Estimating parameters in stochastic compartmental models using Markov chain methods

IMA Journal of Mathemathics Applied in Medicine and Biology

Volumn 15, Issue 1, 1998, Pages 19-40

  Gibson, Gavin J ^a   Renshaw, Eric ^b  

^a BIOMATHEMATICS AND STATISTICS SCOTLAND   (United Kingdom)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Hidden Markov models; Markov chain Monte Carlo methods; Parameter estimation; Stochastic compartment models

Indexed keywords

ALGORITHM; ARTICLE; COMPARTMENT MODEL; PARAMETER; STOCHASTIC MODEL; SYSTEM ANALYSIS;

CHAINS; MONTE CARLO METHODS; PARAMETER ESTIMATION; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; UNCERTAINTY ANALYSIS;

COMPARTMENT MODELING; COMPARTMENTAL MODELLING; ESTIMATING PARAMETERS; HIDDEN-MARKOV MODELS; MARKOV CHAIN METHOD; MARKOV CHAIN MONTE CARLO; MARKOV CHAIN MONTE CARLO METHOD; PARAMETERS ESTIMATION; STOCHASTIC COMPARTMENT MODEL; STOCHASTICS;

HIDDEN MARKOV MODELS;

EID: 0031780720     PISSN: 02650746     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb/15.1.19     Document Type: Article

References (29)

1. BESAG, J., & GREEN, P. J. 1993 Spatial statistics and Bayesian computation. J. R. Statist. Soc. B, 55, 25-37.
2. BOX, G. E. P., & JENKINS, G. M. 1970 Time Series Analysis, Forecasting and Control. San Francisco: Holden-Day.
3. BROWER, R. C., FURMAN, M. A., & MOSHE, M. 1978 Critical exponents for the Reggeon quantum spin model. Phys. Lett. B 76, 213-219.
4. BUTTELL, L., COX, J. T., & DURRETT, R. 1993 Estimating the critical values of stochastic growth models. J. Appl. Probab. 30, 455-461.
5. COWLES, M. K., & CARLIN, B. P. 1996 Markov chain Monte Carlo convergence diagnostics: A comparative review. J. Am. Stat. Soc. 91, 883-904.
6. COX, J. T., & DURRETT, R. 1988 Limit theorems for the spread of epidemics and forest fires. Stoch. Proc. Applic. 30, 171-191.
7. DRAPER, D. 1995 Assessment and propagation of model uncertainty, (with discussion). J. R. Statist. Soc. B 57, 45-97.
8. DURRETT, R., & LEVIN, S. 1994 Stochastic spatial models - A users guide to ecological applications, Phil. Trans. R. Soc. Lond. B 343, 363-394.
9. GELFAND, A. E., & SMITH, A. F. M. 1990 Sampling-based approaches to calculating marginal densities. J. Am. Statist. Assoc. 85, 398-409.
10. GIBSON, G. J. 1997 Markov chain Monte Carlo methods for fitting spatio-temporal stochastic models in plant epidemiology, Appl. Stat. 46, 215-233.
11. GREEN, P. J. 1995 Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-732.
12. HASTINGS, W. K. 1970 Monte Carlo sampling methods using Markov chains, and their applications. Biometrika 57, 97-109.
13. ISHAM, V. 1991. Assessing the variability of stochastic epidemics. Math. Biosc. 107, 209-224.
14. JOHNSON, N. I., & KOTZ, S. 1970 Continuous Univariate Distributions, Vol. 1. New York: Wiley.
15. LEVIN, S., & DURRETT, R. 1996 From individuals to epidemics. Phil. Trans. R. Soc. Lond. B 351, 1615-1621.
16. LIGGETT, T. M. 1985 Interacting Particle Systems. New York: Springer-Verlag.
17. METROPOLIS, M., ROSENBLUTH, A. W., ROSENBLUTH, M. N., TELLER A. H., & TELLER, E. 1953 Equations of state calculation by fast computing machines. J. Chem. Phys. 21, 1087-1093.
18. MURRAY, J. 1989 Mathematical Biology. Springer-Verlag.
19. NEWTON, M. A., GUTTORP, P., ABKOWITZ, J. L. 1992 Bayesian inference by simulation in a stochastic model from hematology. In: Computing Science and Statistics, Vol. 24 (H. J. Newton, ed.), pp. 449-455. Fairfax Station, VA: Interface Foundation of North America.
20. RENSHAW, E. 1991 Modelling Biological Populations in Space and Time. Cambridge University Press.
21. RICHARDSON, S. & GREEN, P. J. 1997 On Bayesian analysis of mixtures with an unknown number of components (with discussion). J. R. Statist. Soc. B 59, 731-792.
22. RIPLEY, B. D. 1987 Stochastic Simulation. New York: Wiley.
23. SATO, K., MATSUDA, H., & SASAKI, A. 1994 Pathogen invasion and host extinction in lattice structured populations. J. Math. Biol. 32, 251-268.
24. SINCLAIR, A. 1993 Algorithms for Random Generation and Counting. Boston: Birkhauser.
25. SMITH, A. F. M., & ROBERTS, G. O. 1993 Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. R. Statist. Soc. B 55, 2-23.
26. STARR, J. M. RODGERS, T. R., IMPALLOMENI, M. 1997 Hospital-acquired Clostridium difficile diarrhoea and herd immunity. Lancet 349, 426-428.
27. WHITTLE, P. 1957 On the use of the normal approximation in the treatment of stochastic processes. J. R. Statist. Soc. B 19, 266-281.
28. WOLFRAM, S. 1991 Mathematica. Reading, MA: Addison-Wesley.
29. YAKOWITZ, S. BLOUNT, M. & GANI, J. 1996 Computing marginal expectations for large compartment models with applications to AIDS evolution in a prison system. J. IMA Math. Appl. Med. Biol. 13, 223-244.