Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of factors not explicitly included in the mathematical model. For this, independent Gaussian noise is commonly chosen, with its use so widespread that researchers typically provide no explicit justification for this choice. This noise model assumes `random' latent factors affect the system in ephemeral fashion resulting in unsystematic deviation of observables from their modelled counterparts. However, like the deterministically modelled parts of a system, these latent factors can have persistent effects on observables. Here, we use experimental data from dynamical systems drawn from cardiac physiology and electrochemistry to demonstrate that highly persistent differences between observations and modelled quantities can occur. Considering the case when persistent noise arises due only to measurement imperfections, we use the Fisher information matrix to quantify how uncertainty in parameter estimates is artificially reduced when erroneously assuming independent noise. We present a workflow to diagnose persistent noise from model fits and describe how to remodel accounting for correlated errors.
翻译:普通等式模型用于描述整个生物学的动态过程。 为了对这些模型进行基于概率的参数推断, 有必要指定一个统计过程, 代表数学模型中未明确包括的因素的贡献。 为此, 通常选择独立高斯噪音, 其使用范围很广, 研究人员通常不为这种选择提供明确的理由。 这个噪音模型假定“ 随机” 潜在因素以短暂的方式影响系统, 导致观测结果与模拟的对等系统不系统地偏离。 但是, 象一个系统的确定性模拟部分一样, 这些潜在因素可能会对可观测到的事物产生持久影响。 我们在这里使用从心脏生理学和电化学学中提取的动态系统中的实验数据来证明观测和模型数量之间能够发生高度持久的差异。 考虑到由于测量不完善而出现持续噪音的情况, 我们使用渔业信息矩阵来量化参数估计的不确定性在错误地假设独立噪音时是如何人为地减少的。 我们提出了一个工作流程, 来分析模型匹配的持久性噪音, 并描述如何对相关错误的计算进行重新建模。