The L-decomposable and the bi-decomposable models are two families of distributions on the set $S_n$ of all permutations of the first $n$ positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these Markov bases, we show that not all bi-decomposable distributions can be approximated arbitrarily well by strictly positive bi-decomposable distributions.
conditional independence, Markov basis, closure of exponential family, permutation, L-decomposable
62E10, 62H05, 60C05