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Convergence of Slice Sampler Markov Chains
Author(s) -
Roberts Gareth O.,
Rosenthal Jeffrey S.
Publication year - 1999
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00198
Subject(s) - ergodicity , markov chain , convergence (economics) , variable (mathematics) , mathematics , monotone polygon , total variation , variation (astronomy) , algorithm , computer science , statistics , mathematical analysis , geometry , physics , economics , economic growth , astrophysics
We analyse theoretical properties of the slice sampler. We find that the algorithm has extremely robust geometric ergodicity properties. For the case of just one auxiliary variable, we demonstrate that the algorithm is stochastically monotone, and we deduce analytic bounds on the total variation distance from stationarity of the method by using Foster–Lyapunov drift condition methodology.