Bayesian and subset-selection methods for parameter estimation in mechanistic models with limited data: A review and comparison

Abstract

Parameters in mathematical models require accurate estimation for the model to give reliable predictions. When data are limited, weighted least-squares methods sometimes result in unreliable parameter estimates. Two popular approaches to combat this issue are subset-selection and Bayesian estimation. Subset-selection ranks model parameters from most- to least-estimable based on prior parameter knowledge and available data. The ranked list is used to determine which parameters should be estimated, and which should be fixed at initial guesses to avoid overfitting. Bayesian estimation methods summarize prior knowledge about parameters using probability distributions. Simple Bayesian methods result in objective functions with penalty terms that keep parameter estimates near their initial guesses unless there is considerable information in the data. Subset-selection and Bayesian methods result in different parameter estimates using the same data and similar prior information. A hydroisomerization case study is presented comparing the merits and shortcoming of each approach. Bayesian estimation is preferred if prior parameter knowledge is reliable, but provides misleading results when the modeler is overly confident about poor parameter guesses. Subset-selection methods are more computationally expensive, less susceptible to problems arising from poor initial guesses, and provide additional information about influences of model parameters and opportunities for model simplification.