I don’t think this is correct . You can calibrate a threshold for a metric empirically without interpreting the metric probabilistically. Ie that z > N is empirically a good threshold for anomaly detection calls for no necessary further interpretation.
Sure, but for most processes that’ll yield disappointing performance.
Any tool can be used without regard for the consequences, but knowing a tool’s statistical properties yields know-how about the consequences of its application. It’s often a matter of the costs of error / stakes of the most problem at hand. Cheap solutions are often the best for cheap problems.
