A variational Bayesian spatial interaction model for estimating revenue and demand at business facilities

We study the problem of estimating potential revenue or demand at business facilities and understanding its generating mechanism. This problem arises in different fields such as operation research or urban science, and more generally, it is crucial for businesses' planning and decision making. We develop a Bayesian spatial interaction model, henceforth BSIM, which provides probabilistic predictions about revenues generated by a particular business location provided their features and the potential customers' characteristics in a given region. BSIM explicitly accounts for the competition among the competitive facilities through a probability value determined by evaluating a store-specific Gaussian distribution at a given customer location. We propose a scalable variational inference framework that, while being significantly faster than competing Markov Chain Monte Carlo inference schemes, exhibits comparable performances in terms of parameters identification and uncertainty quantification. We demonstrate the benefits of BSIM in various synthetic settings characterised by an increasing number of stores and customers. Finally, we construct a real-world, large spatial dataset for pub activities in London, UK, which includes over 1,500 pubs and 150,000 customer regions. We demonstrate how BSIM outperforms competing approaches on this large dataset in terms of prediction performances while providing results that are both interpretable and consistent with related indicators observed for the London region.