June 2024 Bayesian hierarchical modelling of sparse count processes in retail analytics
James Pitkin, Ioanna Manolopoulou, Gordon Ross
Author Affiliations +
Ann. Appl. Stat. 18(2): 946-965 (June 2024). DOI: 10.1214/23-AOAS1811


The field of retail analytics has been transformed by the availability of rich data, which can be used to perform tasks such as demand forecasting and inventory management. However, one task which has proved more challenging is the forecasting of demand for products which exhibit very few sales. The sparsity of the resulting data limits the degree to which traditional analytics can be deployed. To combat this, we represent sales data as a structured sparse multivariate point process, which allows for features such as autocorrelation, cross-correlation, and temporal clustering, known to be present in sparse sales data. We introduce a Bayesian point process model to capture these phenomena, which includes a hurdle component to cope with sparsity and an exciting component to cope with temporal clustering within and across products. We then cast this model within a Bayesian hierarchical framework, to allow the borrowing of information across different products, which is key in addressing the data sparsity per product. We conduct a detailed analysis, using real sales data, to show that this model outperforms existing methods in terms of predictive power, and we discuss the interpretation of the inference.

Funding Statement

This work has been carried out with the financial support of the EPSRC, the Alan Turing Institute, and dunnhumby ltd, our industrial partner.


Access to anonymised electronic point of sale data granted by our industrial partner dunnhumby ltd.


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James Pitkin. Ioanna Manolopoulou. Gordon Ross. "Bayesian hierarchical modelling of sparse count processes in retail analytics." Ann. Appl. Stat. 18 (2) 946 - 965, June 2024. https://doi.org/10.1214/23-AOAS1811


Received: 1 May 2021; Revised: 1 July 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1811

Keywords: cross-excitation , demand forecasting , Hawkes process , hurdle model , intermittent demand , self-excitation , slow-moving-inventory

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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