A novel method is employed for collecting optimizer statistics for optimizing database queries by gathering feedback from the query execution engine about the observed cardinality of predicates and constructing and maintaining multidimensional histograms. This makes use of the correlation between data columns without employing an inefficient data scan. The maximum entropy principle is used to approximate the true data distribution by a histogram distribution that is as "simple" as possible while being consistent with the observed predicate cardinalities. Changes in the underlying data are readily adapted to, automatically detecting and eliminating inconsistent feedback information in an efficient manner. The size of the histogram is controlled by retaining only the most "important" feedback.