On parameter estimation in population models

Theoretical Population Biology

Volumn 70, Issue 4, 2006, Pages 498-510

  Ross, J V ^a   Taimre, T ^a   Pollett, P K ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Cross entropy method; Density dependence; Euphydryas editha bayensis; Markov chains; Stochastic SIS logistic model

Indexed keywords

BUTTERFLY; DENSITY DEPENDENCE; MARKOV CHAIN; NUMERICAL MODEL; POPULATION MODELING;

ANIMAL; ARTICLE; BUTTERFLY; PROBABILITY; STATISTICS; THEORETICAL MODEL;

ANIMALS; BUTTERFLIES; MARKOV CHAINS; MODELS, THEORETICAL; STOCHASTIC PROCESSES;

EUPHYDRYAS EDITHA BAYENSIS;

EID: 33845528570     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2006.08.001     Document Type: Article

References (48)

1. Anderson W. Continuous-time Markov Chains: An Applications-Oriented Approach (1991), Springer, New York
2. Bailey N.T.J. The Mathematical Theory of Epidemics (1957), Griffin, London
3. Barbour A.D. On a functional central limit theorem for Markov population processes. Adv. Appl. Probab. 6 (1974) 21-39
4. Barbour A.D. Quasi-stationary distributions in Markov population processes. Adv. Appl. Probab. 8 (1976) 296-314
5. Barbour A.D. Equilibrium distributions Markov population processes. Adv. Appl. Probab. 12 (1980) 591-614
6. Barbour A.D. Density-dependent Markov population processes. In: Jäger W., Rost H., and Tautu P. (Eds). Biological Growth and Spread, Lecture Notes in Biomathematics vol. 38 (1980), Springer, Berlin 36-49
7. Barbour A.D., and Pugliese A. Asymptotic behaviour of a metapopulation model. J. Math. Biol. 49 (2004) 468-500
8. Barbour A.D., and Pugliese A. Asymptotic behavior of a metapopulation model. Ann. Appl. Probab. 15 (2005) 1306-1338
9. Bartholomew D.J. Continuous time diffusion models with random duration of interest. J. Math. Sociol. 4 (1976) 187-199
10. Bartlett M.S. Some evolutionary stochastic processes. J. Roy. Statist. Soc. Ser. B 11 (1949) 211-229
11. Bartlett, M.S., 1956. Deterministic and stochastic models for recurrent epidemics. Proceedings of the Third Berkeley Symposium on Mathematics Statistical Probability, vol. 4, pp. 81-109.
12. Clancy D. A stochastic SIS infection model incorporating indirect transmission. J. Appl. Probab. 42 (2005) 726-737
13. Clancy D., O'Neill P.D., and Pollett P.K. Approximations for the long-term behaviour of an open-population epidemic model. Methodol. Comput. Appl. Probab. 3 (2001) 75-95
14. Daley D.J., and Kendall D.G. Stochastic rumours. J. Inst. Math. Appl. 1 (1965) 42-55
15. 0 in models for infectious diseases in heterogenous populations. J. Math. Biol. 28 (1990) 365-382
16. Fan H., Söderström T., Mossberg M., Carlsson B., and Zou Y. Estimation of continuous-time AR process parameters from discrete-time data. IEE Trans. Signal Process. 47 (1999) 1232-1244
17. Feigin P.D. Maximum likelihood estimation for continuous-time stochastic processes. Adv. Appl. Probab. 8 (1976) 712-736
18. Feller W. Die grundlagen der volterraschen theorie des kampfes ums dasein in wahrscheinlichkeitsteoretischer behandlung. Acta Biotheoret. 5 (1939) 11-40
19. Foley P. Predicting extinction times from environmental stochasticity and carrying capacity. Cons. Biol. 8 (1994) 124-137
20. Franco, J.C.G., 2003. Maximum likelihood estimation of mean reverting processes: 〈www.investmentscience.com/Content/howtoArticles/MLE_for_OR_mean_reverting.pdf〉 (downloaded on 16th May 2006).
21. Gibbens R.J., Hunt P.J., and Kelly F.P. Bistability in communications networks. In: Grimmett G.R., and Welsh D.J.A. (Eds). Disorder in Physical Systems (1990), Oxford University Press, Oxford 113-127
