Distributional assumptions and observed conservatism in the theory of signal detectability
type: Item
instance of: scholarly article
title: Distributional assumptions and observed conservatism in the theory of signal detectability
zbMATH Open document ID: 0763.92014
DOI: 10.1016/0022-2496(91)90043-S
author: Laurence T. Maloney
author: Ewart A. C. Thomas
published in: Journal of Mathematical Psychology
publication date: 1992-06-28T00:00:00Z
review text: A model of the observer's behaviour from the theory of signal detectability (TSD) is investigated. The main characteristics of this model are distribution functions of the noise, noise and signal, and corresponding probability distributions. Certain assumptions on the type of these distributions are also always supposed. As usual they are supposed to be Gaussian with the same standard deviation, and certain means. The decision rule that allows the observer to distinguish noise or signal with noise in a given trial is also a characteristic of the TSD model. The process of estimation of these variables to identify the empirical observer to match the observer's behaviour to a specific model observer is considered. It is concluded that the classical model that is mostly used by the experimenter might not match the one used by the observer. Necessary and sufficient conditions for an optimal observer to appear conservative when fitted by distributions different from those governing his choices are derived. The results presented show also that conventional distributional assumptions made in fitting observer's data in signal detection tasks are potential sources of error, and appeared to be unnecessary. Two subsets of TSD called location TSD and S3 are defined. They represent the generalisations of the equal-variance Gaussian TSD where the distribution is considered to be different from the Gaussian, and some other conditional assumptions are posed on the distribution functions and their probabilities. The Gaussian and Laplacian distributions are members of S3, and S3 is a subset of the location TSD. It is shown that the choices of distributions mimic the observer's conservative behaviour. A more general class of location-scale TSDs that includes all TSD types mentioned before is also briefly considered. That class doesn't restrict the type of distribution functions as well as has a free scaling parameter in the location definition. The problem of uniqueness of the location…
Mathematics Subject Classification ID: 91E30
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 94A13
zbMATH DE Number: 34264
zbMATH Keywords: Gaussian distributions
zbMATH Keywords: observer's behaviour
zbMATH Keywords: noise
zbMATH Keywords: decision rule
zbMATH Keywords: estimation
zbMATH Keywords: signal detection
zbMATH Keywords: location TSD
zbMATH Keywords: S3
zbMATH Keywords: Laplacian distributions
zbMATH Keywords: location-scale TSDs
zbMATH Keywords: problem of uniqueness
zbMATH Keywords: sensory criterion rule
zbMATH Keywords: isosensitivity curve
zbMATH Keywords: receiver operating characteristic
zbMATH Keywords: empirically observable part
zbMATH Keywords: contour
zbMATH Keywords: distributional information
zbMATH Keywords: conservative observers
zbMATH Keywords: radical observers
reviewed by: Frada Burstein
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 34264