Comparison of frequentist and bayesian confidence analysis methods on a viscoelastic stenosis model

Abstract

We compare the performance of three methods for quantifying uncertainty in model parameters: asymptotic theory, bootstrapping, and Bayesian estimation. We study these methods on an existing model for one-dimensional wave propagation in a viscoelastic medium, as well as corresponding data from lab experiments using a homogeneous, tissue-mimicking gel phantom. In addition to parameter estimation, we use the results from the three algorithms to quantify complex correlations between our model parameters, which are best seen using the more computationally expensive bootstrapping or Bayesian methods. We also hold constant the parameter causing the most complex correlation, obtaining results from all three methods which are more consistent than those obtained when estimating all parameters. Concerns regarding computational time and algorithm complexity are incorporated into a discussion on differences between the frequentist and Bayesian perspectives.