selection-effect treatment can introduce biases comparable to or exceeding statistical uncertainties on w in realistic survey simulations, with Malmquist bias less than 0.03 on average but sensitivity to the intrinsic scatter model flagged as a concern for future surveys [5]. The anchor paper's calibration sector is a different layer of analysis—it does not replace hierarchical light-curve modeling but rather asks whether residual calibration structure, after such modeling, is the sector carrying the evidence. The two approaches are complementary: Steve addresses selection and population systematics at the light-curve level, while the quotient construction addresses whether those systematics constitute the physical sector responsible for an anomaly [1][5].

Competing explanations and the boundary of the claim

The anchor paper positions itself against a landscape of competing explanations for DESI-era anomalies. Ye reports that Bayesian model comparison reveals strong evidence of nonminimally coupled gravity over GR and ΛCDM, with a Bayes factor favoring modified gravity as a bridge across cosmological tensions [3]. Kessler et al. examine one-parameter dynamical dark energy models and find hints for oscillations, while noting that agnostic priors on new parameters significantly increase the prior volume and affect Bayesian evidence [4]. The anchor paper does not directly compare its sector-level framework against these specific model families; instead it argues that such family-level Bayes factors answer a coarser question than sector activation, and that a claim of late-time background, ruler, or calibration support requires the grouped outputs to be consistent with internal diagnostics and to survive controlled data-block replacement tests [1].

The boundary of the anchor paper's contribution is explicit in its own framing: it is a statistical framework, not a new-physics result. It does not analyze specific DESI data to deliver a sector-level verdict, and its sector partition depends on predeclared physical activation events and a declared detection basis [1]. The paper requires pattern-neutral priors and sparsity scans rather than a single privileged default, and it defines prior-sensitivity and sector-partition diagnostics because the declared partition remains part of the statistical model [1]. Earlier work by Gillet et al. on Bayesian data-analysis averaging for high-redshift luminosity functions showed how relative evidence can weigh disparate datasets within a physically motivated model [6], and Carter et al. demonstrated that Bayesian conclusions about fractal bubble cosmologies depend strongly on priors chosen for the density parameter [10]. These precedents reinforce the anchor paper's own caution: sector-level claims are only as robust as the specification choices and validation diagnostics that accompany them [1].

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This research page is built on 10 peer-reviewed studies — published from 2005 to 2026, 4 from 2024 or later, collectively cited 150 times — selected as the most relevant from 10 studies that passed quality screening, drawn from 52 papers retrieved from a database of over 500 million.

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