Model parameter estimation with imprecise information

Abstract

Model parameter estimation is a well-known inverse problem, as long as single-value point data are available as observations of system performance measurement. However, classical statistical methods, such as the minimization of an objective function or maximum likelihood, are no longer straightforward, when measurements are imprecise in nature. Typical examples of the latter include censored data and binary information. Here, we explore Approximate Bayesian Computation as a simple method to perform model parameter estimation with such imprecise information. We demonstrate the method for the example of a plain rainfall–runoff model and illustrate the advantages and shortcomings. Last, we outline the value of Shapley values to determine which type of observation contributes to the parameter estimation and which are of minor importance. HIGHLIGHTS Approximate Bayesian Computation is a likelihood-free approach for inverse parameter estimation.; The method is both computationally simple and versatile to use imprecise information.; Censored and binary data are useful observations for parameter estimation.; Shapley values allow us to estimate the significance of a specific type of observation.; The Monte-Carlo based method is computationally expensive.;

Keywords

• approximate bayesian computation
• binary data
• calibration
• imprecise information
• inverse modeling
• shapley value