The relationship between confidence intervals and distributions of estimators for parameters of deterministic models

A Symmetric-Bounded (SB) method for parameter estimation enables estimating parameters in cases where maximum-likelihood (ML) methods are unsuitable. We here extend the SB-method to quantify the accuracy of point estimates and to link profile-based confidence intervals to the distribution of parameter estimators. We compare ML and SB methods for parameter estimates of Weibull and exponential models using Monte-Carlo-generated data. The SB-method performs at least as well as the ML-method. The SB-method is subsequently applied to real-world biological data (two coupled growth trajectories) where ML is unsuitable to quantify the accuracy of four underlying metabolic parameters of a deterministic growth model. The model fits the data perfectly. However, two of these parameters turn out to have narrow confidence intervals, while the remaining two do not. This discrepancy is elucidated by the shapes of the 2D confidence regions, which reveal the interdependence of the latter two parameters. Recommendations are proposed for increasing accuracy of parameters for mechanistic models for biological processes.