Estimating Primary Demand for Substitutable Products from Sales Transaction Data
提出一种仅利用销售和产品可得性数据来估计替代需求与流失需求的方法，结合多项逻辑特模型与非齐次泊松过程，通过期望最大化算法高效求解，适用于库存缺货或产品展示受限场景。
We propose a method for estimating substitute and lost demand when only sales and product availability data are observable, not all products are displayed in all periods (e.g., due to stockouts or availability controls), and the seller knows its aggregate market share. The model combines a multinomial logit (MNL) choice model with a nonhomogeneous Poisson model of arrivals over multiple periods. Our key idea is to view the problem in terms of primary (or first-choice) demand; that is, the demand that would have been observed if all products had been available in all periods. We then apply the expectation-maximization (EM) method to this model, and we treat the observed demand as an incomplete observation of primary demand. This leads to an efficient, iterative procedure for estimating the parameters of the model. All limit points of the procedure are provably stationary points of the incomplete data log-likelihood function. Every iteration of the algorithm consists of simple, closed-form calculations. We illustrate the effectiveness of the procedure on simulated data and two industry data sets.