Large Structures Seminar: Dario Gasbarra

A local train stops at stations 0, 1, . . . , T and passengers getting in and out a wagon are counted at every station. Since passengers are not labeled and with the same ticket it is possible to travel across all the line, when a passenger gets off the train, it is not known from which station he started. The distribution of the individual trips satisfies a constrained system of linear diophanitine equations, which typically is underdetermined. Nevertheless we show that, when i.i.d. realizations are collected , the probability distribution of the travel lengths, depending on the passenger’s departure station is identifiable. We use a Bayesian data augmentation, where the the distribution of the individual trips is the hidden variable. The posterior distribution is explored by the fiber walk Markov chain Monte introduced by Diaconis and Sturmfels 1998.