Metropolis–Hastings sampling of paths

We consider the previously unsolved problem of sampling paths according to a given distribution from a general network. The problem is difficult because of the combinatorial number of alternatives, which prohibits a complete enumeration of all paths and hence also forbids to compute the normalizing constant of the sampling distribution. The problem is important because the ability to sample from a known distribution introduces mathematical rigor into many applications, including the estimation of choice models with sampling of alternatives that can be formalized as paths in a decision network (most obviously route choice), probabilistic map matching, dynamic traffic assignment, and route guidance.

► Sampling of paths according to given distributions in general networks. ► Wide range of transportation-related applications. ► Applicability to large real-world problem instances. ► Thorough experimental analysis of algorithmic correctness and efficiency.