Only through perturbation can relaxation times be estimated.

Area of Science:

• Mathematical modeling
• Statistical inference
• Dynamical systems analysis

Background:

• Model parameter estimation is critical but often overlooked in scientific studies.
• Existing methods for Ornstein-Uhlenbeck processes are sensitive to finite sample sizes, degrading accuracy.
• The time constant estimator is particularly affected by limited data.

Purpose of the Study:

• To address the limitations of current parameter estimation techniques for Ornstein-Uhlenbeck processes with finite sample sizes.
• To develop and present an alternative, more robust method for parameter estimation.
• To enhance the quality of estimation, particularly for the system's time constant.

Main Methods:

• Developed a novel parameter estimation solution based on system perturbation.
• Observed system trajectories under conditions far from equilibrium.
• Validated the method through computer experiments and simulations.

Main Results:

• Demonstrated a striking improvement in the quality of parameter estimation compared to traditional methods.
• Showcased the effectiveness of the perturbation-based approach, especially for the time constant.
• Validated the findings in simulated applications within neuroscience and pharmacokinetics.

Conclusions:

• The proposed perturbation-based method offers a significant advancement in parameter estimation for Ornstein-Uhlenbeck processes.
• This approach is vital for optimizing experimental design, maximizing information from limited data.
• The findings are particularly relevant for expensive or difficult-to-obtain biological and pharmacokinetic samples.