In this data-rich age, datasets often contain many observations and variables. Verifying the quality of a large dataset is a formidable task that is not to be completed by manual inspection. Therefore, methods that automatically perform well even when the dataset contains anomalous data points are needed. Robust procedures are designed to have this type of stability. A new general purpose robust estimator is introduced. This Bayesian procedure applies Gibbs sampling and data augmentation to achieve robustness by weighting the observations in the likelihood of Bayes' theorem. Because this new estimator relies upon simulation, it has several advantages over existing robust methods. The derivation of the new method will be presented along with examples that compare the new method to existing procedures.