  We propose the mathematical notion of information gain as a way of
quantitatively assessing the value of biosignature missions. This makes it
simple to determine how mission value depends on design parameters, prior
knowledge, and input assumptions. We demonstrate the utility of this framework
by applying it to a plethora of case examples: the minimal number of samples
needed to determine a trend in the occurrence rate of a signal as a function of
an environmental variable, and how much cost should be allocated to each class
of object; the relative impact of false positives and false negatives, with
applications to Enceladus data and how best to combine two signals; the optimum
tradeoff between resolution and coverage in the search for lurkers or other
spatially restricted signals, with application to our current state of
knowledge for solar system bodies; the best way to deduce a habitability
boundary; the optimal amount of money to spend on different mission aspects;
when to include an additional instrument on a mission; the optimal mission
lifetime; and when to follow/challenge the predictions of a habitability model.
In each case, we generate concrete, quantitative recommendations for optimising
mission design, mission selection, and/or target selection.
