Thinning of a Markov chain

Thinning keeps every $L$th state of a Markov chain. The retained chain has transition kernel $K^L$ and the same stationary distribution. It is generally still dependent, and reducing correlation between retained draws does not by itself improve precision per original transition. Keep all post-warmup draws unless storage or later processing requires thinning; assess precision using the effective sample size of a Markov chain.