The University of Montana
Department of Mathematical Sciences

Technical report #10/2007

Reduced models of algae growth

Heikki Haario*, Leonid Kalachev**, and Marko Laine***
*Lappeenranta University of Technology, Lappeenranta, Finland
**University of Montana, Missoula, MT, USA
***Finnish Meteorological institute, Helsinki, Finland

Abstract

The simulation of biological systems often is plagued with a high noise level in the data as well as models loaded with a large number of correlated parameters. As a results, the parameters are poorly identified by the data and the reliability of the model predictions may remain questionable. Recently, the advance of Bayesian sampling methods has provided new methods 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 may 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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