Numerous studies have examined the acoustic correlates of sentential stress and its underlying linguistic functionality. However, the mechanism that connects stress cues to the listener's attentional processing has remained unclear. Also, the learnability versus innateness of stress perception has not been widely discussed. In this work, we introduce a novel perspective to the study of sentential stress and put forward the hypothesis that perceived sentence stress in speech is related to the unpredictability of prosodic features, thereby capturing the attention of the listener. As predictability is based on the statistical structure of the speech input, the hypothesis also suggests that stress perception is a result of general statistical learning mechanisms. To study this idea, computational simulations are performed where temporal prosodic trajectories are modeled with an n-gram model. Probabilities of the feature trajectories are subsequently evaluated on a set of novel utterances and compared to human perception of stress. The results show that the low-probability regions of F0 and energy trajectories are strongly correlated with stress perception, giving support to the idea that attention and unpredictability of sensory stimulus are mutually connected.