Bayesian methods for inverse problems offer higher robustness to noise and uncertainty than deterministic, yet accurate, inference methods. Both types of techniques typically focus on finding optimal model parameters that minimize an objective function, which compares model output with some acquired data. However, uncertainties coming from different sources, such as: (1) the material manufacturing process, (2) material’s mechanical properties, (3) measurement errors, or (4) the model and its parameters, may cause inference errors and loss of information should they are not properly taken into account. These uncertainties might have important safety and economic consequences in damage-related applications, such as in structural health monitoring of aerospace structures. This paper aims at illustrating the benefits of using probability based methods instead of deterministic approaches. A case study is presented, which illustrates the use of a hyper-robust Bayesian damage localization method when compared to a deterministic one. The results show that Bayesian inverse problem is more robust to data noise and uncertainties stemming from the model parameters than deterministic methods.