Probabilistic modeling for symbolic data

Symbolic data refer to variables whose 'values' might be, e.g., intervals, sets of categories, or even frequency distributions. Symbolic data analysis provides exploratory methods for revealing the structure of such data and proceeds typically by heuristical, even if suggestive methods that generalize criteria and algorithms from classical multivariate statistics. In contrast, this paper proposes to base the analysis of symbolic data on probability models as well and to derive statistical tools by standard methods (such as maximum likelihood). This approach is exemplified for the case of multivariate interval data where we consider minimum volume hypercubes, average intervals, clustering and regression models, also with reference to previous work.