PEAS: A toolbox to assess the accuracy of estimated parameters in environmental models

This paper presents a Matlab™ toolbox to assess the accuracy of the estimated parameters of environmental models, based on their approximate confidence regions. Before describing the application, the underlying theory is briefly recalled to familiarize the reader with the numerical methods involved. The software, named PEAS as an acronym for Parameter Estimation Accuracy Software, performs both the estimation and the accuracy analysis, using a user-friendly graphical interface to minimize the required programming. The user is required to specify the model structure according to the Matlab/Simulink™ syntax, supply the experimental data, provide an initial parameter guess and select an estimation method. PEAS provides several model assessment tools, in addition to parameter estimation, such as error function plotting, trajectory sensitivity, Monte Carlo analysis, all useful to assess the adequacy of the experimental data to the estimation problem. After the parameters have been estimated, the reliability assessment is performed: approximate and exact confidence regions are computed and a confidence test is produced. The Monte Carlo analysis is available for approximate accuracy assessment whenever the model structure prevents the application of the confidence regions method. The software, which is freely available for research purposes, is demonstrated here with two examples: a dynamical and an algebraic model. In both cases, software usage and outputs are presented and commented. The examples show how the user is guided through the application of the methods and how warning messages are returned if the estimation does not satisfy the accuracy criteria.