A statistical view on the reference ratio method

The recently introduced reference ratio method (Hamelryck et al.(2010)) allows combining distributions over fine grained variables with distributions over coarse grained variables in a meaningful way. This problem is a major bottleneck in the prediction, simulation and design of protein structure and dynamics. Hamelryck et al. introduce the reference ratio method in this context, and show that the method provides a rigorous statistical explanation of the so called potentials of mean force (PMFs). These potentials are widely used in protein structure prediction and simulation, but their physical justification is highly disputed (Thomas and Dill(1996); BenNaim(1997); Koppensteiner and Sippl(1998)). The reference ratio method clarifies, justifies and extends the scope of these potentials. As the reference ratio method is of general relevance for statistical purposes, we present the method here in a general statistical setting. Subsequently, we discuss two example applications of the method. First, we present a simple educational example, where the method is applied to independent normal distributions. Secondly, we reinterpret an example originating from Hamelryck et al.; in this example, the reference ratio method is used to combine a detailed distribution over the dihedral angles of a protein with a distribution that describes the compactness of the protein. Finally, we outline the relation between the reference ratio method and PMFs.