  The problem of recovering (count and sum) range queries over multidimensional
data only on the basis of aggregate information on such data is addressed. This
problem can be formalized as follows. Suppose that a transformation T producing
a summary from a multidimensional data set is used. Now, given a data set D, a
summary S=T(D) and a range query r on D, the problem consists of studying r by
modelling it as a random variable defined over the sample space of all the data
sets D' such that T(D) = S. The study of such a random variable, done by the
definition of its probability distribution and the computation of its mean
value and variance, represents a well-founded, theoretical probabilistic
approach for estimating the query only on the basis of the available
information (that is the summary S) without assumptions on original data.
