Abstract Many economic models of consumer demand require researchers to partition sets of products or attributes prior to the analysis. These models are common in applied problems when the product space is large or spans multiple categories. While the partition is traditionally fixed a priori, we let the partition be a model parameter and propose a Bayesian method for inference. The challenge is that demand systems are commonly multivariate models that are not conditionally conjugate with respect to partition indices, precluding the use of Gibbs sampling. We solve this problem by constructing a new location-scale partition distribution that can generate random-walk Metropolis–Hastings proposals and also serve as a prior. Our method is illustrated in the context of a store-level category demand model, where we find that allowing for partition uncertainty is important for preserving model flexibility, improving demand forecasts, and learning about the structure of demand. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

中文翻译：

---

具有随机分区的需求模型

摘要 许多消费者需求的经济模型要求研究人员在分析之前对产品或属性集进行划分。当产品空间很大或跨越多个类别时，这些模型在应用问题中很常见。虽然传统上分区是先验固定的，但我们让分区作为模型参数并提出贝叶斯推理方法。挑战在于需求系统通常是多变量模型，它们在分区索引方面不是条件共轭的，因此无法使用 Gibbs 抽样。我们通过构建一个新的位置尺度分区分布来解决这个问题，该分布可以生成随机游走 Metropolis-Hastings 提议，也可以作为先验。我们的方法在商店级别的类别需求模型的背景下进行了说明，我们发现允许分区不确定性对于保持模型灵活性、改进需求预测和了解需求结构很重要。本文的补充材料，包括对可用于复制作品的材料的标准化描述，可作为在线补充材料获得。