B6/B7: follow-up to severe 90% credible-interval undercoverage¶

Unpublished scientific diagnosis; no automatic inference qualification.

The source first empirical wave fitted 2,400 B6 and 1,600 B7 actual matched/misspecified models. At 400 independent datasets per scenario, B6 matched-prior posterior population-mean 90% coverage was 70.75% (rank 1), 62.00% (rank 2) and 62.00% (unequal sparse rank 2). B7's x/y population mean and cross-covariance coverage was also far below 90%. Source-run GitHub evidence #37965949039.

This requires a fail-closed scientific response, rather than simply adding methods or authorizing publication.

Registered next experiment: same data, two chain schedules¶

scripts/run_bayesian_convergence_probe.py calls the existing prior and likelihood generator and existing learned B6/B7 Gibbs code. For each independently seeded prior-generated dataset, it performs:

Eight matched prior-generated datasets per combination: B6 rank-1/rank-2; B7 rank-1 paired/asynchronous and rank-2 paired/asynchronous. Total 96 actual Gibbs model refits (48 independently generated datasets × two chain schedules). This is a mechanism-diagnostic pilot, not a replacement for the 400-refit coverage study. All paired observation-data seeds and fit exceptions are persisted in cases.csv, with SHA256 evidence.

Identifiability and diagnostics¶

Compare rotation-invariant integrated population means/variances and joint planar x/y cross-covariance with ArviZ R-hat, bulk ESS, and posterior 90% interval widths on the two schedules. Do not diagnose mixing from individual sign/rotation-unidentified loading columns. The B6 helper also evaluates coverage of pointwise mean and covariance at the prespecified midpoint; the B7 helper evaluates midpoint x/y means and cross covariance.

The recorded rhat_max is a maximum over the summary variables and the recorded bulk ESS is a minimum. Missing or nonfinite diagnostics must not be silently accepted or imputed. Good diagnostics on these integrated quantities still do not certify every high- dimensional posterior functional.

Potential findings and decisions: - If longer chains markedly improve coverage, first improve mixing, diagnostics, independent initialization and convergence thresholds. Do not simply prescribe a new arbitrary sweep count. - If R-hat/ESS are poor even for long chains, treat the Gibbs chain as inferentially untrustworthy, investigate parameterization and joint mixing, and repeat under stronger alternative samplers. - If R-hat/ESS improve but matched-prior coverage remains poor, audit the precision/conditional update algebra, prior/likelihood truth match, posterior quantile assembly and parameter functional interpretation. An independent reference posterior (e.g. independent MCMC implementation in a separate backend) is required to identify coding bias versus nonidentification. - Irrespective of these pilot results, run separate sufficiently long-chain SBC ranks and empirical coverage with predeclared Monte Carlo precision and independent comparator recovery.

No 1.2 production release or claim of scientifically calibrated Bayesian FPCA/MFPCA is authorized. The source main remains protected, and these procedures stay opt-in research APIs.