Confidence sequences are collections of confidence regions that simultaneously cover the true parameter for every sample size at a prescribed confidence level. Tightening these sequences is of practical interest and can be achieved by incorporating prior information through the method of mixture martingales. However, confidence sequences built from informative priors are vulnerable to misspecification and may become vacuous when the prior is poorly chosen. We study this trade-off for Gaussian observations with known variance. By combining the method of mixtures with a global informative prior whose tails are polynomial or exponential and the extended Ville's inequality, we construct confidence sequences that are sharper than their non-informative counterparts whenever the prior is well specified, yet remain bounded under arbitrary misspecification. The theory is illustrated with several classical priors.

翻译：置信序列是置信区域的集合，这些区域能在指定置信水平下同时覆盖每个样本大小的真实参数。收紧这些序列具有实际意义，可通过混合鞅方法纳入先验信息来实现。然而，基于信息性先验构建的置信序列容易受到错误设定的影响，当先验选择不当时可能变得空泛。我们针对已知方差的高斯观测值研究这一权衡。通过将尾部为多项式或指数的全局信息性先验与扩展的维尔不等式相结合的混合方法，我们构建了当先验规范设定时比非信息性对应序列更尖锐、且在任意错误设定下仍保持有界的置信序列。该理论通过若干经典先验示例加以阐明。