Kybernetika 45 no. 2, 169-188, 2009

Asymptotic Behaviour of a BIPF Algorithm with an Improper Target

Claudio Asci and Mauro Piccioni


The BIPF algorithm is a Markovian algorithm with the purpose of simulating certain probability distributions supported by contingency tables belonging to hierarchical log-linear models. The updating steps of the algorithm depend only on the required expected marginal tables over the maximal terms of the hierarchical model. Usually these tables are marginals of a positive joint table, in which case it is well known that the algorithm is a blocking Gibbs Sampler. But the algorithm makes sense even when these marginals do not come from a joint table. In this case the target distribution of the algorithm is necessarily improper. In this paper we investigate the simplest non trivial case, i. e. the $2\times2\times2$ hierarchical interaction. Our result is that the algorithm is asymptotically attracted by a limit cycle in law.


marginal problem, log-linear models, null Markov chains


60J05, 65C40, 62F15