Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be observed in batches, each of which is based on a large number of such trials and can be modeled via multinomial distributions. We postulate that the multinomial probabilities of the categories vary randomly depending on batches. The challenge is to predict accurately on cumulative data based on data up to a few batches as early as possible. On the theoretical front, we first derive sufficient conditions of asymptotic normality of the estimates of the multinomial cell probabilities and present corresponding suitable transformations. Then, in a Bayesian framework, we consider hierarchical priors using multivariate normal and inverse Wishart distributions and establish the posterior convergence. The desired inference is arrived at using these results and ensuing Gibbs sampling. The methodology is demonstrated with election data from two different settings—one from India and the other from the United States. Additional insights of the effectiveness of the proposed methodology are attained through a simulation study.

中文翻译：

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使用多项数据序列的贝叶斯模型根据部分信息预测选举

预测选举获胜者对于多个利益相关者来说都很重要。为了表述这个问题，我们考虑一个独立的分类数据序列，每个数据序列都有有限数量的可能结果。假设数据是分批观察的，每批数据都基于大量此类试验，并且可以通过多项分布进行建模。我们假设类别的多项概率根据批次随机变化。挑战在于尽早根据最多几个批次的数据准确预测累积数据。在理论方面，我们首先推导出多项单元概率估计的渐近正态性的充分条件，并提出相应的合适变换。然后，在贝叶斯框架中，我们使用多元正态和逆 Wishart 分布考虑分层先验，并建立后验收敛。使用这些结果和随后的吉布斯采样得出所需的推论。该方法通过来自两个不同环境（一个来自印度，另一个来自美国）的选举数据得到了证明。通过模拟研究获得了对所提出方法的有效性的更多见解。