  In this letter, we introduce a novel message-passing algorithm for a class of
problems which can be mathematically understood as estimating volume-related
properties of random polytopes. Unlike the usual approach consisting in
approximating the real-valued cavity marginal distributions by a few
parameters, we propose a weighted message-passing algorithm to deal with the
entire function. Various alternatives of how to implement our approach are
discussed and numerical results for random polytopes are compared with results
using the Hit-and-Run algorithm.
