Egocentric perception has grown rapidly with the advent of immersive computing devices. Human gaze prediction is an important problem in analyzing egocentric videos and has largely been tackled through either saliency-based modeling or highly supervised learning. In this work, we tackle the problem of jointly predicting human gaze points and temporal segmentation of egocentric videos, in an unsupervised manner without using any training data. We introduce an \textit{unsupervised} computational model that draws inspiration from cognitive psychology models of human attention and event perception. We use Grenander's pattern theory formalism to represent spatial-temporal features and model \textit{surprise} as a mechanism to predict gaze fixation points and temporally segment egocentric videos. Extensive evaluation on two publicly available datasets - GTEA and GTEA+ datasets show that the proposed model is able to outperform all unsupervised baselines and some supervised gaze prediction baselines. Finally, we show that the model can also temporally segment egocentric videos with a performance comparable to more complex, fully supervised deep learning baselines.