Geometric Ergodicity of Gibbs and Block Gibbs Samplers for a Hierarchical Random Effects Model
نویسندگان
چکیده
منابع مشابه
Geometric Ergodicity of Gibbs Samplers
Due to a demand for reliable methods for exploring intractable probability distributions, the popularity of Markov chain Monte Carlo (MCMC) techniques continues to grow. In any MCMC analysis, the convergence rate of the associated Markov chain is of practical and theoretical importance. A geometrically ergodic chain converges to its target distribution at a geometric rate. In this dissertation,...
متن کاملGeometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models
We consider two Bayesian hierarchical one-way random effects models and establish geometric ergodicity of the corresponding random scan Gibbs samplers. Geometric ergodicity, along with a moment condition, guarantees a central limit theorem for sample means and quantiles. In addition, it ensures the consistency of various methods for estimating the variance in the asymptotic normal distribution....
متن کاملOn the Geometric Ergodicity of Two-variable Gibbs Samplers
A Markov chain is geometrically ergodic if it converges to its invariant distribution at a geometric rate in total variation norm. We study geometric ergodicity of deterministic and random scan versions of the two-variable Gibbs sampler. We give a sufficient condition which simultaneously guarantees both versions are geometrically ergodic. We also develop a method for simultaneously establishin...
متن کاملSufficient Burn - in for Gibbs Samplers for a Hierarchical Random Effects Model
We consider Gibbs and block Gibbs samplers for a Bayesian hierarchical version of the one-way random effects model. Drift and minorization conditions are established for the underlying Markov chains. The drift and minorization are used in conjunction with results from J. S. Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558– 566] and G. O. Roberts and R. L. Tweedie [Stochastic Process. Appl. 80 ...
متن کاملUniform Ergodicity of the Iterated Conditional SMC and Geometric Ergodicity of Particle Gibbs samplers
We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers [1]. Our main findings are that the essential boundedness of potential functions associated with the i-cSMC algorithm provide necessary and sufficient conditions for the uniform ergodicity of the i-cSMC M...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 1998
ISSN: 0047-259X
DOI: 10.1006/jmva.1998.1778