Experimental Bayesian reversible scale interweaving — not calibrated¶

This method is a posterior-preserving computational proposal for the unreleased B6/B7 Gaussian functional factor Gibbs samplers. Do not infer that enabling it provides valid credible intervals, better mixing or an approved 1.2 API. Exact prior/likelihood simulation produced severe population undercoverage and poor chain diagnostics even at 1,200 warmup and 600 retained samples. Blocker #255.

Posterior-invariant transformation¶

For a single latent factor column \(k\), the native observation model is (y_i=B_i(\mu+Lz_i)+\varepsilon_i), with (L_{\cdot k}\sim N(0,\tau^2 I_q)), (z_{ik}\sim N(0,1)) and fixed Gaussian observation noise. The planar model has (L\in\mathbb R^{2q\times K}), shared participant scores and channel-specific observation noise.

For a symmetric random-walk proposal (a\sim N(0,s^2)), propose

This leaves all reconstructed latent curves exactly unchanged. It does not change the likelihood or the true posterior. The complete Metropolis log-acceptance ratio is

where \(d_L=q\) in B6, \(d_L=2q\) in B7 and \(n\) is the number of unique participants. The final Jacobian factor is essential for detailed balance. Code tests independently recompute this ratio from Gaussian densities and verify that applying the inverse scale move negates the forward log ratio.

Opt in with scale_interweave_proposal_sd=0.25 when calling fit_bayesian_sparse_fpca or fit_bayesian_planar_factor via the experimental Bayesian namespace only. Default scale_interweave_proposal_sd=0 is a strict no-op, preserving the earlier sampler's random-number sequence and published/research comparison baseline.

The returned evidence reports attempted and accepted scale moves, proposal SD, and explicitly false inferential-qualification flags. Sign/rotation unidentifiability is still present; scale moves target only a continuous coupling ridge. R-hat/ESS for identifiable functional-population summaries are still required.

Independent evidence required¶

The workflow science-b6-b7-reversible-scale-mh.yml checks exact Jacobian/likelihood invariance in Python 3.11–3.13 and runs 72 actual Gibbs fits on 36 independent known-truth datasets (6 per six combinations, each fit twice with and without scale moves). Both versions receive identical data and model hyperparameters. The pilot uses 400 warmup sweeps, 200 retained posterior draws per chain and the source matched priors; it reports invariant R-hat/ESS, acceptance rates and failures without automatic inferential decisions.

This is a mechanism test, not the 400-refit prior SBC or a definitive Bayesian sampler comparison. If scale moves fail to improve invariant ESS and R-hat, the kernel should not be advertised as a scientific solution. Even if improved, independent NUTS references, chain convergence, rank-based SBC and adequate empirical predictive coverage remain obligatory before any research-method qualification.

The original expensive 13,600-attempt study is manually triggered only. The earlier original F5 AR1 comparison artifact is recovered through science-f5-recover-original-oracle-artifact.yml without replaying its 1,800 fits, and the historical literal null label is preserved. The new F5 method still requires externally known scalar AR1 phi, not in-sample estimated dependence.

No root namespace, stable 1.1.0 functionality, protected main, production release flags or public deployment are promoted by this research tranche.

Completed paired computation: no reliable mixing improvement¶

The actual source run #37976468861 completed 72/72 original-versus-scale-MH Bayesian Gibbs fits with zero fitting exceptions. Its original immutable evidence artifact is 11639357048, using exact code head 3d55d101a6fc1a32ffcf7420121b79e3295d95ed. The paired 36 independent matched-prior datasets are the independent units, six per scenario, not 72 independent replications of the same effect.

The scale-MH acceptance-rate medians were approximately 0.51–0.57 across the six scenarios. Despite the correct invariant target and active proposals, these results do not show a general mixing improvement; rank-2 and asynchronous conditions frequently worsened. Neither variant comes close to adequate R-hat and ESS for inferential qualification.

Decision: do not recommend enabling scale interweaving as a solution to the Bayesian blocker. Preserve its mathematically reversible implementation only as opt-in, unqualified experimental research, and prioritize more fundamental posterior parameterization and independent reference MCMC. This small pilot cannot prove equivalence or superiority of posterior uncertainty, and it is not a rank-based SBC.