Uncertainties and interdependence of porous parameters using Bayesian model-based analysis

Traditional modeling for sound propagation in porous media has been done knowing the macroscopic physical parameters intrinsic to the material. Using Bayesian model-based analysis the uncertainties of these parameters and their effect on the accuracy of the selected model can be studied. The Horoshenkov Model [Horoshenkov, et al., JASA vol 139 (2016)], or similarly Miki Model [Miki, JASJ, vol 11, pp.25-28 (1990)], can be used to estimate the mean pore size and porosity of the material under test from measurements of surface impedance or absorption coe cient using glass beads of known diameter and layer thickness as an experimental model. The accuracy of these models can be compared using quantitative measures such as mean, variance and the interdependence of the estimated parameters. This paper discusses the error and likelihood of several models using the experimentally measured data sets.