= Computational statistics
<Computational statistics> develops and studies computational procedures for <statistical inference>. It includes numerical evaluation of <likelihood functions>, simulation from <probability distributions> and assessment of uncertainty when an exact symbolic calculation is unavailable. The statistical question and the numerical approximation both need error control.
For example, if independent simulations $X_1,\ldots,X_M$ follow a model and $g(X)$ has finite <variance>, the <Monte Carlo estimator> $\widehat\mu=M^{-1}\sum_jg(X_j)$ estimates $\mu=\mathbb E[g(X)]$, with <variance> $\operatorname{Var}(g(X))/M$. Halving its <standard deviation> therefore requires four times as many independent simulations. An optimization routine finding a maximum of a <likelihood function> and a simulation routine estimating an <integral> solve different computational tasks, even when both are steps in the same analysis.
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