This work introduces a framework for patient-specific calibration to characterize the properties of the abdominal aortic aneurysm (AAA) wall and the intraluminal thrombus (ILT). The study integrates medical imaging and biomechanics to improve the evaluation of rupture risk. We used 3D cine-magnetic resonance imaging (MRI) from four patients to reconstruct the geometries at end-diastolic and peak systolic phases. Finite element (FE) models were developed using an anisotropic Gasser-Holzapfel formulation for the wall and a neo-Hookean model for the ILT. To identify the material parameters, we performed 200 FE simulations for each patient sampling the parameter space. A Gaussian process surrogate model and Bayesian optimization were used to minimize the error between simulated and MRI-derived displacements. A key part of this study is the validation of these fitted parameters using experimental data from biaxial tests performed on the same patients' tissue samples. This comparison confirmed that the computational adjustment is consistent with the mechanical behavior observed in the laboratory. The results showed that including the ILT in the models is essential to avoid overestimating the peak wall stress (PWS). Specifically, models without ILT showed up to 90% higher stress values. The presence of the thrombus shifts the stress concentrations toward regions of the wall not covered by the ILT. In conclusion, the proposed methodology accurately reproduces physiological deformation patterns. The validation with biaxial experimental data demonstrates that this framework is a robust tool for personalized clinical assessment of AAA.