SUMMARYWe consider inferring transit route-level origin-destination (OD) flows using large amounts of automatic passenger counter (APC) boarding and alighting data based on a statistical formulation. One critical problem is that we need to enumerate the OD flow matrices that are consistent with the APC data for each bus trip to evaluate the model likelihood function. The OD enumeration problem has not been addressed satisfactorily in the literature. Thus, we propose a novel sampler to avoid the need to enumerate OD flow matrices by generating them recursively from the first alighting stop to the last stop of the bus route of interest. A Markov chain Monte Carlo (MCMC) method that incorporates the proposed sampler is developed to simulate the posterior distributions of the OD flows. Numerical investigations on an operational bus route under a realistic OD structure demonstrate the superiority of the proposed MCMC method over an existing MCMC method and a state-of-the-practice method.