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Prediction is a very important element of human intelligence and plays a major role in human behavior, perception, and learning. This paper presents the development of a mathematical model of the prediction mechanism in the context of a Bayes filter, which is the predominant schema used for integrating temporal data in the field of robot mapping and localization problems. We propose a generalized anticipatory Bayes filter that uses revised sensor values obtained from the prediction process at the measurement-update step to enhance the performance of the sensor model. The development of a generalized anticipatory Bayes filter is not only an extension of the original Bayes filter, but also a mathematical model of the human prediction mechanism of sensory processing. This work was verified by experiments using observed data.