Hey KimJohansson.

I just read the wiki and the basic idea is that you are using probabilistic information to estimate a quantity known as Sm (which according to the wiki entry is the information about the relevant sensory neurons involved given the signal and other data).

The way it estimates this is by using Maximum Likelihood Estimation and the basic idea is that you find solutions that give estimates of your variables (Sm in this case) by finding the biggest probability in the distribution that corresponds to that particular estimate.

MLE estimators in statistics are often the best estimators that you can get (or if they are biased, they are usually very good).

In short its taking the signal data X(n), the concept models M, and the parameters in the model that you are trying to estimate Sm and its specifying a probability distribution (also known as likelihood) in which it finds the estimates of these values by finding the highest probability corresponding to those estimates.

When you maximize a function in mathematics you get its derivative, set it to zero and then solve for the particular input values. You also have to check that the second derivative is less than zero for it to be a local maximum and if you get multiple solutions, then you need to evaluate each one for being a global maximum or a local maximum.