When a response pattern does not fit a selected measurement model, one may resort to robust ability estimation. Two popular robust methods are biweight and Huber weight. So far, research on these methods has been quite limited. This article proposes the maximum a posteriori biweight (BMAP) and Huber weight (HMAP) estimation methods. These methods use the Bayesian prior distribution to compensate for information lost due to aberrant responses. They may also be more resistant to the detrimental effects of downweighting the nonaberrant responses. The effectiveness of BMAP and HMAP was evaluated through a Monte Carlo simulation. Results show that both methods, especially BMAP, are more effective than the original biweight and Huber weight in correcting mild forms of aberrant behavior.