Random set theory is a fascinating branch of mathematics that amalgamates techniques from topology, convex geometry, and probability theory. Social scientists routinely conduct empirical work with data and modelling assumptions that reveal a set to which the parameter of interest belongs, but...

Many real phenomena may be modeled as random closed sets in Rd, of different Hausdorff dimensions. Of particular interest are cases in which their Hausdorff dimension, say n, is strictly less than d, such as fiber processes, boundaries of germ–grain models, and n-facets of random...

In this paper we consider the regression problem for random sets of the Boolean-model type. Regression modeling of the Boolean random sets using some explanatory variables are classified according to the type of these variables as propagation, growth or propagation-growth models. The maximum...