复杂模型中参数不可识别性的刻画
Delineating Parameter Unidentifiabilities in Complex Models
摘要：
科学家使用数学建模来理解和预测复杂物理系统的特性。在高度参数化的模型中，参数之间经常存在关系，模型预测在这些关系上是相同的，或者几乎相同。这些分别被称为结构或实际不可识别性。它们很难诊断，并且不可能从数据中进行可靠的参数估计。它们还意味着存在一个潜在的模型简化。我们描述了一个可扩展的方法来检测不可识别性，并定义它们的功能关系，通用模型。这允许模型简化，以及对不能从数据估计的参数（或其函数）的评价。我们的算法可以识别的功能，如冗余机制和快速时标子系统，以及在这种近似是有效的制度。我们的算法基于一种新的量化区域参数敏感性：多尺度的草率。传统上，参数敏感性和参数估计问题的条件之间的联系是局部的，通过Fisher信息矩阵。这在无限小测量不确定度的范围内是有效的。我们证明了多尺度的草率和周围的参数估计的测量不确定性是不可忽略的置信区域的几何之间的对偶。进一步的理论关系，提供连接多尺度草率的似然比检验。从这一点，我们表明，局部灵敏度分析（通常这样做）是不足以确定参数估计的可靠性，即使是简单的（非）线性系统。我们的算法提供了一个易处理的替代方案。最后，我们将我们的方法应用到一个大规模的，基准系统生物学模型NF- $κ$ B，发现以前未知的unidentifiabilities。
英文摘要：
Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or nearly so. These are known as structural or practical unidentifiabilities, respectively. They are hard to diagnose and make reliable parameter estimation from data impossible. They furthermore imply the existence of an underlying model simplification. We describe a scalable method for detecting unidentifiabilities, and the functional relations defining them, for generic models. This allows for model simplification, and appreciation of which parameters (or functions thereof) cannot be estimated from data. Our algorithm can identify features such as redundant mechanisms and fast timescale subsystems, as well as the regimes in which such approximations are valid. We base our algorithm on a novel quantification of regional parametric sensitivity: multiscale sloppiness. Traditionally, the link between parametric sensitivity and the conditioning of the parameter estimation problem is made locally, through the Fisher Information Matrix. This is valid in the regime of infinitesimal measurement uncertainty. We demonstrate the duality between multiscale sloppiness and the geometry of confidence regions surrounding parameter estimates made where measurement uncertainty is non-negligible. Further theoretical relationships are provided linking multiscale sloppiness to the Likelihood-ratio test. From this, we show that a local sensitivity analysis (as typically done) is insufficient for determining the reliability of parameter estimation, even with simple (non)linear systems. Our algorithm provides a tractable alternative. We finally apply our methods to a large-scale, benchmark Systems Biology model of NF-$κ$B, uncovering previously unknown unidentifiabilities.
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