Hierarchical Bayesian Regression for Multi-Location Sales Transaction
  Forecasting
John Mark Agosta Mario Inchiosa
The features in many prediction models naturally take the form of a
hierarchy. The lower levels represent individuals or events. These units group
naturally into locations and intervals or other aggregates, often at multiple
levels. Levels of groupings may intersect and join, much as relational database
tables do. Besides representing the structure of the data, predictive features
in hierarchical models can be assigned to their proper levels. Such models lend
themselves to hierarchical Bayes solution methods that ``share'' results of
inference between groups by generalizing over the case of individual models for
each group versus one model that aggregates all groups into one.
  In this paper we show our work-in-progress applying a hierarchical Bayesian
model to forecast purchases throughout the day at store franchises, with
groupings over locations and days of the week. We demonstrate using the
\textsf{stan} package on individual sales transaction data collected over the
course of a year. We show how this solves the dilemma of having limited data
and hence modest accuracy for each day and location, while being able to scale
to a large number of locations with improved accuracy.