|Muon tomography is a novel imaging technique that uses cosmic rays (muons) to image cargo containers to detect shielded packages of high-Z nuclear materials. Muons have high energy and are capable of penetrating meters of rock, which make it suitable to examine cargos. The advantage of muon tomography is that it does not require an artificial source. It complements other active and passive detection techniques, such as neutron imaging, X-ray, gamma ray (Compton camera), etc. In our work, we are developing Bayesian image reconstruction methods for muon tomography. We aim to improve the detection performance of muon tomography by incorporating prior distribution on muon scattering images and by developing accurate statistical model of muon scattering data. We evaluated the performance of our method using the receiver operating characteristic (ROC) and found that the Bayesian approach can greatly improve the detection performance. This work is done in collaboration with LANL and is supported by DOE.