#3214. On the empirical indistinguishability of knowledge structures

September 2026publication date
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Journal’s subject area:
Statistics and Probability;
Arts and Humanities (miscellaneous);
Psychology (all);
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Abstract:
The identifiability issue concerns two model parameter sets predicting an identical probability distribution on the response patterns. Both parameter sets are applied to the same knowledge structure. Empirical indistinguishability is a stronger form of unidentifiability, which involves not only the parameters, but also the structural and combinatorial properties of the model. In particular, as far as knowledge structures are concerned, a consequence of empirical indistinguishability is that the existence of certain knowledge states cannot be empirically established. Most importantly, it is shown that model identifiability cannot guarantee that a certain knowledge structure is empirically distinguishable from others.
Keywords:
empirical indistinguishability; forward and backward gradedness; identifiability; knowledge space theory

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