Exponential default for the precision diagonal; gamma-shape corrections for the Z-ratio and Gibbs paths#168
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…ision diagonal The default precision_scale_prior becomes exponential_prior(eta = 1), the same GammaScalePrior(1, rate) as the previous gamma_prior(shape = 1, eta = 1) at the C++ level; a seeded-fit identity test pins the equivalence. The conjugate_slab gate in extract_prior_inclusion_probabilities() now admits both family strings, keeping the prior-only chain on the Gibbs path under the new default.
…) diagonal
The channel builders carry the diagonal prior K_ii ~ Gamma(alpha, beta)
with the prior weight on the raw diagonals. The spike integral gains a
(s1 s2)^(alpha-1) factor, evaluated by a vectorized generalized
Gauss-Laguerre rule on the shifted product form with the exponentially
scaled Bessel; the slab pair and bridge integrals move their diagonal
axes to generalized Gauss-Laguerre (weight S^(alpha-1) e^(-beta S)); the
node channel folds the weight into the tilt exponent (delta + alpha);
and the clique-2 sweep corrects the alpha = 1 conjugate proposal by an
independence-Metropolis ratio (K_ii_new/K_ii_old)^(alpha-1). The
constants cell and session cache key extend to (delta, eta, alpha,
slab); zratio_cell_constants() accepts scale_shape. At alpha = 1 every
path keeps the existing expressions and RNG stream bit-exactly.
Each generalized channel is checked against a direct Monte Carlo of the
same moment ratio at alpha in {0.5, 2} (normal and Cauchy slabs), the
generalized Laguerre rule against gamma moments, and the spike integral
against stats::integrate; the alpha = 1 engine fixtures are unchanged.
ZRatioEngine gains an alpha parameter (default 1) on set_oracle_params() and enable_calibration(). The block-Gibbs sweep keeps the alpha = 1 conjugate row proposal and accepts with the independence-Metropolis ratio (K_ii_new/K_ii_old)^(alpha-1); the neighborless diagonal draws rgamma(delta + alpha, beta) and the block seed draws rgamma(alpha, beta) at alpha != 1. sample_ggm/sample_mixed read an optional zratio alpha field, and the test interfaces expose it. At alpha = 1 every path draws the identical RNG sequence; the engine reference fixtures are unchanged. An alpha = 2 consistency gate checks the additive tables and the calibrated estimator against the long-run block oracle.
Remove the shape-1 stops in bgm_spec and sample_ggm_prior, pass scale_shape into zratio_cell_constants() on the GGM, mixed, and prior-sampler paths, and forward the cell's alpha to the C++ engine. The graph-law identity gate now runs at shape 0.5 and 2 on both update methods (Bernoulli(0.3) marginal within 0.02 at q = 6), the standardized-cell invariance check covers the gamma cell, and the hierarchical bgm() eligibility test replaces the shape-2 error pin with a shape-2 fit.
The row-block Gibbs at shape != 1 (independence-MH accept (K_ii_new/K_ii_old)^(shape-1) on the joint row proposal) gets two gates: a cross-sampler agreement test against adaptive Metropolis on the same joint-spec prior at shape 2 (mean and per-column KS on thinned diagonals), and a slow-gated SBC block (Gibbs, Gamma(2, 1) diagonal, p = 3, no edge selection) reusing the existing harness via a shape parameter on draw_prior_K. Docs and NEWS drop the shape-1 requirement from the hierarchical spec and describe the generalized constants.
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Summary
precision_scale_priorfor continuous models is now the namedexponential_prior(eta = 1). Numerics are bit-identical to the previousgamma_prior(shape = 1, eta = 1)(both resolve toGammaScalePrior(1, rate)); a seeded-fit identity test pins the equivalence. Theconjugate_slabgate inextract_prior_inclusion_probabilities()now admits both family strings instead of keying on"gamma", which would have demoted prior-only chains from the Gibbs path under the new default.gamma_prior()diagonals of any shape. The Z-ratio constants generalize from the exponential to aGamma(shape, rate)diagonal with the prior weight on the raw diagonals: generalized Gauss-Laguerre pair and bridge axes, a shape-shifted node channel (delta + shape), a vectorized generalized-Laguerre spike integral (exactGamma(nu)^2 beta^(-2 nu)limit at c = 0,nu = delta + shape), and an independence-Metropolis correction(K_ii_new/K_ii_old)^(shape - 1)in the clique-2 sweep and the calibration-oracle Gibbs. The constants cell and session cache extend to(delta, eta, shape, slab), andscale_shapeflows from the spec throughrun_sampler()/sample_ggm_prior()into the C++ engine.Gamma(2, 1)diagonal, p = 3).Verification
test-zratio-gamma-shape.R); generalized-Laguerre moment identities; spike integral againststats::integrate.(delta, eta, shape)across frames.R CMD check --as-cran0 errors / 0 warnings.