Technical clarification to Silbert and Thomas (2013): "decisional separability, model identification, and statistical...

Area of Science:

• Cognitive psychology
• Psychophysics
• Mathematical psychology

Background:

• The Silbert and Thomas (2013) theorem explored equivalences between perceptual and decisional separability.
• Understanding these separability concepts is crucial for modeling human perception and decision-making.

Purpose of the Study:

• To provide a minor technical correction to part (ii) of the main theorem in Silbert and Thomas (2013).
• To clarify the conditions under which perceptual separability can mimic decisional separability.

Main Methods:

• Theoretical analysis of the Silbert and Thomas (2013) theorem.
• Examination of the role of stimulus invariance and covariance matrices in perceptual and decisional separability.

Main Results:

• Part (ii) of the theorem requires the assumption of stimulus invariance for equivalence when mimicking decisional separability with a perceptually separable configuration.
• Stimulus invariance holds when all covariance matrices within the stimulus configuration are identical.
• Part (i) of the theorem remains unaffected, allowing mimicry without restricting covariance matrices.

Conclusions:

• The scope of the equivalence in Silbert and Thomas (2013) is somewhat limited by the requirement of stimulus invariance under specific conditions.
• The findings highlight the importance of considering stimulus properties, such as covariance matrices, in models of perception and decision-making.