| Title:
|
Asymptotic behaviour of a BIPF algorithm with an improper target (English) |
| Author:
|
Asci, Claudio |
| Author:
|
Piccioni, Mauro |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
169-188 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
log-linear models |
| Keyword:
|
marginal problem |
| Keyword:
|
null Markov chains |
| MSC:
|
60J05 |
| MSC:
|
60J22 |
| MSC:
|
62F15 |
| MSC:
|
62H17 |
| MSC:
|
65C40 |
| idZBL:
|
Zbl 1170.60326 |
| idMR:
|
MR2518147 |
| . |
| Date available:
|
2010-06-02T18:26:13Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140071 |
| . |
| Reference:
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