22. Gillespie D.T. The chemical Langevin equation. J. Chem. Phys. 113 (2000) 297-306
23. Harrison S., Quinn J.F., Baughman J.F., Murphy D.D., and Ehrlich P.R. Estimating the effects of scientific study on two butterfly populations. Amer. Nat. 137 (1991) 227-243
24. Kingman J.F.C. Markov population processes. J. Appl. Probab. 6 (1969) 1-18
25. Kurtz T. Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Probab. 7 (1970) 49-58
26. Kurtz T. Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Probab. 8 (1971) 344-356
27. Kurtz T.G. The relationship between stochastic and deterministic models in chemical reactions. J. Chem. Phys. 57 (1973) 2976-2978
28. Levins R. Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull. Entom. Soc. Amer. 15 (1969) 237-240
29. Mangel M., and Tier C. Four facts every conservation biologist should know about persistence. Ecology 75 (1994) 607-614
30. McLaughlin J.F., Hellmann J.J., Boggs C.L., and Ehrlich P.R. Climate change hastens population extinctions. Proc. Nat. Acad. Sci. 99 (2002) 6070-6074
31. McNeil D.R., and Weiss G.H. A large population approach to estimation of parameters in Markov population models. Biometrika 64 (1977) 553-558
32. Mode C.J., and Sleeman C.K. Stochastic Processes in Epidemiology, HIV/AIDS, Other Infectious Diseases and Computers (2000), World Scientific, Singapore
33. NÅsell I. Stochastic models of some endemic infections. Math. Biosci. 179 (2002) 1-19
34. Norris J. Markov Chains (1997), Cambridge University Press, Cambridge
35. Oppenheim I., Shuler K.E., and Weiss G.H. Stochastic theory of nonlinear rate processes with multiple stationary states. Physica 88A (1977) 191-214
36. Pollett P.K. On a model for interference between searching insect parasites. J. Austral. Math. Soc. Ser. B 32 (1990) 133-150
37. Pollett P.K. Diffusion approximations for a circuit switching network with random alternative routing. Austral. Telecom. Res. 25 (1992) 45-52
38. Pollett, P.K., 2001. Diffusion approximations for ecological models. In: Ghassemi, F. (Ed.), Proceedings of the International Congress on Modelling and Simulation, vol. 2, Modelling and Simulation Society of Australia and New Zealand, Canberra, Australia, pp. 843-848.
39. Pollett P.K., and Vassallo A. Diffusion approximations for some simple chemical reaction schemes. Adv. Appl. Probab. 24 (1992) 875-893
40. Reuter, G.E.H., 1961. Competition processes. Proceedings of the Fourth Berkeley Symposium on Mathematics Statistical Probability, vol. 2, pp. 421-430.
41. Ross, J.V., 2006a. A stochastic metapopulation model accounting for habitat dynamics. J. Math. Biol. 52, 788-806.
42. Ross, J.V., 2006b. Stochastic models for mainland-island metapopulations in static and dynamic landscapes. Bull. Math. Biol. 68, 417-449.
43. Rubinstein R.Y., and Kroese D.P. The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation, and Machine Learning (2004), Springer, New York
44. Rybicki, G.B., 1994. Unpublished notes: notes on Gaussian random functions with exponential correlation functions (Ornstein-Uhlenbeck process). From 〈http://www.lanl.gov/DLDSTP/fast/〉.
45. Rybicki G.B., and Press W.H. A class of fast methods for processing irregularly sampled or otherwise inhomogeneous one-dimensional data. Phys. Rev. Lett. 74 (1995) 1060-1063
46. Sidje R.B. EXPOKIT. A software package for computing matrix exponentials. ACM Trans. Math. Software 24 (1998) 130-156
47. Verhulst P.F. Notice sur la loi que la population suit dans son accroisement. Corr. Math. Phys. X (1838) 113-121
48. Weiss G.H., and Dishon M. On the asymptotic behaviour of the stochastic and deterministic models of an epidemic. Math. Biosci. 11 (1971) 261-265