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Positivity of hit-and-run and related algorithms


 
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1. Title Title of document Positivity of hit-and-run and related algorithms
 
2. Creator Author's name, affiliation, country Daniel Rudolf; Friedrich Schiller University Jena; Germany
 
2. Creator Author's name, affiliation, country Mario Ullrich; Friedrich Schiller University Jena; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Spectral gap; positivity; lazy; hit-and-run; Metropolis
 
3. Subject Subject classification 60J05
 
4. Description Abstract We prove positivity of the Markov operators that correspond to the hit-and-run algorithm, random scan Gibbs sampler, slice sampler and Metropolis algorithm with positive proposal. In particular, the results show that it is not necessary to consider the lazy versions of these Markov chains. The proof relies on a well known lemma which relates the positivity of the product $MTM^*$, for some operators $M$ and $T$, to the positivity of $T$. It remains to find that kind of representation of the Markov operator with a positive operator $T$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ERC; DFG
 
7. Date (YYYY-MM-DD) 2013-06-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2507
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2507
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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