Multiplicative random walk Metropolis-Hastings on the real line

Atchadé, Y.F. and Perron, F. (2007). On the geometric ergodicity of Metropolis-Hastings algorithms. Statistics, 41, 77–84.

Buckle, D.J. (1995). Bayesian inference for stable distributions. J. Amer. Statist. Assoc., 90, 605–613.

Chen, M.H. and Kim, S. (2006). Discussion of “Equi-Energy Sampler” by Kou, Zhou and Wong. Ann. Statist., 34, 1629–1635.

Dellaportas, P. and Roberts, G.O. (2003). An Introduction to MCMC. In Spatial Statistics and Computational Methods, Lecture Notes in Statistics Number 173, (J. Møller, ed.). Springer-Verlag, New York, pp. 1–41.

Feller, W. (1971). An Introduction to Probability and its Applications, (Vol. II). Wiley, New York.

Fernandez, C. and Steel, M.F.J. (1998). On Bayesian modeling of fat tails and skewness. J. Amer. Statist. Assoc., 93, 359–371.

Hastings, W.K. (1970). Monte Carlo sampling using Markov chains and their applications. Biometrika, 57, 97–109.

Jasra, A., Holmes, C.C. and Stephens, D.A. (2005). Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Statist. Sci., 20, 50–67.

Jones, G.J. and Hobert, J.P. (1996). Honest exploration of intractable probability distributions via Markov Chain Monte Carlo. Statist. Sci., 16, 312–334.

Kipnis, C. and Varadhan, S.R.S. (1986). Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Comm. Math. Phys., 104, 1–19.

Kou, S.C., Zhou, Q. and Wong, W.H. (2006). Discussion paper equi-energy sampler with applications in statistical inference and statistical mechanics. Ann. Statist., 34, 1581–1619.

Liu, J.S. (2008). Monte Carlo Strategies in Scientific Computing. Springer Verlag, New York.

Mengersen, K.L. and Tweedie, R.L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist., 24, 101–121.

Metropolis, N., Rosenbluth, A., Rosenbluth, R., Teller, A. and Teller, E. (1953). Equation of state calculations by fast computing machines. J. Chem. Phys., 21, 1087–1092.

Meyn, S.P. and Tweedie, R.L. (1993). Markov Chains and Stochastic Stability. Springer-Verlag, London, New York.

Robert, C.P. and Casella, G. (2004). Monte Carlo Statistical Methods. Springer Verlag.

Roberts, G.O. (1999). A note on acceptance rate criteria for CLTs for Metropolis-Hastings algorithms. J. Appl. Probab., 36, 1210–1217.

Roberts, G.O. and Rosenthal, J.S. (1997). Geometric ergodicity and hybrid Markov chains. Electron. Commun. Probab., 2, 13–25.

Roberts, G.O. and Rosenthal, J.S. (1998). Markov-chain Monte Carlo: some practical implications of theoretical results. Canad. J. Statist., 26, 5–20.

Roberts, G.O. and Rosenthal, J.S. (2004). General state space Markov chains and MCMC algorithms. Probab. Surv., 1, 20–71.

Roberts, G.O. and Tweedie, R.L. (1996). Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli, 2, 341–363.

Thode, Jr., H.C. (2002). Testing for Normality. Marcel Dekker, New York.