Optimal scaling of the random walk Metropolis on elliptically symmetric unimodal targets

Bernoulli

Volumn 15, Issue 3, 2009, Pages 774-798

  Sherlock, Chris ^a   Roberts, Gareth ^b  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Optimal acceptance rate; Optimal scaling; Random walk Metropolis

Indexed keywords

EID: 72249090639     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/08-BEJ176     Document Type: Article

References (11)

1. Apostol, T. M. (1974). Mathematical Analysis. Reading, MA: Addison-Wesley. MR0344384
2. Bedard, M. (2007). Weak convergence of Metropolis algorithms for non-iid target distributions. Ann. Appl. Probab. 17 1222-1244. MR2344305
3. Breyer, L. A. and Roberts, G. O. (2000). From Metropolis to diffusions: Gibbs states and optimal scaling. Stochastic Process. Appl. 90 181-206. MR1794535
4. Fang, K. T., Kotz, S. and Ng, K. W. (1990). Symmetric Multivariate and Related Distributions. Monographs on Statistics and Applied Probability 36. London: Chapman and Hall. MR1071174
5. Gelman, A., Roberts, G. O. and Gilks, W. R. (1996). Efficient Metropolis jumping rules. In Bayesian Statistics, 5 (Alicante, 1994) 599-607. New York: Oxford Univ. Press. MR1425429
6. Krzanowski, W. J. (2000). Principles of Multivariate Analysis: A User's Perspective, 2nd ed. Oxford Statistical Science Series 22. New York: The Clarendon Press Oxford Univ. Press. MR 1133626
7. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equations of state calculations by fast computing machine. J. Chem. Phys. 21 1087-1091.
8. Roberts, G. O. (1998). Optimal metropolis algorithms for product measures on the vertices of a hypercube. Stochastics Stochastic Rep. 62 275-283. MR1613256
9. Roberts, G. O., Gelman, A. and Gilks, W. R. (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms. Ann. Appl. Probab. 7 110-120. MR 1428751
10. Roberts, G. O. and Rosenthal, J. S. (2001). Optimal scaling for various Metropolis-Hastings algorithms. Statist. Sci. 16 351-367. MR1888450
11. Sherlock, C. (2006). Methodology for inference on the Markov modulated Poisson process and theory for optimal scaling of the random walk Metropolis. Ph. D. thesis, Lancaster University. Available at http://eprints.lancs.ac.uk/ 850/.