PMID- 31962441
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20200123
LR  - 20211026
IS  - 2470-0053 (Electronic)
IS  - 2470-0045 (Linking)
VI  - 100
IP  - 6-1
DP  - 2019 Dec
TI  - Estimation of parameters from time traces originating from an Ornstein-Uhlenbeck 
      process.
PG  - 062142
LID - 10.1103/PhysRevE.100.062142 [doi]
AB  - 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 spacing (Deltat=0.7968tau) that maximizes the 
      statistical accuracy of the estimate for the decay-time tau of the process for a 
      fixed number of samples N, 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.
FAU - Strey, Helmut H
AU  - Strey HH
AD  - Biomedical Engineering Department and Laufer Center for Physical and Quantitative 
      Biology, Stony Brook University, Stony Brook, New York 11794-5281, USA.
LA  - eng
PT  - Journal Article
PL  - United States
TA  - Phys Rev E
JT  - Physical review. E
JID - 101676019
SB  - IM
EDAT- 2020/01/23 06:00
MHDA- 2020/01/23 06:01
CRDT- 2020/01/23 06:00
PHST- 2019/08/08 00:00 [received]
PHST- 2020/01/23 06:00 [entrez]
PHST- 2020/01/23 06:00 [pubmed]
PHST- 2020/01/23 06:01 [medline]
AID - 10.1103/PhysRevE.100.062142 [doi]
PST - ppublish
SO  - Phys Rev E. 2019 Dec;100(6-1):062142. doi: 10.1103/PhysRevE.100.062142.