Most of the contemporary literature on information freshness solely focuses on the analysis of freshness for martingale estimators, which simply use the most recently received update as the current estimate. While martingale estimators are easier to analyze, they are far from optimal, especially in pull-based update systems, where maximum aposteriori probability (MAP) estimators are known to be optimal, but are analytically challenging. In this work, we introduce a new class of estimators called $p$-MAP estimators, which enable us to model the MAP estimator as a piecewise constant function with finitely many stages, bringing us closer to a full characterization of the MAP estimators when modeling information freshness.

翻译：当前关于信息新鲜度的文献大多仅关注鞅估计器的分析，这类估计器仅使用最近接收的更新作为当前估计值。尽管鞅估计器更易于分析，但其远非最优——特别是在基于拉取的更新系统中，已知最大后验概率估计器具有最优性，但存在解析分析上的挑战。本研究提出了一类名为$p$-MAP估计器的新型估计器，使得我们能够将MAP估计器建模为具有有限阶段的分段常数函数，从而在信息新鲜度建模中更接近对MAP估计器的完整表征。