Multidimensional array database systems are suited for scientific and engineering applications. Data in these applications is often uncertain and imprecise due to errors in the instruments and observations, etc. There are often correlations exhibited in the distribution of values among the cells of an array. Typically, the correlation is stronger for cells that are close to each other and weaker for cells that are far away. We devise a novel data structure, called the A~*-tree (multidimensional Array tree), demonstrating that by taking advantage of the predictable and structured correlations of multidimensional data, we can have a more efficient way of modeling and answering queries on large-scale array data. An A~*-tree is a unified model for storage and inference. The graphical model that is assumed in an A~*-tree is essentially a Bayesian Network. We analyze and experimentally verify the accuracy of an A~*-tree encoding of the underlying joint distribution. We also study the efficiency of query processing over A~*-trees, comparing it to an alternative graphical model.
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