In this paper, we discuss optimal next-sample prediction for families of probability distributions with a locally compact topological group structure. The right-invariant prior was previously shown to yield a posterior predictive distribution minimizing the worst-case Kullback-Leibler risk among all predictive procedures. However, the assumptions for the proof are so strong that they rarely hold in practice and it is unclear when the density functions used in the proof exist. Therefore, we provide a measure-theoretic proof using a more appropriate set of assumptions. As an application, we show a strong optimality result for next-sample prediction for multivariate normal distributions.

翻译：本文讨论了具有局部紧拓扑群结构的概率分布族的最优下一样本预测问题。先前的研究表明，右不变先验能够产生在所有预测方法中最小化最坏情况Kullback-Leibler风险的后验预测分布。然而，该证明的假设条件过于严苛，在实践中很少成立，且证明中使用的密度函数何时存在尚不明确。因此，我们基于更合理的假设条件，提供了一个测度论的证明。作为应用，我们展示了多元正态分布下一样本预测的强最优性结果。