Assessment of parameter uncertainty in plant growth model identification

Abstract

For the parametric identification of plant growth models, we generally face limited or uneven experimental data, and complex nonlinear dynamics. Both aspects make model parametrization and uncertainty analysis a difficult task. The Generalized Least Squares (GLS) estimator is often used since it can provide estimations rather rapidly with an appropriate goodness-of-fit. However, the confidence intervals are generally calculated based on linear approximations which make the uncertainty evaluation unreliable in the case of strong nonlinearity. A Bayesian approach, the Convolution Particle Filtering (CPF), can thus be applied to estimate the unknown parameters along with the hidden states. In this case, the posterior distribution obtained can be used to evaluate the uncertainty of the estimates. In order to improve its performance especially with stochastic models and in the case of rare or irregular experimental data, a conditional iterative version of the Convolution Particle Filtering (ICPF) is proposed. When applied to the Log Normal Allocation and Senescence model (LNAS) with sugar beet data, the two CPF related approaches showed better performance compared to the GLS method. The ICPF approach provided the most reliable estimations. Meanwhile, two sources of the estimation uncertainty were identified: the variance generated by the stochastic nature of the algorithm (relatively small for the ICPF approach) and the residual variance partly due to the noise models.