Bayesian Estimation of Large Choice Models with Adaptive Sampling and Likelihood-Free Inference

Abstract

Understanding how individuals make travel decisions is central to transportation research. Discrete choice models provide a rigorous framework to infer preferences from observed behavior and to anticipate responses to policies. However, their practical application fundamentally relies on the ability to enumerate or sample from a predefined choice set. This assumption breaks down in many important contexts, such as route choice on large-scale networks or activity scheduling, where the number of feasible alternatives is combinatorial. This paper addresses this limitation by introducing estimation methods that do not require explicit enumeration of the choice set. Instead of treating the choice set as a fixed input, we embed alternative generation directly within the estimation process. We develop two complementary approaches. The first relies on adaptive sampling within a Bayesian framework, using only binary comparisons to recover the full model. The second leverages Bayesian optimization for likelihood-free inference (BOLFI), replacing likelihood evaluation with a learned surrogate of the discrepancy between observed and simulated behavior. Both approaches fundamentally bypass the need to enumerate or approximate the full choice set. Using controlled synthetic experiments with known ground truth, we show that these methods recover model parameters with the same accuracy as full choice set estimation, while achieving orders-of-magnitude computational gains. Crucially, their performance scales independently of the size of the choice set. These results demonstrate that discrete choice models can be estimated reliably without enumerating alternatives, substantially expanding the range of problems that can be addressed in practice. In particular, they enable the estimation of behaviorally rich models in settings previously considered intractable, including network-wide route choice and combinatorial activity scheduling.