2015/02/14 by Benjamin Letham, Letham, Benjamin, Lydia M. Letham +3
Computer Science · Mathematics · Decision Sciences · #Bayesian Methods and Mixture Models #Statistical Methods and Bayesian Inference #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.1502.04243
When an item goes out of stock, sales transaction data no longer reflect the\noriginal customer demand, since some customers leave with no purchase while\nothers substitute alternative products for the one that was out of stock. Here\nwe develop a Bayesian hierarchical model for inferring the underlying customer\narrival rate and choice model from sales transaction data and the corresponding\nstock levels. The model uses a nonhomogeneous Poisson process to allow the\narrival rate to vary throughout the day, and allows for a variety of choice\nmodels. Model parameters are inferred using a stochastic gradient MCMC\nalgorithm that can scale to large transaction databases. We fit the model to\ndata from a local bakery and show that it is able to make accurate\nout-of-sample predictions, and to provide actionable insight into lost cookie\nsales.\n