= MCMC trace diagnosis and proposal tuning
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A trace of a <Markov chain Monte Carlo> parameter helps distinguish slow movement, long rejection plateaus, and movement between separated regions. Very small random-walk proposals give high acceptance but slow diffusion; very large proposals produce low acceptance and repeated states. Record acceptance rates alongside <trace plots> and <effective sample size of a Markov chain> before deciding which scale to change. Correlated <posterior> directions often benefit from block proposals with a <covariance> fitted during a preliminary tuning run. A trace alone cannot prove convergence or identify the unique cause of poor movement; dispersed chains and stationary summaries provide additional evidence. Freeze tuning before the main sampling phase, or use adaptation satisfying an appropriate ergodicity theorem.
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