Learning Parameters in Non Linear Ecological Models
This paper builds on our previous work that used a non linear stochastic dynamic programming problem to solve for the optimal level of phosphorus discharged into a watershed. Typically, there is a trade off between profits from agriculture and environmental damage due to excessive levels of phosphorus (from farm animal wastes) in the watershed of a freshwater lake. The optimal management of the level of phosphorus depends not only on the costs and benefits, but also on the physical properties of the lake and on random shocks. Some lakes are more susceptible to damage from excess levels of phosphorus than others. To determine the optimal level of phosphorus for a given lake, it is necessary to learn the physical nature of the lake and its watershed. We adapted the method of optimal control with Bayes' learning of Easley and Kiefer (Econometrica 1988) to this problem. We show that in the context of the dynamic model for the flow of phosphorus in a lake, there is complete learning, i.e., there is no bandit problem in this context. We numerically solve the model and use Monte Carlo methods to solve for the mean time to learn and to determine the sensitivity of the speed of learning with respect to changes in the variance of the shocks
References listed on IDEAS
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- Peterson,G.D. & Carpenter,S.R. & Brock,W.A., 2002. "Uncertainty and the management of multi-state ecosystems : an apparently rational route to collapse," Working papers 10, Wisconsin Madison - Social Systems.
- Karl-Göran Mäler & Anastasios Xepapadeas & Aart de Zeeuw, 2003.
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- John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
- John Rust & Department of Economics & University of Wisconsin, 1994. "Using Randomization to Break the Curse of Dimensionality," Computational Economics 9403001, EconWPA, revised 19 Nov 1996.
- Rust, J., 1994. "Using Randomization to Break the Curse of Dimensionality," Working papers 9429, Wisconsin Madison - Social Systems.
- Ludwig,D. & Carpenter,S. & Brock,W., 2002. "Optimal phosphorus loading for a potentially eutrophic lake," Working papers 9, Wisconsin Madison - Social Systems. Full references (including those not matched with items on IDEAS)
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