Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator

Biometrika

Volumn 102, Issue 2, 2015, Pages 295-313

  Doucet, A ^a   Pitt, M K ^b   Deligiannidis, G ^a   Kohn, R ^c  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Intractable likelihood; Metropolis Hastings algorithm; Particle filter; Sequential Monte Carlo; State space model

Indexed keywords

EID: 84929220466     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asu075     Document Type: Article

References (20)

1. ANDRIEU, C., DOUCET, A. & HOLENSTEIN, R. (2010). Particle Markov chainMonte Carlo methods (with Discussion). J. R. Statist. Soc. B 72, 269-342.
2. ANDRIEU, C. & ROBERTS, G. O. (2009). The pseudo-marginal approach for efficient Monte Carlo computations. Ann. Statist. 37, 697-725.
3. ANDRIEU, C. & VIHOLA, M. (2015). Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms. Ann. Appl. Prob. 25, 1030-77.
4. BAXENDALE, P. (2005). Renewal theory and computable convergence rates for geometrically ergodic Markov chains. Ann. Appl. Prob. 15, 700-38.
5. BEAUMONT, M. (2003). Estimation of population growth or decline in genetically monitored populations. Genetics 164, 1139-60.
6. BÉRARD, J., DEL MORAL, P. & DOUCET, A. (2014). A lognormal central limit theorem for particle approximations of normalizing constants. Electron. J. Prob. 19, 1-28.
7. CHERNOV, M., GALLANT, A. R., GHYSELS, E. & TAUCHEN, G. (2003). Alternative models of stock price dynamics. J. Economet. 116, 225-57.
8. DOUC, R. & ROBERT, C. P. (2011). A vanilla Rao-Blackwellization of Metropolis-Hastings algorithms. Ann. Statist. 39, 261-77.
9. GEYER, C. J. (1992). Practical Markov chain Monte Carlo. Statist. Sci. 7, 473-83.
10. HÄGGSTRÖM, O. & ROSENTHAL, J. S. (2007). On variance conditions for Markov chain central limit theorems. Electron. Commun. Prob. 12, 454-64.
11. HUANG, X. & TAUCHEN, G. (2005). The relative contribution of jumps to total price variation. J. Finan. Economet. 3, 456-99.
12. KIPNIS, C.&VARADHAN, S. R. S. (1986). Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Commun. Math. Phys. 104, 1-19.
13. LIN, L., LIU, K. F. & SLOAN, J. (2000). A noisy Monte Carlo algorithm. Phys. Rev. D 61, article no. 074505.
14. PESKUN, P. H. (1973). Optimum Monte-Carlo sampling using Markov chains. Biometrika 60, 607-12.
15. PITT, M. K., SILVA, R., GIORDANI, P.&KOHN, R. (2012). On some properties ofMarkov chain Monte Carlo simulation methods based on the particle filter. J. Economet. 171, 134-51.
16. ROBERTS, G. O. & TWEEDIE, R. L. (1996). Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83, 95-110.
17. RUDOLF, D.&ULLRICH, M. (2013). Positivity of hit-and-run and related algorithms. Electron. Commun. Prob. 18, 1-8.
18. SHERLOCK, C., THIERY, A. H., ROBERTS, G. O. & ROSENTHAL, J. S. (2015). On the efficiency of pseudo-marginal random walk Metropolis algorithms. Ann. Statist. 43, 238-75.
19. TIERNEY, L. (1994). Markov chains for exploring posterior distributions (with Discussion). Ann. Statist. 21, 1701-62.
20. TIERNEY, L. (1998). A note on Metropolis-Hastings kernels for general state spaces. Ann. Appl. Prob. 8, 1-9.