On sequential Monte Carlo, partial rejection control and approximate Bayesian computation

Statistics and Computing

Volumn 22, Issue 6, 2012, Pages 1209-1222

  Peters, G W ^a,b   Fan, Y ^b   Sisson, S A ^b  

^a CSIRO   (Australia)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Approximate Bayesian computation; Bayesian computation; Likelihood free inference; Partial rejection control; Sequential Monte Carlo samplers

Indexed keywords

EID: 84867997236     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-012-9315-y     Document Type: Article

References (41)

1. Andrieu, C., Freitas, N. D., Doucet, A., Jordan, M.: An introduction to MCMC for machine learning. Mach. Learn. 50, 5-43 (2003).
2. Arulampalam, S., Maskell, S., Gorodon, N., Clapp, T.: A tutorial on particle filters for on-line non-linear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process. 50(2), 174-188 (2002).
3. Beaumont, M. A., Zhang, W., Balding, D. J.: Approximate Bayesian computation in population genetics. Genetics 162, 2025-2035 (2002).
4. Beaumont, M. A., Cornuet, J.-M., Marin, J.-M., Robert, C. P.: Adaptivity for ABC algorithms: The ABC-PMC scheme. Biometrika 96, 983-990 (2009).
5. Blum, M. G. B.: Approximate Bayesian computation: A non-parametric perspective. J. Am. Stat. Assoc. 105, 1178-1187 (2010).
6. Bortot, P., Coles, S. G., Sisson, S. A.: Inference for stereological extremes. J. Am. Stat. Assoc. 102, 84-92 (2007).
7. Chopin, N.: Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Stat. 32, 2385-2411 (2004).
8. Cornebise, J., Moulines, E., Olsson, J.: Adaptive methods for sequential importance sampling with application to state space models. In: Proc. 16th European Sig. Proc. Conference, Lausanne (2008).
9. Crisan, D., Doucet, A.: A survey of convergence results on particle filtering for practitioners. IEEE Trans. Signal Process. 50(3), 736-746 (2002).
10. Csilleŕy, K., Blum, M. G. B., Gaggiotti, O. E., Francois, O.: Approximate Bayesian computation (ABC) in practice. Trends Ecol. Evol. 25, 410-418 (2010).
11. Del Moral, P.: Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems. Ann. Appl. Probab. 8, 438-495 (1998).
12. Del Moral, P.: Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Springer, New York (2004).
13. Del Moral, P., Doucet, A., Jasra, A.: Sequential Monte Carlo samplers. J. R. Stat. Soc. B 68, 411-436 (2006).
14. Del Moral, P., Doucet, A., Jasra, A.: An adaptive sequential Monte Carlo method for approximate Bayesian computation. Stat. Comput. (2011). doi: 10. 1007/s11222-011-9271-y.
15. Doucet, A., Johansen, A. M.: A tutorial on particle filtering and smoothing: Fifteen years later. In: Crisan, D., Rozovsky, B. (eds.) Oxford Handbook of Nonlinear Filtering. Oxford University Press, Oxford (2009).
16. Doucet, A., de Freitas, N., Gordon, N. (eds.): Sequential Monte Carlo Methods in Practice. Springer, New York (2001).
17. Drovandi, C. C., Pettitt, A. N.: Estimation of parameters for macroparasite population evolution using approximate Bayesian computation. Biometrics 67, 225-233 (2011).
18. Fan, Y., Leslie, D. S., Wand, M. P.: Generalised linear mixed model analysis via sequential Monte Carlo sampling. Electron. J. Stat. 2, 916-938 (2008).
19. Fearnhead, P., Papaspiliopoulos, O., Roberts, G. O.: Particle filters for partially-observed diffusions. J. R. Stat. Soc. B 70, 755-777 (2008).
20. Gisler, A., Wüthrich, M. V.: Credibility for the chain ladder reserving method. ASTIN Bull. 38, 565-600 (2008).
21. Jasra, A., Doucet, A.: Stability of sequential Monte Carlo samplers via the Foster-Lyapunov condition. Stat. Probab. Lett. 78, 3062-3069 (2008).
22. Johansen, A., Doucet, A.: A note on auxiliary particle filters. Stat. Probab. Lett. 78(12), 1498-1504 (2008).
23. Kitigawa, G.: Monte Carlo filter and smoother for non-Gaussian, non-linear state space models. J. Comput. Graph. Stat. 5, 1-25 (1996).
24. Kunsch, H. R.: Recursive Monte Carlo filters: Algorithms and theoretical analysis. Ann. Stat. 33, 1983-2021 (2005).
25. Liu, J., Chen, R.: Sequential Monte Carlo for dynamic systems. J. Am. Stat. Assoc. 93, 1032-1044 (1998).
26. Liu, J., Chen, R., Wong, W.: Rejection control and sequential importance sampling. J. Am. Stat. Assoc. 93, 1022-1031 (1998).
27. Liu, J. S.: Monte Carlo Strategies in Scientific Computing. Springer, Berlin (2001).
28. Mack, T.: Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bull. 23, 213-225 (1993).
29. Marjoram, P., Molitor, J., Plagnol, V., Tavaré, S.: Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. USA 100, 15324-15328 (2003).
30. Peters, G. W.: Topics in sequential Monte Carlo samplers. Master's thesis, University of Cambridge (2005).
31. Peters, G. W., Wüthrich, M. V., Shevchenko, P. V.: Chain ladder method: Bayesian bootstrap versus classical bootstrap. Insur. Math. Econ. 47, 36-51 (2010).
32. Pitt, M., Shephard, N.: Filtering via simulation: Auxiliary particle filters. J. Am. Stat. Assoc. 94(446), 590-591 (1999).
33. Ratmann, O., Andrieu, C., Hinkley, T., Wiuf, C., Richardson, S.: Model criticism based on likelihood-free inference, with an application to protein network evolution. Proc. Natl. Acad. Sci. USA 106, 10576-10581 (2009).
34. Sisson, S. A., Fan, Y.: Likelihood-free Markov Chain Monte Carlo. In: Brooks, S. P., Gelman, A., Jones, G., Meng, X.-L. (eds.) Handbook of Markov chain Monte Carlo, pp. 319-341. CRC Press, London (2011).
35. Sisson, S. A., Fan, Y., Tanaka, M. M.: Sequential Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. 104, 1760-1765 (2007). Errata 106, 16889 (2009).
36. Tavaré, S., Balding, D. J., Griffiths, R. C., Donnelly, P.: Inferring coalescence times from DNA sequence data. Genetics 145, 505-518 (1997).
37. Toni, T., Welch, D., Strelkowa, N., Ipsen, A., Stumpf, M. P. H.: Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6, 187-202 (2009).
38. West, M.: Approximating posterior distributions by mixtures. J. R. Stat. Soc. B 55, 409-422 (1993).
39. Wilkinson, R. D.: Approximate Bayesian computation (ABC) gives exact results under the assumption of model error. Technical report (2008), http://arxiv. org/abs/0811. 3355.
40. Wüthrich, M. V., Merz, M.: Stochastic Claims Reserving Methods in Insurance. Wiley, New York (2008).
41. Yao, J.: Bayesian approach for prediction error in chain ladder claims reserving. In: 38th International ASTIN Colloquium, July (2008).