Statistical inference for partially observed markov processes via the R package pomp

Journal of Statistical Software

Volumn 69, Issue , 2016, Pages 1-43

  King, Aaron A ^a   Nguyen, Dao ^a   Ionides, Edward L ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Hidden markov model; Markov processes; Maximum likelihood; Mechanistic model; Plug and play; R; Sequential Monte Carlo; State space model; Stochastic dynamical system; Time series

Indexed keywords

EID: 84962110822     PISSN: 15487660     EISSN: None     Source Type: Journal    
DOI: 10.18637/jss.v069.i12     Document Type: Article

References (65)

1. Anderson R, May R (1991). Infectious Diseases of Humans. Oxford University Press, Oxford.
2. Andrieu C, Doucet A, Holenstein R (2010). “Particle Markov Chain Monte Carlo Methods.” Journal of the Royal Statistical Society B, 72(3), 269–342. doi:10.1111/j.1467-9868.2009.00736.x.
3. Andrieu C, Roberts G (2009). “The Pseudo-Marginal Approach for Efficient Computation.” The Annals of Statistics, 37(2), 697–725. doi:10.1214/07-aos574.
4. Arulampalam M, Maskell S, Gordon N, Clapp T (2002). “A Tutorial on Particle Filters for Online Nonlinear, Non-Gaussian Bayesian Tracking.” IEEE Transactions on Signal Processing, 50, 174–188. doi:10.1109/78.978374.
5. Beaumont M (2010). “Approximate Bayesian Computation in Evolution and Ecology.” Annual Review of Ecology, Evolution, and Systematics, 41, 379–406. doi:10.1146/annurev-ecolsys-102209-144621.
6. Bhadra A (2010). “Discussion of ‘Particle Markov Chain Monte Carlo Methods’ by C. Andrieu, A. Doucet and R. Holenstein.” Journal of the Royal Statistical Society B, 72, 314–315. doi:10.1111/j.1467-9868.2009.00736.x.
7. Bhadra A, Ionides E, Laneri K, Pascual M, Bouma M, Dhiman R (2011). “Malaria in Northwest India: Data Analysis via Partially Observed Stochastic Differential Equation Models Driven by Lévy Noise.” Journal of the American Statistical Association, 106(494), 440–451. doi:10.1198/jasa.2011.ap10323.
8. Blackwood J, Cummings D, Broutin H, Iamsirithaworn S, Rohani P (2013a). “Deciphering the Impacts of Vaccination and Immunity on Pertussis Epidemiology in Thailand.” Proceedings of the National Academy of Sciences of the United States of America, 110(23), 9595–9600. doi:10.1073/pnas.1220908110.
9. Blackwood J, Streicker D, Altizer S, Rohani P (2013b). “Resolving the Roles of Immunity, Pathogenesis, and Immigration for Rabies Persistence in Vampire Bats.” Proceedings of the National Academy of Sciences of the United States of America, 110(51), 20837–20842. doi:10.1073/pnas.1308817110.
10. Blake I, Martin R, Goel A, Khetsuriani N, Everts J, Wolff C, Wassilak S, Aylward R, Grassly N (2014). “The Role of Older Children and Adults in Wild Poliovirus Transmission.” Proceedings of the National Academy of Sciences of the United States of America, 111(29), 10604–10609. doi:10.1073/pnas.1323688111.
11. Bretó C (2014). “On Idiosyncratic Stochasticity of Financial Leverage Effects.” Statistics & Probability Letters, 91, 20–26. doi:10.1016/j.spl.2014.04.003.
12. Bretó C, He D, Ionides E, King AA (2009). “Time Series Analysis via Mechanistic Models.” The Annals of Applied Statistics, 3, 319–348. doi:10.1214/08-aoas201.
13. Bretó C, Ionides E (2011). “Compound Markov Counting Processes and Their Applications to Modeling Infinitesimally Over-Dispersed Systems.” Stochastic Processes and their Applications, 121(11), 2571–2591. doi:10.1016/j.spa.2011.07.005.
14. Cappé O, Godsill SJ, Moulines E (2007). “An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo.” Proceedings of the IEEE, 95(5), 899–924. doi: 10.1109/jproc.2007.893250.
15. Chambers J (1998). Programming with Data. Springer-Verlag, New York.
16. Commandeur J, Koopman S, Ooms M (2011). “Statistical Software for State Space Methods.” Journal of Statistical Software, 41(1), 1–18. doi:10.18637/jss.v041.i01.
17. Coulson T, Rohani P, Pascual M (2004). “Skeletons, Noise and Population Growth: The End of an Old Debate?” Trends in Ecology and Evolution, 19, 359–364. doi:10.1016/j.tree.2004.05.008.
18. Douc R, Cappé O, Moulines E (2005). “Comparison of Resampling Schemes for Particle Filtering.” In Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005, pp. 64–69. IEEE. doi:10.1109/ispa.2005.195385.
19. Doucet A, Johansen A (2009). “A Tutorial on Particle Filtering and Smoothing: Fifteen Years Later.” In D Crisan, B Rozovsky (eds.), Oxford Handbook of Nonlinear Filtering. Oxford University Press.
