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Tasks that require information about the world imply a trade-off between thetime spent on observation and the variance of the response. In particular, fastdecisions need to rely on uncertain information. However, standard estimates ofinformation processing capabilities, such as the dynamic range, are definedbased on mean values that assume infinite observation times. Here, we show thatlimiting the observation time results in distributions of responses whosevariance increases with the temporal correlations in a system and, importantly,affects a system's confidence in distinguishing inputs and thereby makingdecisions. To quantify the ability to distinguish features of an input, wepropose several measures and demonstrate them on the prime example of arecurrent neural network that represents an input rate by a response firingaveraged over a finite observation time. We show analytically and insimulations that the optimal tuning of the network depends on the availableobservation time, implying that tasks require a ``useful'' rather than maximalsensitivity. Interestingly, this shifts the optimal dynamic regime fromcritical to subcritical for finite observation times and highlights theimportance of incorporating the finite observation times concept in futurestudies of information processing capabilities in a principled manner.

Available observation time regulates optimal balance between sensitivity and confidence