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Biometrika 1978 65(3):503-509; doi:10.1093/biomet/65.3.503
© 1978 by Biometrika Trust
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The threshold hypothesis for flash perception

DAVID EAVES and A. H. BURR

1Department of Mathematics, Simon Fraser University Burnaby, British Columbia
2Department of Biological Sciences, Simon Fraser University

The threshold hypothesis holds that the vector of L population proportions of flashes seen corresponding to L different flash intensities lies on a certain discrete family of curves in the unit L-cube. Tests are described of this sharp hypothesis against vague alternative hypotheses that these proportions are more or less unrelated. The calculations are described for the posterior distributions of the threshold number N of photons needed for flash perceptions and of a photon receptivity coefficient {alpha}. Each N indexes a curve over a > 0. The long standing data of Hecht, Shlaer & Pirenne (1942) are analysed and support the hypothesis. The posterior distributions of (N, {alpha}), of N, and posterior density of a are also given.

Key Words: Bayesian hypothesis test • Conditional prior ignorance • Visual threshold


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