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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.

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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.

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