We derive general bounds on the probability that the empirical first-passage time $\overline{\tau}_n\equiv \sum_{i=1}^n\tau_i/n$ of a reversible ergodic Markov process inferred from a sample of $n$ independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct non-asymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.

翻译：我们得出了一个一般的界限,即经验性第一通过时间 $\ overline\tau ⁇ n\equiv\ sum ⁇ i=1\n\tau_i/n$,这是从独立实现的抽样中推断的可逆的ergodic Markov 过程,它有可能偏离真正的平均第一通过时间,其幅度大于任一方向的任何一定数量。我们构建了非被动性信任间隔,在难以捉摸的小抽样制度中保持这种间隔,从而填补了无药方法和巴伊西亚方法之间的差距,而巴伊西亚方法对先前的信念敏感,并往往低估了小型抽样环境中的不确定性。我们基于措施的浓度结果允许在动态推断中进行无模式错误控制和可靠的错误估计,因此对于在有限取样的情况下分析实验和模拟数据非常重要。