Abstract
Bayesian inference is a conscientious statistical method which is successfully used in many branches of physics and engineering. Compared to conventional approaches, it makes highly efficient use of information hidden in a measured quantity by predicting the distribution of future data points based on posterior information. Here we apply this method to determine the stress-relaxation time and the solvent and polymer contributions to the frequency dependent viscosity of a viscoelastic Jeffrey’s fluid by the analysis of the measured trajectory of an optically trapped Brownian particle. When comparing the results to those obtained from the auto-correlation function, mean-squared displacement or the power spectrum, we find Bayesian inference to be much more accurate and less affected by systematic errors.
Highlights
Bayesian inference is a conscientious statistical method which is successfully used in many branches of physics and engineering
Often one only makes partial use of the information provided by the data, e.g., the correlation function, power spectral density in the context of Brownian motion, to an equation which is assumed to describe the underlying process, mainly using least-squares fitting routines
Using the Bayes’ theorem, the probable parameter values concealed in given discrete observations can be obtained with the corresponding probabilities[33,34]. Such a Bayesian theory based time domain method is thorough, accurate and avoids limitations such as non-trivial Fourier transformations, data range dependent uncertainty observed in the measurement from the auto-correlation function (ACF), power spectral density (PSD), mean-squared displacement function (MSD) etc
Summary
Bayesian inference is a conscientious statistical method which is successfully used in many branches of physics and engineering. Bayesian inference with proper likelihood function added to the prior knowledge about the parameters can provide reliable and efficient measurements of the probable values of the parameters with the related uncertainties, for a given set of data.
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