In this paper, a modeling extension for the description of wave propagation in rigid porous media at high frequencies is used. To better characterize the visco-inertial and thermal interactions between the fluid and the structure in this regime, two additional characteristic viscous and thermal surfaces R and R0 are taken into account, as initially introduced in Kergomard, Lafarge, and Gilbert [Acta Acust. Acust. 99(4), 557–571 (2013)]. This extends the modeling order of the dynamic tortuosity and compressibility. A sensitivity analysis is performed on the additional parameters, showing that only the viscous surface R has an influence on transmitted waves in the high frequency regime, for materials having a low viscous characteristic length. A general Bayesian inference is then conducted to infer simultaneously the posterior probability densities of the parameters associated with the visco-inertial effects, i.e., the porosity, tortuosity, the viscous characteristic length, and the viscous characteristic surface. The proposed method is based on the measurement of waves transmitted by a slab of rigid porous material in the time domain. Bayesian inference results obtained on three different porous materials are presented.