20. Earn D, He D, Loeb M, Fonseca K, Lee B, Dushoff J (2012). “Effects of School Closure on Incidence of Pandemic Influenza in Alberta, Canada.” The Annals of Internal Medicine, 156(3), 173–181. doi:10.7326/0003-4819-156-3-201202070-00005.
21. Ellner S, Bailey B, Bobashev G, Gallant A, Grenfell B, Nychka D (1998). “Noise and Nonlinearity in Measles Epidemics: Combining Mechanistic and Statistical Approaches to Population Modeling.” American Naturalist, 151(5), 425–440. doi:10.1086/286130.
22. Genolini C (2008). “A (Not So) Short Introduction to S4.” R Foundation for Statistical Computing. URL https://CRAN.R-project.org/doc/contrib/Genolini-S4tutorialV0-5en.pdf.
23. Gillespie D (1977). “Exact Stochastic Simulation of Coupled Chemical Reactions.” Journal of Physical Chemistry, 81(25), 2340–2361. doi:10.1021/j100540a008.
24. Gompertz B (1825). “On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies.” Philosophical Transactions of the Royal Society of London, 115, 513–583. doi:10.1098/rstl.1825.0026.
25. He D, Dushoff J, Day T, Ma J, Earn D (2013). “Inferring the Causes of the Three Waves of the 1918 Influenza Pandemic in England and Wales.” Proceedings of the Royal Society of London B, 280(1766), 20131345. doi:10.1098/rspb.2013.1345.
26. He D, Ionides E, King A (2010). “Plug-and-Play Inference for Disease Dynamics: Measles in Large and Small Towns as a Case Study.” Journal of the Royal Society Interface, 7(43), 271–283. doi:10.1098/rsif.2009.0151.
27. Ionides E (2011). “Discussion of ‘Feature Matching in Time Series Modeling’ by Y. Xia and H. Tong.” Statistical Science, 26, 49–52. doi:10.1214/11-sts345c.
28. Ionides E, Bhadra A, Atchadé Y, King A (2011). “Iterated Filtering.” The Annals of Statistics, 39(3), 1776–1802. doi:10.1214/11-aos886.
29. Ionides E, Bretó C, King A (2006). “Inference for Nonlinear Dynamical Systems.” Proceedings of the National Academy of Sciences of the United States of America, 103(49), 18438–18443. doi:10.1073/pnas.0603181103.
30. Ionides E, Nguyen D, Atchadé Y, Stoev S, King A (2015). “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, 112(3), 719–724. doi:10.1073/pnas.1410597112.
31. Johnson S (2014). The NLopt Nonlinear-Optimization Package. Version 2.4.2, URL http://ab-initio.mit.edu/nlopt.
32. Kane M, Emerson J, Weston S (2013). “Scalable Strategies for Computing with Massive Data.” Journal of Statistical Software, 55(1). doi:10.18637/jss.v055.i14.
33. Kantas N, Doucet A, Singh S, Maciejowski J (2015). “On Particle Methods for Parameter Estimation in State-Space Models.” Statistical Science, 30(3), 328–351. doi:doi:10.1214/14-STS511.
34. Keeling M, Rohani P (2008). Modeling Infectious Diseases in Humans and Animals. Princeton University Press, Princeton.
35. Kendall B, Briggs C, Murdoch W, Turchin P, Ellner S, McCauley E, Nisbet R, Wood S (1999). “Why Do Populations Cycle? A Synthesis of Statistical and Mechanistic Modeling Approaches.” Ecology, 80(6), 1789–1805. doi:10.1890/0012-9658(1999)080[1789:wdpcas]2.0.co;2.
36. Kendall B, Ellner S, McCauley E, Wood S, Briggs C, Murdoch W, Turchin P (2005). “Population Cycles in the Pine Looper Moth: Dynamical Tests of Mechanistic Hypotheses.” Ecological Monographs, 75(2), 259–276. doi:10.1890/03-4056.
37. Kermack W, McKendrick A (1927). “A Contribution to the Mathematical Theory of Epidemics.” Proceedings of the Royal Society of London A, 115, 700–721. doi:10.1098/rspa.1927.0118.
38. King A, Cellès M, Magpantay F, Rohani P (2015). “Avoidable Errors in the Modelling of Outbreaks of Emerging Pathogens, with Special Reference to Ebola.” Proceedings of the Royal Society of London B, 282(1806), 20150347. doi:10.1098/rspb.2015.0347.
39. King A, Ionides E, Bretó C, Ellner S, Ferrari M, Kendall B, Lavine M, Nguyen D, Reuman D, Wearing H, Wood S (2016). pomp: Statistical Inference for Partially Observed Markov Processes. R package version 1.4.1.1, URL https://CRAN.R-project.org/package=pomp.
40. King A, Ionides E, Pascual M, Bouma M (2008). “Inapparent Infections and Cholera Dynamics.” Nature, 454(7206), 877–880. doi:10.1038/nature07084.
41. King AA (2015). subplex: Unconstrained Optimization Using the Subplex Algorithm. R package, version 1.1-6, URL https://CRAN.R-project.org/package=subplex.
