Acoustic Wavenumber Spectroscopy (AWS) is a technique for nondestructive testing and evaluation capable of identifying local damage in thin plates through the estimation of the characteristic wavenumber of propagating elastic waves. Current state of the art in AWS estimates wavenumber based on the maximum data fit of the wavenumber dispersion curve and derives thickness deterministically through the Lamb wave equations. Successful determination of thickness from the measurements through inverse analysis is dependent upon two aspects: uncertainties regarding material properties of the system (parametric uncertainty) and uncertainties regarding data collected in the field under less than ideal conditions (experimental uncertainty). Thus, the deterministic approach may lead to large false positives in the presence of parametric and experimental uncertainties. The focus of this paper is to develop a stochastic approach for inferring thickness from the measurements in which both parametric and experimental uncertainties are accounted for. Herein, parametric uncertainty is managed by calibrating material-dependent properties using wavenumber measurements. Experimental uncertainty is controlled through incorporation of expert judgment by means of an elicited prior uncertainty of thickness. The technological advancement produced in this study is demonstrated on a case study application of an aluminum plate with imposed thinning.