= Monte Carlo standard error
{title2=$\operatorname{MCSE}(\bar h)\simeq\sqrt{\sigma_h^2/N_{\rm eff}}$}
The <Monte Carlo standard error> estimates the <standard deviation> of a simulation-based estimate across repeated simulation runs. For an average of $N$ <independent random variables> with finite <variance> $\sigma_h^2$, it is $\sigma_h/\sqrt N$. Under a suitable <central limit theorem> for <Markov chain Monte Carlo>, correlated draws instead give the approximation $\sigma_h/\sqrt{N_{\rm eff}}$, where $N_{\rm eff}$ is the <effective sample size of a Markov chain> for the particular estimated function $h$. This measures numerical uncertainty in an estimate, not uncertainty in the unknown parameter itself.
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