### mcse (se_mean)

Quick definition The standard error of the mean of the posterior draws (not to be confused with the standard deviation of the posterior draws) is the uncertainty associated with the Monte Carlo approximation. This quantity approaches 0 as the sample size goes to infinity, whereas the standard deviation of the posterior draws approaches the standard deviation of the posterior distribution.

#### More details

When estimating a mean based on a sample of \(M\) independent draws, the estimation error is proportional to \(1/M\). If the draws are positively correlated, as they typ￼ically are when drawn using MCMC methods, the error is proportional to \(1/\sqrt{n_{eff}}\) where \(n_{eff}\) is the effective sample size. Thus it is standard practice to also monitor (an estimate of) the effective sample size until it is large enough for the estimation or inference task at hand.