Pitkin, James; (2018) Applications of Bayesian mixture models and self-exciting processes to retail analytics. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Retail analytics has been transformed by big data, which has led to many retailers using detailed analytics to improve performance at a range of operational levels. This is the case with the collaborator of this research, dunnhumby, who have large amounts of retailer data derived from the numerous activities that retailers operate at. This thesis focuses on two challenges retailers face; the analysis of products through their price elasticity coefficients and demand forecasting of products known as slow-moving inventory. The analysis of products in terms of their price elasticity coefficients is well studied. Existing approaches are hampered by the challenging nature of cross-elasticity data, as cross-elasticity coefficients typically vary in dimension and exhibit an inherent censoring. We address these problems by developing a systematic model-based approach by reinterpreting the cross-elasticity coefficients as realisations of variable length order statistics sequences, and develop a nonparametric Bayesian methodology to cluster these sequences. Our approach uses the Dirichlet process mixture model that allows data to dictate the appropriate number of clusters and provides interpretable parameters characterising the decay of the leading entries. Slow-moving inventory are characterised by having intermittent demand, in that the demand is populated with an abundance of zero sales and that, when a sale does a occur, it is often followed by a quick succession of sales. This demand intermittency inhibits the use of traditional analytics which crucially affects optimal inventory management. To combat this, we represent intermittent demand as a structured multivariate point process which allows for auto- and cross- correlation frequently observed in sparse sales data. Our approach uses a hurdle component to cope with zero sales inflation, the Hawkes process to capture the temporal clustering and a hierarchal structure to pool information across products. We illustrate our methods on real retailer data, from access granted by dunnhumby.

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