Hidden Markov models are widely used to infer latent state sequences from sequential data, but Viterbi decoding reports only one most likely complete path. When decoded states carry scientific meaning, this single maximizer can conceal pathwise uncertainty created by multiple near-optimal trajectories. Conditional on a fitted HMM, we introduce the tropical Viterbi tube: the set of hidden trajectories whose complete-data log-score lies within a tolerance of the Viterbi optimum. State, transition, and change-status projections show which local features remain compatible with globally near-optimal complete paths, giving a pathwise uncertainty layer for HMMs in sequence analysis, ecology, finance, biomedical monitoring, and related domains. The tube is a posterior superlevel set on complete hidden-path space, with tolerance interpreted as a log posterior-odds loss relative to a Viterbi path. Calibrating the tolerance to a target posterior mass gives an HPD-threshold credible region for the complete latent path and conservative simultaneous projected bands. We prove monotonicity, step-function behavior, and deterministic stability guarantees, and compute projected tubes exactly by max-plus forward-backward recursions in O(TK^2) time for dense transitions. Posterior tube mass and HPD calibration are separate pathwise calculations approximated by FFBS. In a public bat-tracking application, robust foraging tube segments are enriched for feeding buzzes, whereas robust commuting segments are depleted: at eta = 0.005, enrichment is 2.25 with 95% bootstrap interval (1.73, 2.85) for robust foraging and 0.27 with interval (0.16, 0.44) for robust commuting.

翻译：隐马尔可夫模型广泛用于从序列数据推断潜在状态序列，但维特比解码仅报告一条最可能的完整路径。当解码状态承载科学意义时，单一最大值可能掩盖由多条近似最优轨迹导致的路径不确定性。基于已拟合的HMM，我们提出热带维特比管：其定义为完整数据对数得分处于维特比最优值容忍度范围内的隐藏轨迹集合。状态、转移及变化状态投影可揭示哪些局部特征仍与全局近似最优完整路径兼容，从而为序列分析、生态学、金融、生物医学监测及相关领域的HMM提供路径级不确定性层。该管是完整隐藏路径空间上的后验超水平集，容忍度可解释为相对维特比路径的对数后验优势比损失。将容忍度校准至目标后验质量可得到完整潜在路径的HPD阈值可信域及保守的联合投影带。我们证明其单调性、阶梯函数行为及确定性稳定保证，并通过最大加向前-向后递推在O(TK^2)时间内精确计算稠密转移矩阵的投影管。后验管质量与HPD校准作为独立路径计算，通过FFBS方法近似实现。在公开蝙蝠追踪应用中，鲁棒取食管段富集捕食嗡嗡声，而鲁棒通勤管段则呈现缺失：当η=0.005时，鲁棒取食富集比为2.25（95%自助法区间1.73-2.85），鲁棒通勤富集比为0.27（区间0.16-0.44）。