Gibbs sampling

Source: examples/tmcmc_and_gibbs.py

Gibbs is useful when parameters have very different scales or are weakly coupled, and you want per-parameter tuning of the proposal.

---

Scalar Gibbs (one parameter at a time)

gibbs = mc.Gibbs(n_samples=10_000, proposal_std=0.5)
result = gibbs.run(problem, x0=[0.0, 0.0])

print(result.mean())
print(f"per-block acc: {gibbs.block_acceptance_rates}")

By default, each dimension gets its own scalar MH update with the same proposal_std.

---

Per-block proposal std

gibbs = mc.Gibbs(
    n_samples=10_000,
    blocks=[[0], [1]],          # one param per block
    proposal_std=[0.8, 0.5],    # different std per block
)
result = gibbs.run(problem, x0=[0.0, 0.0])

---

Block updates

Update multiple parameters jointly per block:

# 4-D problem: update params 0,1 together, then 2,3 together
gibbs = mc.Gibbs(
    n_samples=10_000,
    blocks=[[0, 1], [2, 3]],
    proposal_std=[0.5, 0.3],
)
result = gibbs.run(problem_4d, x0=[0, 0, 0, 0])

---

Acceptance rates

gibbs.block_acceptance_rates   # list: one rate per block
gibbs.acceptance_rate          # mean over all blocks

Target: 20–40% per block for scalar updates.