On the Estimation of Parameters from Time Traces originating from an Ornstein-Uhlenbeck Process
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In this article, we develop a Bayesian approach to estimate parameters from time traces that originate from an overdamped Brownian particle in a harmonic oscillator. We show that least-square fitting the autocorrelation function, which is often the standard way of analyzing such data, is significantly overestimating the confidence in the fitted parameters. Here, we develop a rigorous maximum likelihood theory that properly captures the underlying statistics. This claim is further supported by simulating time series with subsequent application of least-square and maximum likelihood methods. Our result suggests that it is quite dangerous to apply least-squares to autocorrelation functions since an overestimation of confidence could easily lead to irreproducibility of results. To see whether our results apply to other methods where autocorrelation functions are fitted by least-squares, we explored the analysis of membrane fluctuations and fluorescence correlation spectroscopy. In both cases, least-square fits significantly overestimated the confidence in the fitted parameters. We conclude by emphasizing the need for the development of proper maximum likelihood approaches for these methods.
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