ABSTRACT

The Non-Parametric Predictive Inference Model for Multinomial Data (NPI-M) is an imprecise probabilities model used to represent the available information about a categorical variable. It presents some advantages over another imprecise probabilities model frequently used in the literature called Imprecise Dirichlet Model (IDM), which assumes previous knowledge about the data through a parameter. The Approximate Non-Parametric Predictive Inference Model for Multinomial Data (A-NPI-M) is a model similar to the NPI-M that can be expressed by reachable sets of probability intervals, is easier to manage, and is non-parametric. As a novelty, in this work, we analyze the main properties of A-NPI-M credal sets, comparing them with the properties of credal sets associated with the IDM. Moreover, we present procedures to calculate the most important uncertainty measures on A-NPI-M credal sets. Those procedures represent useful tools to make the A-NPI-M very suitable to be used in practical applications.

摘要

多项式数据的非参数预测推理模型（NPI-M）是一种不精确的概率模型，用于表示有关分类变量的可用信息。相对于文献中经常使用的另一个不精确概率模型，即不精确Dirichlet模型（IDM），它具有一些优势，该模型通过参数假设了有关数据的先前知识。多项数据的近似非参数预测推理模型（A-NPI-M）是类似于NPI-M的模型，可以用可到达的概率间隔集表示，更易于管理，并且是非参数的。作为一项新颖性，在这项工作中，我们分析了A-NPI-M creset集的主要属性，并将它们与与IDM相关联的credal set的属性进行了比较。而且，我们介绍了计算A-NPI-M crecreset上最重要的不确定性度量的程序。这些过程代表了使A-NPI-M非常适合在实际应用中使用的有用工具。