Asymptotic behaviour of a BIPF algorithm with an improper target

Claudio Asci; Mauro Piccioni

Kybernetika (2009)

  • Volume: 45, Issue: 2, page 169-188
  • ISSN: 0023-5954

Abstract

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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 × 2 × 2 hierarchical interaction. Our result is that the algorithm is asymptotically attracted by a limit cycle in law.

How to cite

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Asci, Claudio, and Piccioni, Mauro. "Asymptotic behaviour of a BIPF algorithm with an improper target." Kybernetika 45.2 (2009): 169-188. <http://eudml.org/doc/37729>.

@article{Asci2009,
abstract = {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 $2\times 2\times 2$ hierarchical interaction. Our result is that the algorithm is asymptotically attracted by a limit cycle in law.},
author = {Asci, Claudio, Piccioni, Mauro},
journal = {Kybernetika},
keywords = {log-linear models; marginal problem; null Markov chains; log-linear models; marginal problem; null Markov chains},
language = {eng},
number = {2},
pages = {169-188},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Asymptotic behaviour of a BIPF algorithm with an improper target},
url = {http://eudml.org/doc/37729},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Asci, Claudio
AU - Piccioni, Mauro
TI - Asymptotic behaviour of a BIPF algorithm with an improper target
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 2
SP - 169
EP - 188
AB - 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 $2\times 2\times 2$ hierarchical interaction. Our result is that the algorithm is asymptotically attracted by a limit cycle in law.
LA - eng
KW - log-linear models; marginal problem; null Markov chains; log-linear models; marginal problem; null Markov chains
UR - http://eudml.org/doc/37729
ER -

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