Scanning and prediction in multi-dimensional data arrays

The problem of sequentially scanning and predicting data arranged in a multi-dimensional array is considered. We introduce the notion of a scandictor, which is any scheme for the sequential scanning and prediction of such data. The scandictability of a probabilistic data-array is defined as the best achievable expected "scandiction" performance on that array. We derive a lower bound on scandiction performance that is shown to be tight for various cases of interest.