fix: diagonal-prior scale unification and full-space Jacobian

[MaartenMarsman]

Summary

Two correctness fixes to the GGM gradient and prior code that were carried as a parked WIP for several weeks; same fixes ported to the mixed-MRF Kyy block.

Fix 1 — Diagonal-prior scale unification (GGM + mixed-MRF). The interaction prior already operated on the partial-association scale K_yy_ij = -K_ij/2, but the diagonal prior was evaluated at raw K_ii, so the two priors referred to different quantities. Every site now evaluates the diagonal prior at K_ii/2 (i.e. -K_yy_ii):

• both NUTS gradient paths in GGMModel and MixedMRFModel
• all MH ratios in GGMModel (update_edge_parameter, update_diagonal_parameter, both branches of update_edge_indicator_parameter_pair, tune_proposal_sd)
• the continuous-block MH ratios in mixed_mrf_metropolis.cpp

The diagonal-prior adjoint becomes grad(K_ii/2) * Phi(:,i) after the chain-rule factor of 2 is absorbed.

User-visible effect: gamma_prior(shape, rate) is now interpreted as a prior on K_ii/2 rather than K_ii, so the implied mean of K_ii doubles. The default gamma_prior(1, 1) now corresponds to E[K_ii] = 2 rather than 1. The SBC prior simulator in test-sbc-ggm.R is rewritten to match.

Fix 2 — Full-space Jacobian aligned with theta-space (GGM). logp_and_gradient_full now uses the graph-agnostic Cholesky-to-K Jacobian
ldj = p*log(2) + 2*sum(psi) + sum_{k<p-1} (p-1-k)*psi_k
plus a per-column Pfaffian correction
pfaffian = 0.5 * sum_q log det(A_q diag(M_q^{-1}) A_q^T)
giving the correct RATTLE manifold-marginal under any diagonal mass. At identity mass the new full-space target agrees with theta-space at corresponding (theta, x). The Pfaffian adjoint flows back via two triangular solves through chol(G_q). The previous (deg_higher + 2) * psi_k form did not represent any RATTLE measure correction and conditioned on the active edge set incorrectly.

prior_test_interface.cpp gains an optional inv_mass_diag argument so the mass-weighted Pfaffian can be exercised from tests.

The matching mixed-MRF Fix 2 port is queued separately — the mixed-MRF Kyy block still carries the pre-fix Jacobian, and the projection helpers already build the required mass-weighted A_q matrices.

Test plan

• devtools::load_all() rebuilds cleanly
• devtools::test() passes locally
• test-sbc-ggm.R SBC ranks remain uniform under the rewritten prior simulator
• sample_ggm_prior diagonal-mean test hits the new 2 * shape/rate expectation
• Finite-difference check on logp_and_gradient_full with random diagonal mass agrees with analytic gradient (~1e-6 per coordinate)
• Theta-space vs full-space logp agreement at identity mass (~1e-10)

[codecov]

Codecov Report

❌ Patch coverage is 76.92308% with 27 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.49%. Comparing base (2853ca5) to head (6499840).
⚠️ Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
src/models/mixed/mixed_mrf_metropolis.cpp	36.00%	16 Missing ⚠️
src/models/ggm/ggm_gradient.cpp	90.16%	6 Missing ⚠️
src/models/ggm/ggm_model.cpp	76.47%	4 Missing ⚠️
src/prior_test_interface.cpp	75.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #103      +/-   ##
==========================================
- Coverage   87.00%   86.49%   -0.52%     
==========================================
  Files          77       77              
  Lines       13146    13267     +121     
==========================================
+ Hits        11438    11475      +37     
- Misses       1708     1792      +84     

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