Identifiability: Why Can the Same Result Have Different Explanations?

Identifiability does not ask whether an explanation exists. It asks whether observations can distinguish one explanation from another. Suppose a household uses 100 extra kilowatt-hours this month. From the total bill alone, the cause might be longer use of a heater or a fault in the hot-water system. If both causes produce the same result, the cause has not been uniquely identified.

The concept is close to observability but not identical to it. Observability asks whether signals allow us to infer an internal state. Identifiability goes further by asking whether several mechanisms could leave the same signals. Nor is it the same as accuracy: a model may fit the available data very well without being the only explanation.

Identifiability makes “insufficient evidence” more precise. Gathering more of the same aggregate data may not help. We may need separate meters, a changed observation condition, or a signal for which the competing explanations make different predictions. The real question is not how elegant an explanation sounds, but whether it has consequences that can distinguish it from its rivals.