P.H. Baxendale (2005), Renewal theory and computable convergence rates for geometrically
ergodic Markov chains. Ann. Appl. Prob. 15, 700–738.
N.H. Bingham, C.M. Goldie, and J.L. Teugels (1987), Regular Variation. Cambridge University
Press, Cambridge.
R. Douc, E. Moulines, and J.S. Rosenthal (2004), Quantitative bounds on convergence of
time-inhomogeneous Markov chains. Ann. Appl. Prob. 14, 1643–1665.
R. Douc, E. Moulines, and P. Soulier (2007), Computable convergence rates for sub-geometric
ergodic Markov chains. Bernoulli 13, 831–848.
G. Fort and E. Moulines (2000), Computable Bounds For Subgeometrical And Geometrical
Ergodicity. Available at: http://citeseer.ist.psu.edu/fort00computable.html
G. Fort and E. Moulines (2003), Polynomial ergodicity of Markov transition kernels. Stoch.
Proc. Appl. 103, 57–99.
C. Geyer (1992), Practical Markov chain Monte Carlo. Stat. Sci., Vol. 7, No. 4, 473–483.
W.K. Hastings (1970), Monte Carlo sampling methods using Markov chains and their applications.
Biometrika 57, 97–109.
S.F. Jarner and G.O. Roberts (2002), Polynomial convergence rates of Markov chains. Ann.
Appl. Prob., 224–247, 2002.
G.L. Jones and J.P. Hobert (2001), Honest exploration of intractable probability distributions
via Markov chain Monte Carlo. Stat. Sci. 16, 312–334.
G.L. Jones and J.P. Hobert (2004). Sufficient burn-in for Gibbs samplers for a hierarchical
random effects model. Ann. Stat. 32, 784–817.
J. Liu (1996), Metropolized independent sampling with comparisons to rejection sampling
and importance sampling. Stat. and Comput. 6, 113–119.
D. Marchev and J.P. Hobert (2004), Geometric ergodicity of van Dyk and Meng’s algorithm
for the multivariate Student’s t model. J. Amer. Stat. Assoc. 99, 228–238.
K. L. Mengersen and R. L. Tweedie (1996), Rates of convergence of the Hastings and
Metropolis algorithms. Ann. Stat. 24, 101–121.
S.P. Meyn and R.L. Tweedie (1993), Markov chains and stochastic stability. Springer-Verlag,
London. Available at: http://probability.ca/MT/
G.O. Roberts (1999), A note on acceptance rate criteria for CLTs for Metropolis-Hastings
algorithms. J. Appl. Prob. 36, 1210–1217.
G.O. Roberts and J.S. Rosenthal (1998), Markov chain Monte Carlo: Some practical implications
of theoretical results (with discussion). Can. J. Stat. 26, 5–31.
G.O. Roberts and J.S. Rosenthal (2004), General state space Markov chains and MCMC
algorithms. Prob. Surv. 1, 20–71.
G.O. Roberts and R.L. Tweedie (1996), Geometric Convergence and Central Limit Theorems
for Multidimensional Hastings and Metropolis Algorithms. Biometrika 83, 95–110.
J.S. Rosenthal (1995), Minorization conditions and convergence rates for Markov chain
Monte Carlo. J. Amer. Stat. Assoc. 90, 558–566.
J.S. Rosenthal (1997), Independence sampler Java applet. Available at:
http://probability.ca/jeff/java/exp.html
J.S. Rosenthal (2002), Quantitative convergence rates of Markov chains: A simple account.
Electronic Comm. Prob. 7, 123–128.
R.L. Smith and L. Tierney (1996), Exact transition probabilities for the independence
Metropolis sampler. Preprint.
L. Tierney (1994), Markov chains for exploring posterior distributions (with discussion).
Ann. Stat. 22, 1701–1762.
S. Wolfram (1988), Mathematica: A system for doing mathematics by computer. Addison-
Wesley, New York.