Probabilistic models of perception

Abstract

Mental representations of objects may fluctuate or change from moment to moment. Many models of similarity, identification, classification, and preferential choice are deterministic. These models cannot formally account for perceptual fluctuations. In this thesis, it is assumed that there exists a probability density function for psychological magnitudes (usually assumed to be multivariate normal) and a judgment function which defines how these magnitudes are used to make a particular decision. Based on these ideas, probabilistic models of triad discrimination, similarity, identification and preferential choice are derived and evaluated. Several of these models can account for differences in self-similarity, asymmetric similarities and violations of the triangle inequality because the metric axioms are not assumed to apply to proximity measures among stimulus means. A paradox, created when deterministic models of identification are compared, concerning the universal form of the similarity function and the distance metric, is resolved using a probabilistic model. The use of nonlinear least squares to estimate parameters is illustrated in the case of several of the models. Fechner-Thurstone models, in which stimulus variability, a psychophysical transformation, and psychological variability are formally included, are discussed