Abstract The modeling of multinomial data has seen tremendous progress since Riefer and Batchelder’s (1988) seminal paper. One recurring challenge, however, concerns the availability of relative performance measures that strike an ideal balance between goodness of fit and functional flexibility. One approach to the problem of model selection is Normalized Maximum Likelihood (NML), a solution derived from the Minimum Description Length principle. In the present work we provide an R implementation of a Gibbs sampler that can be used to compute NML for models of joint multinomial data. We discuss the application of NML in different examples, compare NML with Bayes Factors, and show how it constitutes an important addition to researchers’ toolboxes.

中文翻译：

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在多项模型中选择：归一化最大似然的道歉

摘要 自 Riefer 和 Batchelder (1988) 的开创性论文以来，多项数据的建模取得了巨大的进步。然而，一个反复出现的挑战涉及相关性能指标的可用性，这些指标在合身性和功能灵活性之间取得了理想的平衡。模型选择问题的一种方法是归一化最大似然 (NML)，这是一种源自最小描述长度原则的解决方案。在目前的工作中，我们提供了 Gibbs 采样器的 R 实现，可用于计算联合多项数据模型的 NML。我们讨论了 NML 在不同示例中的应用，将 NML 与贝叶斯因子进行了比较，并展示了它如何构成研究人员工具箱的重要补充。