在非线性普通微分方程模型中的有限样本情况的概率比测试统计
Christian Tönsing1,2,3, Bernhard Steiert1, Jens Timmer1,2,3
1Institute of Physics, University of Freiburg, Germany.
PLoS computational biology
|September 22, 2023
概括
在非线性普通微分方程 (ODE) 模型中使用概率比的统计测试通常依赖于大型数据集. 这项研究表明,有限的数据需要纠正以避免不准确的结论.
科学领域:
- 统计 统计 统计 统计
- 计算生物学 计算生物学
- 数学建模的数学建模
背景情况:
- 在测试,模型选择和不确定性量化方面的统计推理中,概率比率是基本的.
- 将概率比转换为p值或置信区间通常需要了解测试统计数据的分布,通常使用非对称 (大数据) 设置进行近似计算.
- 定量分子生物学和动态系统建模经常涉及有限样本大小的非线性普通微分方程 (ODE) 模型,对标准统计方法构成挑战.
研究的目的:
- 在有限样本条件下研究非线性ODE模型中参数的经验概率比的行为.
- 将经验概率比率的分布与非对称近似进行比较.
- 在现实的小数据场景中,评估从非对称理论衍生出的统计值的保守性.
主要方法:
- 对19个已发表的非线性ODE基准模型的参数计算了经验概率.
- 使用原始数据设计,应用了重新采样方法.
- 经验分布与标准非对称近似进行了比较.
主要成果:
- 在有限样本应用中,经验概率比率的分布偏离了非对称近似.
- 对于大样本来说,标准统计值被发现,当应用于小数据集时,它们可能具有反保守性.
- 对概率比率的修正对于有限样本ODE模型中有效的统计推理是必要的.
结论:
- 对于具有有限数据的非线性ODE模型,概率比率的非对称近似通常是不充分的.
- 有限样本校正对于确保统计测试的有效性和保守性以及这些模型的置信区间至关重要.
- 这项研究强调了在定量生物学和处理小数据集的相关领域需要调整统计方法的需要.
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