Bayesian Analysis in Data Cubes

In the last few years, there has been active research on aggregating advanced statistical measures in multi-dimensional data cubes [10] from partitioned subsets of data. In this paper, we propose a compression and aggregation scheme to support Bayesian estimations in data cubes based on the asymptotic properties of Bayesian statistics. The main application of the technique developed in this paper is data warehousing and the associated on-line analytical processing (OLAP) computing. OLAP allows for interactive analysis of multidimensional data to facilitate effective data mining at multiple levels of abstraction. Earlier work in data cubes [10] supports aggregation of simple measures such as sum() and average(). However, the fast development of OLAP technology has led to high demand for more sophisticated data analyzing capabilities, such as prediction, trend monitoring, and exception detection of multidimensional data. Oftentimes, existing simple measures such as sum() and average() become insufficient, and more sophisticated statistical models are desired to be supported in OLAP. Recently, some researchers developed aggregation schemes for more advanced statistical analysis including parametric models such as linear regression [6, 11] general multiple linear regression [5, 14] logistic regression analysis [23] and predictive filters [5], as well as nonparametric statistical models such as naive Bayesian classifiers [4] and linear discriminant analysis [15]. Along this line, we develop an aggregation scheme support Bayesian estimations in data cubes. Bayesian methods are statistical approaches to parameter estimation and statistical inference which use prior distributions over parameters. Bayesian methods have been successfully applied in many different fields such business, computer science, economics, epidemiology, genetics, imaging and political science. The premise of Bayesian statistics is to incorporate prior knowledge, along with a given set of