Hierarchical Bayesian Regression for Multi-Location Sales Transaction Forecasting

TL;DR

This paper presents a hierarchical Bayesian regression approach for multi-location sales forecasting, leveraging data hierarchies to improve accuracy across locations and time periods, especially with limited data per group.

Contribution

It introduces a hierarchical Bayesian model applied to sales data, demonstrating improved scalability and accuracy over traditional methods for multi-location forecasting.

Findings

Hierarchical Bayesian models improve forecast accuracy for multiple locations.

The approach scales well with many locations and limited data per location.

Using Stan enables effective inference on transaction data.

Abstract

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.