Numerically Stable Metropolis-Hastings Sampler

Implementing or repairing a pure-Python (stdlib math/random only) Metropolis-Hastings random-walk sampler whose accept/reject decision is computed entirely in log-space, including exact-zero and -inf handling, entry guard clauses (num_samples<=0 returns ([],0.0); proposal_std<=0 raises ValueError), and validation against repository benchmark thresholds (acceptance-rate bands, multimodal variance floors) with tuning of proposal_std and honest reporting of observed metrics. Excludes gradient-based/adaptive MCMC (HMC, NUTS), numpy/scipy-based implementations, and targets lacking any log-density or density function.

The skill performed at least as well as working without it on the evaluated tasks.