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

Abstract

We employ the Hamiltonian Monte Carlo (HMC) algorithm to estimate model parameters and quantify their uncertainties in a fractional-order lumped-element model of the human ear in a Bayesian inference framework. The model, originally developed by Naghibolhosseini and Long (2018), incorporates fractional-order elements to capture viscoelastic memory effects in ear tissues that otherwise cannot adequately be represented via conventional integer-order models. Using previously optimized model parameters to construct informative priors, we perform Bayesian parameter estimation via the No-U-Turn Sampler (NUTS) implementation. From the inferred posterior distributions, we compute the model's outer-middle ear gain (OMEG) and validate predictions against experimental OMEG derived from DPOAE measurements. Additionally, we compare stapes velocity transfer functions and ear canal pressure gain with established experimental and computational literature. HMC sampling yields well-convergent posterior distributions for all parameters, centered near original optimized values with uncertainty quantified through credible intervals. The posterior predictive OMEG frequency response closely matches the experimental OMEG measurements. Interestingly, the Bayesian-derived parameter sets correctly exhibit stapes velocity resonances near 1 kHz and ear canal pressure gain peaks between 2.5 and 4 kHz, with amplification ranging from 4 to 12 dB, consistent with cadaveric experimental measurements and existing computational models. The model demonstrates a minimal intersubject variability while capturing realistic biological variations within experimentally reported ranges. The present Bayesian HMC simulation approach then provides a robust uncertainty quantification for fractional-order ear model parameter inference, maintaining physiologically consistent predictions across multiple validation datasets. Hence, the proposed framework enhances the model's credibility by establishing a firm foundation for further developing probabilistic diagnostic tools for hearing assessment in the future.