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Bayesian FPCA B2/B3 replication and uncertainty

This definitive tranche extends the immutable B1 comparator evidence without changing any estimator or public API. The earlier PR #208 evidence is retained as pilot/feasibility evidence because its realized replication and tuning grids differed from the design freeze recorded in issue #205.

B2 replication and separation

The primary programme uses 16 deterministic replicates per scenario for each of eight known-truth scenarios:

  • harmonic moderate sparsity;
  • harmonic extreme sparsity;
  • harmonic low-N;
  • harmonic near-tied eigenvalues;
  • localized/non-harmonic triangular-mode univariate truth;
  • simulation-only informative observation retention;
  • paired sparse planar data; and
  • asynchronous coordinate-specific sparse planar data.

Low-N and near-tied regimes are deliberately separate. The informative-observation case is sensitivity evidence only and does not classify the mechanism as MAR/MNAR or imply a correction estimator.

The primary comparison preserves the frozen B1 settings. A secondary native route uses the existing audited bandwidth selectors with a predeclared candidate grid. The asynchronous planar route does not silently reuse the paired selector because no qualified asynchronous selector exists.

The secondary fairness/tuning sensitivity is restricted to the first four replicates of extreme sparsity, low-N, near-tied, localized, and paired-planar scenarios. Native candidates use the Cartesian product of frozen mean/covariance bandwidths multiplied by {0.75, 1.00, 1.25} with the already-qualified 3-fold curve-level predictive criterion. bayesFPCA candidates use K = {5, 6, 7, 8, 9} and retain the successful fit with maximum final ELBO. K = 7 remains the primary B1-compatible setting outside the fairness subset. No truth-tuning or post-hoc favorable parameter search is permitted.

B3 uncertainty calibration

The existing native oracle validation remains the reference for the narrow conditional PACE estimand: known population mean/covariance/eigensystem, score uncertainty conditional on those objects, and direct coverage against known latent scores.

B2/B3 additionally retains fitted-model score covariance from both native and Bayesian fits. Because component signs/order are not identified and near-tied components are especially unstable, fitted score/covariance outputs are aligned to truth through weighted orthogonal Procrustes before known-score inclusion is summarized.

Population objects are re-estimated in every Monte Carlo replicate. The definitive B3 summaries therefore report empirical truth inclusion, pooled and replicate-level standardized-error behavior, covariance failures, and score failures across repeated datasets. These diagnostics quantify the calibration gap that appears when population objects are estimated, but the fitted conditional covariance itself is not relabelled as full population-estimation uncertainty and covariance magnitudes are not compared directly.

Environment lock

The external comparator remains hruffieux/bayesFPCA at exact commit f05b0615632cffe5c63838858d9a956af6588a73.

The CI environment additionally pins:

  • R 4.6.1;
  • abind 1.4-8;
  • ellipse 0.5.0;
  • magic 1.6.1.1;
  • matrixcalc 1.0.6; and
  • pracma 2.4.6.

sessionInfo(), R runtime details, BLAS/LAPACK details, exact package versions and checkout SHA are retained in the evidence artifact.

B4 decision — feasibility, not promotion

B4 has been recorded in issue #205, based on the definitive PR #215 evidence:

  • native_bayesian_feasibility_warranted=true
  • architecture_winner_selected=false
  • automatic_promotion_decision=false

The primary K=7 external bayesFPCA comparison completed 128/128 fits (eight frozen scenarios × 16 replicates) and produced lower mean latent-curve reconstruction ISE than the frozen native comparator in every scenario. Where fitted score covariances were available from both routes, repeated-dataset 95% ellipsoid inclusion was higher for the external Bayesian comparator, but generally remained well below nominal coverage. This is evidence to design and test a native Bayesian approach, not evidence that it should replace the qualified native covariance/PACE routes. Full population-estimation uncertainty remains unresolved.

The comparator is external-only, runs in isolated evidence jobs and is not copied/ported into this MIT codebase or introduced as a runtime dependency.