  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.
