The Differential Evolution Adaptive Metropolis (DREAM) method, a Markov chain Monte Carlo approach, is used for optimization and uncertainty analysis of a radioactive source/shield system using pixelated measured data generated by radiation imagers, where each pixel in the image contains a gamma-ray spectrum with statistical uncertainty. DREAM uses this spectral information to determine source thickness and source strength while also propagating uncertainty from the measured data to the solution. Using measurements simulated with GEANT4, successful parameter reconstruction is demonstrated on a numerical test case in a slab/shield geometry. In the presence of statistical noise of 5-9%, parameters are calculated to better than 95% with 2σ error bars that generally encompass the actual values. In a test problem with real-world measurements, source strength per energy line is calculated to within 78-97% of the actual value.