We present a quotient-space Bayesian formulation for DESI-Era anomaly interpretation. Given a pattern-labeled catalog with map $i\mapsto \mathbf{A}(i)$, the induced posterior $p(\mathbf{A}|D)$, sector inclusion probabilities $P_{\alpha }$, coactivation probabilities $P_{\alpha \beta }$, and grouped Bayes factors $B_{\alpha }(D)$ are exact summaries over predeclared physical activation events. Pairwise comparisons such as $\mathrm{\Lambda }\mathrm{CDM}$ versus $w_0{w}_a\mathrm{CDM}$ remain ordinary Bayes-factor tests between specified families; the quotient construction addresses the coarser question of which physical sector carries posterior support when different sectors are represented by unequal numbers of catalog elements. We derive a sector-resolved DESI-CMB-SN likelihood specification for late-time background, early-time ruler, supernova calibration, perturbation, and gravitational-wave propagation sectors. The construction includes an Alcock-Paczynski/isotropic-scale BAO decomposition, a pure-ruler projection, analytic marginalization of low-rank supernova calibration modes, Fisher-normalized sector priors, inactive-sector leakage tests, log-evidence uncertainty propagation, and prior/sector-partition diagnostics. The result is a quantitative procedure for reporting model-comparison support at the level of physically interpretable sectors.

Close

PrevNext

View figure in article

• Cosmology
• Dark energy