We study the problem of computing a function $f(x_1,...,x_n)$
given that the actual values of the variables $x_i$'s are known
only with some uncertainty. For each variable $x_i$, an interval
$I_i$ is known such that the value of $x_i$ is guaranteed to
fall within this interval. Any such interval can be probed to
obtain the actual value of the underlying variable; however,
there is a cost associated with each such probe. The goal is
to adaptively identify a minimum cost sequence of probes
such that regardless of the actual values taken by the unprobed
$x_i$'s, the value of the function $f$ can be computed to within
a specified precision.
We design online algorithms for this problem when $f$ is either
the selection function or an aggregation function such as sum or
average. We consider three natural models of precision and give
algorithms for each model. We analyze our algorithms in the
framework of competitive analysis and show that our algorithms are
asymptotically optimal. Finally, we also study online algorithms for
functions that are obtained by composing together selection and
aggregation functions.