An outlier can be an observation that arises from a different assumed model or a data point that is far away from the rest of the observations. Outlier detection has always been an indispensable part of any statistical inferences and analysis for its necessity in justifying our data inquiring process. Contaminated datasets without proper outlier treatments could increase the uncertainties in modeling or even produce misleading results. Current outlier detecting methods for Pulsar Timing Array analyses face challenging computational costs in obtaining posterior marginals and are lack of simplicity in implementation. And an outlier detection method has not been established in the present search for Supermassive Black Holes. Thus, we propose an outlier detection method with Gibbs Sampling that is versatile to Bayesian Hierarchical Modeling, thereby enabling the control of outlier contamination in both PTA analyses and Supermassive Black Hole bayesian inferences. We illustrate our proposed method through simulated sinusoidal time series and simulated Pulsar Timing Arrays. We then discuss the method’s validity, versatility, and simplicity in outlier detections based on the simulations’ results. We also apply the proposed outlier detection method to Pulsar J1909 - 3744 and Supermassive Binary Black Hole candidate PG1302 - 102.