ما معنى Burn-in, effective sample size؟

The burn-in is the initial stretch of a chain discarded because it still depends on the starting point. The effective sample size of $n$ correlated draws is $n/(1 + 2\sum_{k \ge 1}\rho_k)$, $\rho_k$ the chain’s autocorrelations: the number of independent draws with the same variance of the mean.