Bayes factors provide a means of objectively ranking a number of plausible statistical models based on their evidential support. Computing Bayes factors is far from straightforward and methodology based on thermodynamic integration can provide stable estimates of the integrated likelihood. This talk will consider a stratified sampling strategy in estimating the thermodynamic integral and will consider issues such as optimal paths and the variance of the overall estimator. The main application considered will be the computation of Bayes factors for dynamical biochemical pathway models based on systems of nonlinear ordinary differential equations (ODE). A large scale study of the ExtraCellular Regulated Kinase (ERK) pathway will be discussed where recent Small Interfering RNA (siRNA) experimental validation of the predictions made using the computed Bayes factors is presented.