Miscellanea. On the generation of the chordless four-cycle

Abstract

In the theory of Markov graphical representations of conditional independencies a special role is played by the chordless four-cycle, representing for four random variables the conditional independencies X ⊥ V |( U, W ) and W ⊥ U |( X, V ). It is not immediately clear how such systems are to be generated. Here we sketch some possible data-generating mechanisms.