Bayesian FPCA after B4: promising comparison, separate research programme¶

Status (8 October 2026): The B1–B4 external-comparator/feasibility programme is closed. The recorded decision is native feasibility warranted, not architectural replacement or production promotion.

What was compared?¶

The definitive B2/B3 design retained eight frozen known-truth scenarios with 16 replicates per scenario, separately exercising ordinary and extreme sparse univariate observations, low sample size, near-tied modes, localized nonharmonic truth, informative observation retention as a simulation-only sensitivity, paired planar data, and coordinate-specific asynchronous planar sampling. External bayesFPCA is pinned in a dedicated environment; the package's native covariance/PACE fitting contracts remain unchanged.

The external comparator completed 128/128 primary fits at K=7, and its mean reconstruction integrated squared error was below the frozen native comparator across all eight scenarios. That is a useful result on latent reconstruction under these tested conditions, not a general guarantee on all sampling regimes, all methods or other performance targets.

What uncertainty did—and did not—show?¶

The B3 repeated-dataset assessment refitted population objects and examined empirical 95% score-ellipsoid inclusion under fitted conditional covariance information. Where both routes exposed covariance results, the external comparator had higher 95% ellipsoid inclusion, yet empirical inclusion still generally fell well below 95%. A fitted conditional score covariance is not the same estimand as full population-parameter/posterior estimation uncertainty. Calibration must be independently addressed before making nominal-coverage claims.

Recorded decision¶

A new native Bayesian method, if pursued, requires independent mathematical design, known-truth recovery/calibration, architectural and licensing review, runtime evidence, public API review and release governance. The GPL external comparator must not be copied or vendored into the MIT implementation.

Relationship to the 1.2 workflow release¶

The ten 1.2 workflows compose existing qualified estimators. No Bayesian estimator, model-choice switch or Bayesian runtime dependency is added by the orchestration programme. Treat B4 as an invitation to a future separate design/feasibility investigation, not a recommendation to replace fit_sparse_fpca() or fit_sparse_mfpca() today.

The definitive records are issue #205 (B4), PR #215 (B2/B3) and the methodological validation note. The retained raw evidence artifact remains authoritative for scenario-level diagnostics; this article is not a substitute for its analysis.