A comparison of techniques for the estimation of model prediction uncertainty

Ecological Modelling

Volumn 115, Issue 1, 1999, Pages 45-59

  Omlin, Martin ^a   Reichert, Peter ^a  

^a SWISS FEDERAL INSTITUTE OF AQUATIC SCIENCE AND TECHNOLOGY   (Switzerland)

Author keywords

Bayes; Frequentist; Identifiability; Overparameterized models; Parsimonous models; Uncertainty

Indexed keywords

BAYESIAN ANALYSIS; ECOLOGICAL MODELING; PARAMETERIZATION;

EID: 0033082586     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3800(98)00174-4     Document Type: Article

References (42)

1. Aldenberg T., Janse J., Kramer P. Fitting the dynamic model pclake to a multi-lake survey through Bayesian statistics. Ecol. Modell. 78:1995;83-99.
2. Asaeda T., Van Bon T. Modelling the effects of macrophytes on algal blooming in eutrophic shallow lakes. Ecol. Model. 104:1997;261-287.
3. Bader F. Kinetics of double-substrate limited growth. Bazin M. Microbial Population Dynamics. 1982;313-325 CRC Press, Boca Raton, FL.
4. Bates D., Watts D. Nonlinear Regression Analysis and its Applications. 1988;Wiley, New York.
5. Beck M. Water quality modeling: a review of the analysis of uncertainty. Water Resour. Res. 23(8):1987;1393-1442.
6. Berger J. The robust Bayesian viewpoint. Kadane J. Robustness of Bayesian Analyses. 1984;63-124 North-Holland, Amsterdam.
7. Bernardo J., Smith A. Bayesian Theory. 1994;Wiley, Chichester.
8. Dabes J., Finn R., Wilke C. Equations of substrate-limited growth: The case for Blackman kinetics. Biotechnol. Bioeng. 15:1973;1159-1177.
9. Dennis B. Discussion: Should ecologists become Bayesians? Ecol. Appl. 6(4):1996;1095-1103.
10. Dilks D., Canale R., Meier P. Development of Bayesian Monte Carlo techniques for water quality model uncertainty. Ecol. Modell. 62:1992;149-162.
11. Ellison A. An introduction to Bayesian inference for ecological research and environmental decision-making. Ecol. Appl. 6(4):1996;1036-1046.
12. Freeze R., Massmann J., Smith L., Sperling T., James B. Hydrogeological decision analysis: 1. A framework. Ground Water. 28(5):1990;738-766.
13. Gelman A., Carlin J., Stern H., Rubin D. Bayesian Data Analysis. 1995;Chapman and Hall, London.
14. Gorelick S., Freeze R., Donohue D., Keely J. Groundwater Contamination-Optimal Capture and Containment. 1993;Lewis Publishers, Boca Raton, FL.
15. Gujer W., Henze M., Mino T., Matsuo T., Wentzel M., Marais G. The activated sludge model no. 2: Biological phosphorus removal. Wat. Sci. Tech. 31(2):1995;1-11.
16. Hampel F. Some thoughts about the foundations of statistics. Morgenthaler S., Ronchetti E., Stahle W. New Directions in Statistical Data Analysis and Robustness. 1993;125-137 Birkhauser, Basel.
17. Henze, M., Grady, C., Gujer, W., Marais, G., Matsuo T., 1986. Activated sludge model no. 1. Scientific and Technical Report 1, IAWPRC Task Group on Mathematical Modeling for Design and Operation of Biological Wastewater Treatment Processes, IAWPRC, London.
18. Henze, M., Gujer, W., Takahashi, M., Matsuo, T., Wentzel, M., Marais, G., 1995. Activated sludge model no. 2. Scientific and Technical Report 3, IAWPRC Task Group on Mathematical Modeling for Design and Operation of Biological Wastewater Treatment Processes, IAWPRC, London.
19. Hornberger G., Spear R. An approach to the preliminary analysis of environmental systems. J. Environ. Manage. 12:1981;7-18.
20. Hornberger G., Spear R. An approach to the analysis of behavior and sensitivity in environmental systems. Beck M., van Straten G. Uncertainty and Forecasting of Water Quality. 1983;101-116 Springer, Berlin.
21. Iman R.L., Conover W.J. Small sample sensitivity analysis techniques for computer models, with an application to risk assessment. Commun. Stat., A: Theory Methods. 9(13):1980;1749-1842.
22. Ljung L. System Identification - Theory for the User. 1987;Prentice Hall, Englewood Cliffs, NJ.
23. Marin C., Medina M., Butcher J. Monte Carlo analysis and Bayesian decision theory for assessing the effects of waste sites on groundwater. J. Contam. Hydrol. 5:1989;1-13.
24. McKay M., Beckman R., Conover W. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics. 21(2):1979;239-245.
25. Michaelis M., Menten M. Die Kinetik der Invertinwirkung. Biochem. Z. 43:1913;333-369.
26. Monod, J., 1942. Recherches sur la croissance des cultures bacteriennes. Paris: Hermann et Cie.
27. Orlob, G.T. (Ed.), 1983. Mathematical Modeling of Water Quality: Streams, Lakes and Reservoirs, Wiley, New York.
28. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical Recipes in C. 2:1992;Cambridge University Press, Cambridge, MA.
29. Reichert P., Omlin M. On the usefulness of overparameterized ecological models. Ecol. Modell. 95:1997;289-299.
30. Rose K., Smith E., Gardner R., Brenkert A., Bartell S. Parameter sensitivities, Monte Carlo filtering and model forecasting under uncertainty. J. Forecasting. 10:1991;117-133.
31. Rubinstein R. Simulation and the Monte Carlo Method. 1981;Wiley, New York.
32. Seber G., Wild C. Nonlinear regression. 1989;Wiley, New York.
33. Sobol I. On the systematic search in a hypercube. SIAM J. Numer. Anal. 16(5):1979;790-793.
34. Sobol I. A Primer for the Monte Carlo Method. 1994;CRC Press, Boca Raton, FL.
35. Söderström T., Stoica P. System Identification. 1989;Prentice Hall, New York.
36. Spriet, J., 1985. Structure characterization - an overview, in: Barker H., Young P. (Eds.), Identification and System Parameter Estimation 1985 - Proceedings of the Seventh IFAC/IFORS Symposium, Pergamon Press, Oxford, pp. 749-756.
37. Stein M. Large sample properties of simulations using latin hypercube sampling. Technometrics. 29(2):1987;143-151.
38. Tiwari J., Hobbie J., Peterson B. Random differential equations as models of ecosystems-III. Bayesian inference for parameters. Math. Biosci. 38:1978;247-258.
39. Varis O., Kuikka S., Taskinen A. Modeling for water quality decisions: uncertainty and subjectivity in information, in objectives and in model structure. Ecol. Modell. 74:1994;91-101.
40. Walley P. Statistical Reasoning with Imprecise Probabilities. 1991;Chapman and Hall, London.
41. Wolfson L., Kadane J., Small M. Bayesian environmental policy decisions: two case studies. Ecol. Appl. 6(4):1996;1056-1066.
42. Yang M., Sykes R. Trophic-dynamic modeling in a shallow eutrophic river ecosystem. Ecol. Modell. 105:1998;129-139.