statistically unique solutions

Is there a mathematical model which statistically predicts a more likely solution over another?  Often times in "real world" physical problems, there is no unique function or solution to determine the evolution of a system.  This occurs in many other sciences and applications.  So, I'm wondering if a statisical prediction of which solutions might work can be found.  In some simple systems, like the kinematic equations for constant acceleration, there are an infinite set of solutions how an object behaves under the influence of a constant acceleration.  All one needs to do to solve the problem is to pick a set of initial conditions for the position and velocity of that object.  However, in some problems like building a three-dimensional image of a brain from magnetoencephalography (MEG), there is no unique image based on the data gathered from the MEG probes.  But there must be some way in which one can determine the most likely image of the many (if not infinite) options...right?