Bayesian Uncertainty Quantification for A Fractional-Order Model of the Human Ear.

Area of Science:

• Biomedical Engineering
• Computational Biology
• Acoustics

Background:

• Conventional integer-order models inadequately represent viscoelastic memory effects in ear tissues.
• Fractional-order elements offer a more accurate approach to modeling ear biomechanics.
• Bayesian inference provides a robust framework for parameter estimation and uncertainty quantification.

Purpose of the Study:

• To estimate parameters and quantify uncertainties in a fractional-order lumped-element human ear model using Bayesian inference.
• To validate the model's predictions against experimental data for outer-middle ear gain (OMEG), stapes velocity, and ear canal pressure gain.
• To establish a foundation for probabilistic diagnostic tools in hearing assessment.

Main Methods:

• Employed the Hamiltonian Monte Carlo (HMC) algorithm, specifically the No-U-Turn Sampler (NUTS) implementation, for Bayesian parameter estimation.
• Utilized previously optimized model parameters to construct informative priors for the Bayesian framework.
• Computed outer-middle ear gain (OMEG) from inferred posterior distributions and compared with DPOAE measurements.

Main Results:

• HMC sampling produced well-convergent posterior distributions with quantified uncertainties via credible intervals.
• The posterior predictive OMEG frequency response closely matched experimental measurements.
• Bayesian-derived parameters accurately predicted stapes velocity resonances and ear canal pressure gain peaks, consistent with literature.

Conclusions:

• The Bayesian HMC simulation approach provides robust uncertainty quantification for fractional-order ear models.
• The model demonstrates minimal intersubject variability while capturing realistic biological variations.
• The framework enhances model credibility and supports the development of probabilistic hearing diagnostic tools.