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Bulletin of Mathematical Biology

, Volume 71, Issue 7, pp 1626–1648 | Cite as

Reduced Models of Algae Growth

  • Heikki Haario
  • Leonid Kalachev
  • Marko Laine
Original Article

Abstract

The simulation of biological systems is often plagued by a high level of noise in the data, as well as by models containing a large number of correlated parameters. As a result, the parameters are poorly identified by the data, and the reliability of the model predictions may be questionable. Bayesian sampling methods provide an avenue for proper statistical analysis in such situations. Nevertheless, simulations should employ models that, on the one hand, are reduced as much as possible, and, on the other hand, are still able to capture the essential features of the phenomena studied. Here, in the case of algae growth modeling, we show how a systematic model reduction can be done. The simplified model is analyzed from both theoretical and statistical points of view.

Keywords

Algae growth modeling Asymptotic methods Model reduction MCMC Adaptive Markov chain Monte Carlo 

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References

  1. Calvetti, D., Kuceyeski, A., Somersalo, E., 2008a. Sampling-based analysis of a spatially distributed model for liver metabolism at steady state. Multiscale Model. Simul. 7(1), 407–431. MATHCrossRefMathSciNetGoogle Scholar
  2. Calvetti, D., Hageman, R., Occhipinti, R., Somersalo, E., 2008b. Dynamic Bayesian sensitivity analysis of a myocardial metabolic model. Math. Biosci. 212(1), 1–21. MATHCrossRefMathSciNetGoogle Scholar
  3. Haario, H., Kalachev, L., Lehtonen, J., Salmi, T., 1999. Asymptotic analysis of chemical reactions. Chem. Eng. Sci. 54, 1131–1143. CrossRefGoogle Scholar
  4. Haario, H., Saksman, E., Tamminen, J., 2001. An adaptive Metropolis algorithm. Bernoulli 7(2), 223–242. MATHCrossRefMathSciNetGoogle Scholar
  5. Haario, H., Laine, M., Lehtinen, M., Saksman, E., Tamminen, J., 2004. MCMC methods for high dimensional inversion in remote sensing. J. R. Stat. Soc. B 66(3), 591–607, 648–649, with discussion. MATHCrossRefMathSciNetGoogle Scholar
  6. Haario, H., Laine, M., Mira, A., Saksman, E., 2006. DRAM: Efficient adaptive MCMC. Stat. Comput. 16, 339–354. CrossRefMathSciNetGoogle Scholar
  7. Malve, O., Laine, M., Haario, H., Kirkkala, T., Sarvala, J., 2007. Bayesian modelling of algal mass occurrences—using adaptive MCMC methods with a lake water quality model. Environ. Model. Softw. 7(22), 966–977. CrossRefGoogle Scholar
  8. Murray, J.D., 1993. Mathematical Biology. Springer, New York. MATHCrossRefGoogle Scholar
  9. Ovaskainen, O., Luoto, M., Ikonen, I., Rekola, H., Meyke, E., Kuussaari, M., 2008. An empirical test of a diffusion model: predicting clouded apollo movements in a novel environment. Am. Nat. 171, 610–619. CrossRefGoogle Scholar
  10. Zheng, C., Ovaskainen, O., Saastamoinen, M., Hanski, I., 2007. Age-dependent survival analyzed with Bayesian models of mark-recapture data. Ecology 88(8), 1970–1976. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  1. 1.Lappeenranta University of TechnologyLappeenrantaFinland
  2. 2.University of MontanaMissoulaUSA
  3. 3.Finnish Meteorological InstituteHelsinkiFinland

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