least observing time and to develop more generally the methods to optimize observing programs of transiting planets with JWST. To simplify the problem and focus clearly on optimization, we employ a simple, three-parameter model and apply it to a wide variety of synthetic observations. We use this simple model to present a rigorous methodology for optimizing observing programs.

To evaluate our observing programs, we consider several statistical measures to find the best fit and to determine the amount of observing time needed to reach a certain level of precision. One important measure is the difference in Shannon entropy between the prior and posterior distributions in our retrievals, which is directly related to the size of the error bars in the Gaussian case and can be compared directly between different observations. However, a more complete measure of the difference between observing programs is the mutual information [@lindley1956; @Chaloner95bayesianexperimental] between the prior and posterior distribution, which additionally accounts for the probability distribution of the observed data, thus marginalizing over the possible outcomes of the observing program. Therefore, we use this measure for our optimization of observing programs. The ideal prior would be a posterior from a previous observation, although we examine simple 