Premium
Efficiency and Convergence Properties of Slice Samplers
Author(s) -
MIRA ANTONIETTA,
TIERNEY LUKE
Publication year - 2002
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00267
Subject(s) - mathematics , markov chain , ergodicity , convergence (economics) , rate of convergence , independence (probability theory) , upper and lower bounds , eigenvalues and eigenvectors , statistics , combinatorics , mathematical analysis , channel (broadcasting) , physics , engineering , quantum mechanics , electrical engineering , economics , economic growth
The slice sampler (SS) is a method of constructing a reversible Markov chain with a specified invariant distribution. Given an independence Metropolis–Hastings algorithm (IMHA) it is always possible to construct a SS that dominates it in the Peskun sense. This means that the resulting SS produces estimates with a smaller asymptotic variance than the IMHA. Furthermore the SS has a smaller second‐largest eigenvalue. This ensures faster convergence to the target distribution. A sufficient condition for uniform ergodicity of the SS is given and an upper bound for the rate of convergence to stationarity is provided.