A note on the IPF algorithm when the marginal problem is unsolvable
Kybernetika (2003)
- Volume: 39, Issue: 6, page [731]-737
- ISSN: 0023-5954
Access Full Article
topAbstract
topHow to cite
topAsci, Claudio, and Piccioni, Mauro. "A note on the IPF algorithm when the marginal problem is unsolvable." Kybernetika 39.6 (2003): [731]-737. <http://eudml.org/doc/33677>.
@article{Asci2003,
abstract = {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.},
author = {Asci, Claudio, Piccioni, Mauro},
journal = {Kybernetika},
keywords = {contingency tables; hierarchical models; partial maximization algorithms; contingency tables; hierarchical model; partial maximization algorithm},
language = {eng},
number = {6},
pages = {[731]-737},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A note on the IPF algorithm when the marginal problem is unsolvable},
url = {http://eudml.org/doc/33677},
volume = {39},
year = {2003},
}
TY - JOUR
AU - Asci, Claudio
AU - Piccioni, Mauro
TI - A note on the IPF algorithm when the marginal problem is unsolvable
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 6
SP - [731]
EP - 737
AB - 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.
LA - eng
KW - contingency tables; hierarchical models; partial maximization algorithms; contingency tables; hierarchical model; partial maximization algorithm
UR - http://eudml.org/doc/33677
ER -
References
top- Csiszár I., 10.1214/aop/1176996454, Ann. Probab. 3 (1975), 146–158 (1975) MR0365798DOI10.1214/aop/1176996454
- Deming W. E., Stephan F. F., 10.1214/aoms/1177731829, Ann. Math. Statist. 11 (1940), 427–444 (1940) MR0003527DOI10.1214/aoms/1177731829
- Haberman S. J., The analysis of frequency data, The University of Chicago Press, Chicago 1974 Zbl0325.62017MR0408098
- Jensen S. T., Johansen, S., Lauritzen S. L., Globally convergent algorithms for maximizing a likelihood function, Biometrika 78 (1991), 867–877 (1991) Zbl0752.62031MR1147024
- Jiroušek R., Solution of the marginal problem and decomposable distributions, Kybernetika 27 (1991), 403–412 (1991) Zbl0752.60009MR1132602
- Lauritzen S. L., Graphical Models, Clarendon Press, Oxford 1996 Zbl1055.62126MR1419991
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.