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Keywords:

  • nonlinear dynamics;
  • data assimilation;
  • parameter estimation;
  • stochastic differential equations;
  • numerical models;
  • state space models;
  • sequential Monte Carlo;
  • particle filters;
  • state augmentation

Abstract

Parameter estimation for stochastic dynamic systems is a core problem for the environmental and ecological sciences. This study considers parameter estimation for a simple nonlinear numerical model of marine biogeochemistry. We present a nonlinear stochastic differential equation based model for estimating parameters from non-Gaussian ocean measurements collected at a coastal ocean observatory. A sequential Monte Carlo procedure, or particle filter, provides for estimation of the time evolving state and also the basis for parameter estimation. Two approaches for estimating static parameters of the system are contrasted. The first is based on likelihood calculations, and the second on augmenting the system state with the static parameters. Sensitivity analysis identified two ecological parameters (in the differential equations model) and one statistical parameter (governing the level of dynamical noise) as candidates for estimation. Computed likelihood surfaces were found to be rough due to the sample based calculations; they also indicated the ubiquitous problem of ecological parameter dependence and identifiability. A modified state augmentation procedure, incorporating a smoothed bootstrap step, was used here for parameter estimation. Realizations for the parameter values provided by this method allowed for calculation of moments and density estimates that matched well the properties of the likelihood. Incorporation of prior information on the parameters was also considered within this context. It is concluded that such a modified state augmentation procedures provides a promising avenue in parameter estimation in numerical models. Copyright © 2011 John Wiley & Sons, Ltd.