In this Chapter we show that by considering eye movements, and in particular,the resulting sequence of gaze shifts, a stochastic process, a wide variety oftools become available for analyses and modelling beyond conventionalstatistical methods. Such tools encompass random walk analyses and more complextechniques borrowed from the pattern recognition and machine learning fields. After a brief, though critical, probabilistic tour of current computationalmodels of eye movements and visual attention, we lay down the basis for gazeshift pattern analysis. To this end, the concepts of Markov Processes, theWiener process and related random walks within the Gaussian framework of theCentral Limit Theorem will be introduced. Then, we will deliberately violatefundamental assumptions of the Central Limit Theorem to elicit a largerperspective, rooted in statistical physics, for analysing and modelling eyemovements in terms of anomalous, non-Gaussian, random walks and modern foragingtheory. Eventually, by resorting to machine learning techniques, we discuss how theanalyses of movement patterns can develop into the inference of hidden patternsof the mind: inferring the observer's task, assessing cognitive impairments,classifying expertise.
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