  We present {batching} as an omnibus device for statistical inference on
simulation output. We consider the classical context of a simulationist
performing statistical inference on an estimator $\theta_n$ (of an unknown
fixed quantity $\theta$) using only the output data $(Y_1,Y_2,\ldots,Y_n)$
gathered from a simulation. By \emph{statistical inference}, we mean
approximating the sampling distribution of the error $\theta_n-\theta$ toward:
(A) estimating an ``assessment'' functional $\psi$, e.g., bias, variance, or
quantile; or (B) constructing a $(1-\alpha)$-confidence region on $\theta$. We
argue that batching is a remarkably simple and effective inference device that
is especially suited for handling dependent output data such as what one
frequently encounters in simulation contexts. We demonstrate that if the number
of batches and the extent of their overlap are chosen correctly, batching
retains bootstrap's attractive theoretical properties of {strong consistency}
and {higher-order accuracy}. For constructing confidence regions, we
characterize two limiting distributions associated with a Studentized
statistic. Our extensive numerical experience confirms theoretical insight,
especially about the effects of batch size and batch overlap.