42. Kitagawa G (1998). “A Self-Organising State Space Model.” Journal of the American Statistical Association, 93(443), 1203–1215. doi:10.1080/01621459.1998.10473780.
43. Lavine J, King A, Andreasen V, Bjørnstad O (2013). “Immune Boosting Explains Regime-Shifts in Prevaccine-Era Pertussis Dynamics.” PLoS ONE, 8(8), e72086. doi:10.1371/journal.pone.0072086.
44. Liu J (2001). Monte Carlo Strategies in Scientific Computing. Springer-Verlag, New York. doi:10.1007/978-0-387-76371-2.
45. Liu J, West M (2001). “Combining Parameter and State Estimation in Simulation-Based Filtering.” In A Doucet, N Freitas, N Gordon (eds.), Sequential Monte Carlo Methods in Practice, pp. 197–224. Springer-Verlag, New York.
46. Marin JM, Pudlo P, Robert CP, Ryder R (2012). “Approximate Bayesian Computational Methods.” Statistics and Computing, 22(6), 1167–1180. doi:10.1007/s11222-011-9288-2.
47. Ratmann O, Andrieu C, Wiuf C, Richardson S (2009). “Model Criticism Based on Likelihood-Free Inference, with an Application to Protein Network Evolution.” Proceedings of the National Academy of Sciences of the United States of America, 106(26), 10576–10581. doi:10.1073/pnas.0807882106.
48. R Core Team (2016). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
49. Reddingius J (1971). Gambling for Existence. A Discussion of Some Theoretical Problems in Animal Population Ecology. B. J. Brill, Leiden.
50. Reuman D, Desharnais R, Costantino R, Ahmad O, Cohen J (2006). “Power Spectra Reveal the Influence Of Stochasticity on Nonlinear Population Dynamics.” Proceedings of the National Academy of Sciences of the United States of America, 103(49), 18860–18865. doi:10.1073/pnas.0608571103.
51. Revolution Analytics, Weston S (2014). foreach: Foreach Looping Construct for R. R package version 1.4.2, URL https://CRAN.R-project.org/package=foreach.
52. Ricker W (1954). “Stock and Recruitment.” Journal of the Fisheries Research Board of Canada, 11, 559–623. doi:10.1139/f54-039.
53. Rowan T (1990). Functional Stability Analysis of Numerical Algorithms. Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin.
54. Roy M, Bouma M, Ionides E, Dhiman, C R, Pascual M (2012). “The Potential Elimination of Plasmodium Vivax Malaria by Relapse Treatment: Insights from a Transmission Model and Surveillance Data from NW India.” PLoS Neglected Tropical Diseases, 7(1), e1979. doi:10.1371/journal.pntd.0001979.
55. Shaman J, Karspeck A (2012). “Forecasting Seasonal Outbreaks of Influenza.” Proceedings of the National Academy of Sciences of the United States of America, 109(50), 20425–20430. doi:10.1073/pnas.1208772109.
56. Shrestha S, Foxman B, Weinberger DM, Steiner C, Viboud C, Rohani P (2013). “Identifying the Interaction between Influenza and Pneumococcal Pneumonia Using Incidence Data.” Science Translational Medicine, 5(191), 191ra84. doi:10.1126/scitranslmed.3005982.
57. Shrestha S, King A, Rohani P (2011). “Statistical Inference for Multi-Pathogen Systems.” PLoS Computational Biology, 7, e1002135. doi:10.1371/journal.pcbi.1002135.
58. Sisson S, Fan Y, Tanaka M (2007). “Sequential Monte Carlo without Likelihoods.” Proceedings of the National Academy of Sciences of the United States of America, 104(6), 1760–1765. doi:10.1073/pnas.0607208104.
59. Smith A (1993). “Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregression.” Journal of Applied Econometrics, 8(S1), S63–S84. doi:10.1002/jae.3950080506.
60. Toni T, Welch D, Strelkowa N, Ipsen A, Stumpf M (2009). “Approximate Bayesian Computation Scheme for Parameter Inference and Model Selection in Dynamical Systems.” Journal of the Royal Society Interface, 6(31), 187–202. doi:10.1098/rsif.2008.0172.
61. Wan EA, Merwe R (2000). “The Unscented Kalman Filter for Nonlinear Estimation.” In Adaptive Systems for Signal Processing, Communications, and Control, pp. 153–158. doi: 10.1109/asspcc.2000.882463.
62. Wood S (2001). “Partially Specified Ecological Models.” Ecological Monographs, 71, 1–25. doi:10.1890/0012-9615(2001)071[0001:psem]2.0.co;2.
63. Wood S (2010). “Statistical Inference for Noisy Nonlinear Ecological Dynamic Systems.” Nature, 466(7310), 1102–1104. doi:10.1038/nature09319.
64. Xia Y, Tong H (2011). “Feature Matching in Time Series Modelling.” Statistical Science, 26(1), 21–46. doi:10.1214/10-sts345.
65. Ypma J (2014). nloptr: R Interface to NLopt. R package, version 1.0.0, URL https://CRAN.R-project.org/package=nloptr.