使用非线性相关函数从时间序列中高效,非参数的消除噪声和恢复概率分布:添加噪声
Mainak Dhar1, Joseph A Dickinson1, Mark A Berg1
1Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA.
The Journal of chemical physics
|August 2, 2023
概括
本研究引入了一种使用非线性相关函数的新型非参数方法,以有效地将单分子时间序列数据中的信号与噪声分开. 这种方法提高了分析复杂系统的分辨率和准确性,而不需要先前的模型.
科学领域:
- 物理化学 物理化学
- 生物物理学的生物物理.
- 统计力学 统计力学
背景情况:
- 单分子实验生成反映热运动的时间序列数据.
- 在分析此类数据时,区分真实信号与噪声是一个重大挑战.
- 现有的方法可能需要先前的系统知识或对系统属性施加限制.
研究的目的:
- 在时间序列数据中开发一个完全非参数的信号噪声分离方法.
- 为了能够在没有先验模型的情况下准确地描述复杂系统.
- 为了提高分析单分子波动数据的分辨率和准确性.
主要方法:
- 利用非线性相关函数进行信号噪声分离.
- 该方法是非参数的,不需要关于系统模型,连续性,离散性,状态数量或马克维特征的假设.
- 噪音纠正的相关函数被转换为格林函数,时刻产生平衡概率分布.
主要成果:
- 在三态系统的合成数据上演示了该方法,与时间组合相比,显示了优越的时间和状态空间分辨率.
- 需要为数据质量限制制定公式,表明信号与噪声比至少为0.5,以便实现实际的趋同.
- 恢复了国家位置,人口和汇率,其准确性与使用实验基准数据的参数方法相比.
结论:
- 非线性相关函数方法为分析单分子实验中的杂时间序列数据提供了强大而通用的方法.
- 这种非参数技术显著提高了解决系统动态和平衡属性的能力.
- 开发的公式提供了关于可靠信号恢复的数据要求的关键指导.
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