Information gain as a tool for assessing biosignature missions

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 optimizing mission design, mission selection and/or target selection.