Distributional assumptions and observed conservatism in the theory of signal detectability
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- scale TSD is defined but not solved. Some assumptions on the sensory criterion rule are also made. Conservative and radical types of observer are defined based on the value of payoffs and prior odds that s/he chooses in a sensory criterion rule. They are compared with the optimal one that was considered before. The isosensitivity curve as a receiver operating characteristic is considered representing the empirically observable part of the TSD model. The relationship between isosensitivity curves (contour) and various types of TSD is studied. It is proved that in location TSD distributional information can be completely identified from the correspondent isosensitivity curve without any preliminary assumptions about the observer's underlying distribution. Some suggestions about how to represent isosensitivity curves in practice using different types of distributions are presented.
scientific article; zbMATH DE number 34264