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.

中文翻译：

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确定性模型参数的置信区间与估计量分布之间的关系

用于参数估计的对称有界 (SB) 方法可以在最大似然 (ML) 方法不适合的情况下估计参数。我们在这里扩展 SB 方法来量化点估计的准确性，并将基于轮廓的置信区间与参数估计量的分布联系起来。我们使用蒙特卡罗生成的数据比较了威布尔和指数模型参数估计的 ML 和 SB 方法。SB 方法的性能至少与 ML 方法一样好。SB 方法随后应用于现实世界的生物数据（两个耦合的生长轨迹），其中 ML 不适合量化确定性生长模型的四个基础代谢参数的准确性。该模型与数据完美契合。然而，其中两个参数的置信区间很窄，而其余两个则没有。二维置信区域的形状阐明了这种差异，它揭示了后两个参数的相互依赖性。提出了提高生物过程机械模型参数准确性的建议。