Inference for dynamic and latent variable models via iterated, perturbed Bayes maps

Proceedings of the National Academy of Sciences of the United States of America

Volumn 112, Issue 3, 2015, Pages 719-724

  Ionidesa, Edward L ^a   Nguyen, Dao ^a   Atchadé, Yves ^b   Stoev, Stilian ^a   King, Aaron A ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

^b Department of Ecology and Evolutionary Biology University of Michigan ^*

Author keywords

Markov process; Maximum likelihood; Particle filter; Sequential monte carlo

Indexed keywords

ALGORITHM; ARTICLE; BAYES THEOREM; BIOLOGICAL PHENOMENA AND FUNCTIONS CONCERNING THE ENTIRE ORGANISM; CONCEPTUAL FRAMEWORK; CONTROLLED STUDY; MONTE CARLO METHOD; PRIORITY JOURNAL; PROBABILITY; PROCESS MODEL; STRUCTURAL EQUATION MODELING; CHOLERA; HUMAN; STATISTICAL MODEL; THEORETICAL MODEL; TRANSMISSION; MARKOV CHAIN; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; MAXIMUM LIKELIHOOD METHOD;

ALGORITHMS; BAYES THEOREM; CHOLERA; HUMANS; LIKELIHOOD FUNCTIONS; MODELS, THEORETICAL;

EID: 84921327887     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1410597112/-/DCSupplemental     Document Type: Article

References (36)

1. Ionides EL, Bretó C, King AA (2006) Inference for nonlinear dynamical systems. Proc Natl Acad Sci USA 103(49):18438-18443.
2. Ionides EL, Bhadra A, Atchadé Y, King AA (2011) Iterated filtering. Ann Stat 39(3): 1776-1802.
3. Doucet A, Jacob PE, Rubenthaler S (2013) Derivative-free estimation of the score vector and observed information matrix with application to state-space models. arxiv: 1304.5768.
4. Lindström E, Ionides EL, Frydendall J, Madsen H (2012) Efficient iterated filtering. System Identification (Elsevier, New York), Vol 16, pp 1785-1790.
5. Lele SR, Dennis B, Lutscher F (2007) Data cloning: Easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods. Ecol Lett 10(7):551-563.
6. Lele SR, Nadeem K, Schmuland B (2010) Estimability and likelihood inference for generalized linear mixed models using data cloning. J Am Stat Assoc 105(492): 1617-1625.
7. Doucet A, Godsill SJ, Robert CP (2002) Marginal maximum a posteriori estimation using Markov chain Monte Carlo. Stat Comput 12(1):77-84.
8. Gaetan C, Yao J-F (2003) A multiple-imputation Metropolis version of the EM algorithm. Biometrika 90(3):643-654.
9. Jacquier E, Johannes M, Polson N (2007) MCMC maximum likelihood for latent state models. J Econom 137(2):615-640.
10. King AA, Ionides EL, Pascual M, Bouma MJ (2008) Inapparent infections and cholera dynamics. Nature 454(7206):877-880.
11. Laneri K, et al. (2010) Forcing versus feedback: Epidemic malaria and monsoon rains in NW India. PLoS Comput Biol. 6(9):e1000898.
12. He D, Ionides EL, King AA (2010) Plug-and-play inference for disease dynamics: Measles in large and small populations as a case study. J R Soc Interface 7(43):271-283.
13. Blackwood JC, Cummings DAT, Broutin H, Iamsirithaworn S, Rohani P (2013) Deciphering the impacts of vaccination and immunity on pertussis epidemiology in Thailand. Proc Natl Acad Sci USA 110(23):9595-9600.
14. Shrestha S, Foxman B, Weinberger DM, Steiner C, Viboud C, Rohani P (2013) Identifying the interaction between influenza and pneumococcal pneumonia using incidence data. Sci Transl Med 5:191ra84.
15. Blake IM, et al. (2014) The role of older children and adults in wild poliovirus transmission. Proc Natl Acad Sci USA 111(29):10604-10609.
16. Bretó C, He D, Ionides EL, King AA (2009) Time series analysis via mechanistic models. Ann Appl Stat 3:319-348.
17. Andrieu C, Doucet A, Holenstein R (2010) Particle Markov chain Monte Carlo methods. J R Stat Soc Ser B 72(3):269-342.
18. Toni T, Welch D, Strelkowa N, Ipsen A, Stumpf MP (2009) Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J R Soc Interface 6(31):187-202.
19. Wood SN (2010) Statistical inference for noisy nonlinear ecological dynamic systems. Nature 466(7310):1102-1104.
20. Shaman J, Karspeck A (2012) Forecasting seasonal outbreaks of influenza. Proc Natl Acad Sci USA 109(50):20425-20430.
21. Kitagawa G (1998) A self-organising state-space model. J Am Stat Assoc 93: 1203-1215.
22. Liu J, West M (2001) Combined parameter and state estimation in simulation-based filtering. Sequential Monte Carlo Methods in Practice, eds Doucet A, de Freitas N, Gordon NJ (Springer, New York), pp 197-224.
23. Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear, non-Gaussian Bayesian tracking. IEEE Trans Signal Process 50(2): 174-188.
24. Doucet A, de Freitas N, Gordon NJ, eds (2001) Sequential Monte Carlo Methods in Practice (Springer, New York).
25. Ingber L (1993) Simulated annealing: Practice versus theory. Math Comput Model 18: 29-57.
26. Le Gland F, Oudjane N (2004) Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters. Ann Appl Probab 14(1): 144-187.
27. Eveson SP (1995) Hilbert's projective metric and the spectral properties of positive linear operators. Proc London Math Soc 3(2):411-440.
28. Del Moral P, Doucet A (2004) Particle motions in absorbing medium with hard and soft obstacles. Stochastic Anal Appl 22(5):1175-1207.
29. Whiteley N, Kantas N, Jasra A (2012) Linear variance bounds for particle approximations of time-homogeneous Feynman-Kac formulae. Stochastic Process Appl 122(4):1840-1865.
30. Bhadra A (2010) Discussion of 'particle Markov chain Monte Carlo methods' by C. Andrieu, A. Doucet and R. Holenstein. J R Stat Soc B 72:314-315.
31. Wilkinson DJ (2012) Stochastic Modelling for Systems Biology (Chapman & Hall, Boca Raton, FL).
32. Keeling M, Rohani P (2009) Modeling Infectious Diseases in Humans and Animals (Princeton Univ. Press, Princeton, NJ).
33. King AA, Ionides EL, Bretó CM, Ellner S, Kendall B (2009) pomp: Statistical inference for partially observed Markov processes (R package). Available at cran.r-project.org/ web/packages/pomp.
34. Yang W, Karspeck A, Shaman J (2014) Comparison of filtering methods for the modeling and retrospective forecasting of influenza epidemics. PLOS Comput Biol 10(4):e1003583.
35. Julier S, Uhlmann J (2004) Unscented filtering and nonlinear estimation. Proc IEEE 92(3):401-422.
36. Cappé O, Godsill S, Moulines E (2007) An overview of existing methods and recent advances in sequential Monte Carlo. Proc IEEE 95(5):899-924.