You can miss this section which describes some of the theoretical background of the work. The algorithms are based around a 'Bayesian' formalism that has been established in Bioinformatics by such people as David Haussler, Gary Churchill, Anders Krogh, Richard Durbin, Sean Eddy and Graeme Mitchinson, as well as many others. In this formalism there is assumed to be a generative model of the process that you are observing, which has probabilities to generate a number of different observations. Deciding whether this model fits a previously unseen piece of data or not is the first decision to make. Given that the data fits, a second question is what actual processes were the most likely to produce the observed data. Both these questions fit naturally into a Bayesian framework where the result is a posterior probability having seen the data.
For people coming from a bioinformatics/biology background where the last paragraph may seem very confusing, it is only because this a different (and well established) field with their own terminology to describe the algorithms. In fact the methods a very close to standard techniques presented in bioinformatics. The generative models that we use are the models that are implied by the standard bioinformatics tools. For example, the Smith-Waterman algorithm implies a process of evolution with certain probabilities for seeing say an Leucine to Valine substitution and certain probabilities for creating and extending a insertion (gap). As you can see you can almost replace the word 'probability' with 'score' to return to the standard method, and mathematically it is almost that easy: the score is related to the log of the probability.
Perhaps a better known example is the relationship between the old profile technology, as developped by Gribskov and Gibson along with others, and its probabilistic partner, profile Hidden Markov Models (profile HMMs). In terms of the actual algorithm these two methods are very similar: it is simply that the profile HMM has a strong probabilistic model underlying it, allowing well established techniques to be used in its generation.