Planning to Plan for the Survey: Optimization

In order to run the survey most efficiently, I need to run Monte Carlo simulations of thousands of potential observing runs to find the best distribution of time, stars, masses, and signal to noise. Compounded with this, if I run the survey most efficiently, what is the probability I will be able to conclude anything from the results?

Monte Carlo method works based on a modification of a sort of random walk. From an initial guess of parameters, a step is randomly generated according to a Gaussian (or other type of) distribution function. The step is automatically excepted if the survey efficiency (or other metric) is higher. If the survey efficiency is lower, then the point is accepted with a probability proportional to the difference is efficiencies and some "temperature". The "temperature" decreases through out the simulation so that the point goes to the nearest extrema at the end of the simulation.

So inside this method, I need to calculate some survey efficiency at each point given the specific set of parameters. This happens by running many, many simulated surveys and either seeing the average number of planets measured or the number of planets measured out of those present. I think the survey should be run for both methods of efficiency measurement.

For each star within a survey, predicted probabilities will govern the random assignment of a planet to a star. If a star has a planet, more predictions will randomly assign the planet a mass and orbit. Noise will be applied to the respective RV curve, and the computer will try to recover the original planet.

While that is the overall picture, right now I need to read through the literature to discover what the theoretical distributions are. Also, I need to figure out how to randomly draw numbers from a power law distribution in IDL. IDL can give out numbers with various Gaussian, Poisson, flat, binomial, etc. distributions, but no power law that I can find. I have a theory about how to convert flat distributions to power law, but I am not entirely certain about it. (Never mind I found randomp which gives a power law distribution)