Metropolis–Hastings sampling of paths |
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Institution: | 1. Institute for Transport Studies, University of Leeds, 36-40 University Road, Leeds LS2 9JT, UK;2. Department of Technology, Management and Economics, Technical University of Denmark, Bygningstorvet 116B 2800 Kgs. Lyngby, Denmark |
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Abstract: | 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. |
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