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By Berhane K., Thomas D. C.

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Theory, the optimal way to package evidence concerning the signal is to use the likelihood r a t i o ~ t h e ratio of the density of sensory data assuming a signal trial to the density of the same data assuming a noise-alone trial. Large values of the likelihood ratio favor the presence of the signal. However there remains considerable flexibility in the choice of a decision statistic: any strictly increasing function of the likelihood ratio produces an equivalent decision rule and leads to identical detection performance.

COSS analysis provides an algorithm for estimating these weights in empirical data. ,. -,. (lid') 2 z e 1 The Representational Measurement Approach to Problems 17 observer's do not usually employ equal weights, even when, as in Nosofsky's paradigm, they should; rather, the pattern of weights takes on a variety of shapes depending on the structure of stimuli and the demands of a particular task. Berg (1989), Berg (1990), and Berg and Green (1990) discuss tasks that produce rather different weight patterns.

Green and R. D. Luce, in S. ), Attention and Performance (Vol. IV), New York: Academic Press, 1973, pp. 557 and 562. Reprinted with permission. inconsistencies, choice models are typically framed in terms of choice probabilities Pa,^, the probability of selecting an option a from Set A of alternatives. A random utility model for the choice probabilities involves the assumption that each alternative a is associated with a random variable U a that measures the (uncertain) value or utility of that alternative.

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