Estimation of parameters from time traces originating from an Ornstein-Uhlenbeck process.
Estimation of parameters from time traces originating from an Ornstein-Uhlenbeck process.
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根据 Ornstein-Uhlenbeck 过程的时间轨迹估计参数。
DOI：
10.1103/physreve.100.062142
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Strey,HelmutH
中科院分区：
文献类型：
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作者：
Strey,HelmutH
在本文中，我们开发了一种贝叶斯方法来估计源自谐波势或Ornstein-Uhlenbeck过程（OU）中的过阻尼布朗粒子的时间轨迹的参数。我们发现，自相关函数的最小二乘拟合（通常是分析此类数据的标准方法）明显低估了拟合参数的置信区间。在这里，我们开发了一个严格的最大似然理论，可以正确地捕获潜在的统计数据。从解析解中，我们发现存在一个最优测量间隔，使过程衰减时间估计的统计精度在固定样本数量下最大化，其作用类似于OU过程的Nyquist-Shannon定理。为了支持我们的主张，我们用最小二乘法和最大似然法模拟了时间序列。我们的结果表明，在系统偏离真实参数值和置信区间的数量级低估方面，对自相关函数应用最小二乘是相当危险的。为了了解我们的发现是否适用于其他自相关函数通常由最小二乘拟合的方法，我们探索了膜波动和荧光相关光谱的分析。在这两种情况下，最小二乘拟合都表现出与真实参数值的系统性偏差，并且明显低估了它们的置信区间。这一事实强调需要为这些方法发展适当的最大似然方法。总之，我们的结果对自相关函数中导致单指数衰减的过程的参数估计具有很强的意义。我们的分析可以直接应用于单组分动态光散射实验或光阱标定实验。
In this article, we develop a Bayesian approach to estimate parameters from time traces that originate from an overdamped Brownian particle in a harmonic potential, or Ornstein-Uhlenbeck process (OU). We show that least-square fitting the autocorrelation function, which is often the standard way of analyzing such data, is significantly underestimating the confidence intervals of the fitted parameters. Here, we develop a rigorous maximum likelihood theory that properly captures the underlying statistics. From the analytic solution, we found that there exists an optimal measurement spacingthat maximizes the statistical accuracy of the estimate for the decay-timeof the process for a fixed number of samples, which plays a similar role than the Nyquist-Shannon theorem for the OU process. To support our claims, we simulated time series with subsequent application of least-square and our maximum likelihood method. Our results suggest that it is quite dangerous to apply least-squares to autocorrelation functions both in terms of systematic deviations from the true parameter values and an order-of-magnitude underestimation of confidence intervals. To see whether our findings apply to other methods where autocorrelation functions are typically fitted by least-squares, we explored the analysis of membrane fluctuations and fluorescence correlation spectroscopy. In both cases, least-square fits exhibit systematic deviations from the true parameter values and significantly underestimate their confidence intervals. This fact emphasizes the need for the development of proper maximum likelihood approaches for such methods. In summary, our results have strong implications for parameter estimation for processes that result in a single exponential decay in the autocorrelation function. Our analysis can directly be applied to single-component dynamic light scattering experiments or optical trap calibration experiments.