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A note on the IPF algorithm when the marginal problem is unsolvable

Claudio Asci;  Mauro Piccioni — 2003

Kybernetika

In this paper we analyze the asymptotic behavior of the IPF algorithm for the problem of finding a 2x2x2 contingency table whose pair marginals are all equal to a specified 2x2 table, depending on a parameter. When this parameter lies below a certain threshold the marginal problem has no solution. We show that in this case the IPF has a “period three limit cycle” attracting all positive initial tables, and a bifurcation occur when the parameter crosses the threshold.

Asymptotic behaviour of a BIPF algorithm with an improper target

Claudio Asci;  Mauro Piccioni — 2009

Kybernetika

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...

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