B1432
Title: Inference for nonhomogeneous Bellman-Harris processes with applications to transportation analytics
Authors: Pramita Bagchi - George Washington University (United States) [presenting]
Anand Vidyashankar - George Mason University (United States)
Abstract: Vehicle sharing systems such as bikeshare, scooter share, and car share are undergoing continuous improvements to increase the adoption of public transportation. The difficulties of the last-mile problem can only be solved if the system is convenient, reliable, and cost-effective. Big data methods such as learning algorithms combined with optimization techniques are increasingly used to understand the mobility patterns of customers and the demand for vehicles within a transportation system, yielding empirical solutions. While these methods facilitate some data-driven decision-making, they tend to have limited applicability due to the inherent ad hoc nature of the procedures. We develop an alternative approach, based on a non-homogeneous age-dependent branching process, that incorporates differential dynamics of the vehicle usage across time and ``stations''. We then cast various scientific questions as inferential questions concerning the parameters of the model. We address the resulting inferential issues using rigorous statistical and computational approaches. For this reason, we establish central limit theorems concerning functionals of the non-homogeneous age-dependent branching processes and use them to develop algorithms for real-time usage and principled decision making.
