smoothbp

• Fixed the change-point translation move under reparameterise = "omega". omega_translation_step() rescaled the random-effect columns by sigma_re, but those columns always hold centred values. Every other sampling step converts back on write-back, and omega_vec() feeds them straight into the likelihood. The move therefore shifted the subject-level change-points instead of leaving them invariant, while still being accepted with probability one. Results computed with reparameterise = "omega" and a random change-point should be regarded as unreliable and re-run. The default, reparameterise = "none", was never affected.

Sampler efficiency

• The change-point update is now collapsed (Rao-Blackwellised): the linear block (b0, b1, the slope changes) is integrated out analytically before omega is drawn, then resampled from its full conditional given the new omega. Previously omega was drawn conditional on a single draw of those coefficients and vice versa, so the chain traversed the strong omega-delta dependence one axis at a time. On a single-change-point model this raised bulk ESS for omega from a median of 394 to 5588 out of 5000 posterior draws, cut the worst R-hat from 1.090 to 1.006, and cost about 14% more time per fit. Posterior marginals are unchanged; only the efficiency differs. Note that the collapse necessarily runs in this direction. omega cannot be integrated out of the delta update, since it enters through d = t - omega and the transition weight s(d; rho) and that integral has no closed form. The linear block can be integrated out of the omega update because it is conditionally Gaussian, and that breaks the same dependence. Models that place finite bounds on a linear coefficient (prior_normal(lb=, ub=) on b0, b1 or deltas) keep the previous conditional update, because the marginal likelihood of a box-truncated Gaussian is not available in closed form.
• Added a joint translation move for the population intercept and the group-level random intercepts, b0 -> b0 + c and u_j -> u_j - c. Only the sum b0 + u_j is identified within a group, so updating the fixed coefficients conditional on the random intercepts and vice versa could not traverse the ridge between them: b0 reached a bulk effective sample size of 91 out of 4000 draws on the vignette's random-intercept model while every other parameter mixed freely. The move raises that to 3558 at no measurable cost in run time. The shift leaves the mean function exactly invariant, so c is drawn from its prior-only conditional and accepted outright; it is skipped when invariance would not hold (no intercept column, or observations outside every group). Note that the package documentation previously described the fixed and group-level intercepts as being updated in a single joint block. They were not, which is what the low effective sample size reflected.
• The spike-and-slab inclusion indicators now use a collapsed (Rao-Blackwellised) update: the slab coefficient is integrated out analytically before the indicator is drawn, then resampled given the new indicator. Previously each indicator was drawn at the current coefficient, so an excluded coefficient sat wherever the diffuse slab put it, fitted badly, and rarely re-entered. The indicator and its coefficient locked together and indicator ESS fell into the tens. This targets the same posterior as before (it is a better sampler of it, not a different model), so posterior inclusion probabilities keep their meaning.
• The collapsed update also honours bounded slabs (prior_normal(lb=, ub=) on deltas or b1), which the previous indicator update ignored, and uses the learned sigma_re rather than the fixed-effect prior as the slab for random-effect columns.

Validation

• tools/sbc_ecdf_bands.R now puts every estimated parameter on the SBC figure and writes PASS/FAIL, interval-coverage and run-regime tables to tools/part3_results/. Previously b0, b1 and sigma were checked only on the console and left no artefact, which is why a systematic sigma miscalibration went unnoticed.
• The calibration evidence for this release is four independent SBC runs of 500 replicates each: rho estimated, rho fixed at its generating value, rho fixed under reparameterise = "omega", and a random-intercept run with a population change-point. Every estimated parameter passes in all four on the full sample of 500 fits. The fourth run exists because the other three use b0 = ~ 1, so the new b0/u translation move never fires in them and they carry no evidence about it.
• The simultaneous ECDF confidence band is now drawn from a seed derived from its own shape rather than from the ambient RNG stream. The band is itself a Monte Carlo object, and left unseeded it moved enough between runs that reported deviations drifted by a few hundredths, so a table typed from one run no longer reproduced from the same saved ranks. Consecutive runs now write byte-identical tables.
• Every arm now writes a regime record. The random-intercept arm previously wrote none, which left the one run that exercises the b0/u translation move as the only one whose priors and design were unrecorded.
• The rank, ECDF, coverage and regime files for all four arms are tracked in the repository, each rank file stamped with the smoothbp version that produced it, so the reported numbers can be checked against the source without rerunning 2000 fits.