  Tasks that require information about the world imply a trade-off between the
time spent on observation and the variance of the response. In particular, fast
decisions need to rely on uncertain information. However, standard estimates of
information processing capabilities, such as the dynamic range, are defined
based on mean values that assume infinite observation times. Here, we show that
limiting the observation time results in distributions of responses whose
variance increases with the temporal correlations in a system and, importantly,
affects a system's confidence in distinguishing inputs and thereby making
decisions. To quantify the ability to distinguish features of an input, we
propose several measures and demonstrate them on the prime example of a
recurrent neural network that represents an input rate by a response firing
averaged over a finite observation time. We show analytically and in
simulations that the optimal tuning of the network depends on the available
observation time, implying that tasks require a ``useful'' rather than maximal
sensitivity. Interestingly, this shifts the optimal dynamic regime from
critical to subcritical for finite observation times and highlights the
importance of incorporating the finite observation times concept in future
studies of information processing capabilities in a principled manner.
