Autonomous agents must understand their environment to make decisions. Perception systems often interpret point cloud measurements to extract beliefs about their surroundings. A common strategy is to seek beliefs that are least likely to be false, commonly known as cost-based approaches. These metrics have limitations in practical applications, such as in the presence of noisy measurements, dynamic objects, and debris. Modern solutions integrate additional stages such as segmentation to counteract these limitations, thereby increasing the complexity of the algorithms while being internally flawed. An alternative strategy is to extract beliefs that are best supported by the data. We call these evidence-based methods. This difference allows for robustness to the limitations of using cost-based methods without needing complex additional stages. Essential perception tasks such as object pose estimation, point cloud odometry, and sensor registration are solved using evidence-based methods. The demonstrated approaches are simple, require minimum configuration and tuning, and circumvents the need for additional processing stages.