Maximum entropy psychophysics
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Maximum entropy psychophysics
MAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State Univ Maximum entropy psychophysics versityCorrespond with:Peter KilleenDepartment of Psychology-Box 1104Arizona Slate UniversityTempe, AZ 85287-1104email: killeen@asu.edu FAX: (480) 965-8544 Voice: (480) 965-2555MAXENT ROC 3Bits of the ROC:Signal Detection as Information TransmissionSignal Detection Theory (SDT) and Information Theor Maximum entropy psychophysics y (IT) were the jewels in the crown of 20th century experimental psychology. As an avatar of statistical decision theory. SDT provided a technique forMaximum entropy psychophysics
reducing a 2x2 (able of relations between stimulus and response into measures of detectability and bias, of sensitivity and selectivity, thereby untaMAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State Univ Maximum entropy psychophysics elman (1991). Information theory, the brilliant invention of Claude Shannon (Shannon. 1949). provided algorithms for quantifying the amount of information transmitted by a response. Although both theories were formulated at the same time (the late 1940s), and both concern similar phenomena (quantify Maximum entropy psychophysics ing the accuracy of imperfect discriminations), there has been very little use of one theory to reinforce and complement (he other. By the end of theMaximum entropy psychophysics
2 0’h century, SDT remains an important theory while IT is rarely mentioned.Classic SDT (here. CSDT) is an application of Thurstone scaling (see. c.g.MAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State Univ Maximum entropy psychophysics intensity, some are not. These latter are often of most central concern tosociety, involving measures of complex stimuli such as beauty, qualityMAXENT ROC4of life, impact of punishment. Thurstone suggested a metric for the distance between stimuli that would embrace both the simple and complex: The Maximum entropy psychophysics unit of distance between stimuli would be the standard deviation of the percept associated with the stimulus. Thurstone called the distribution of peMaximum entropy psychophysics
rceptions issuing from a stimulus a "discriminal process”, and its standard deviation Ơ the “discriminal dispersion”. Two such processes are shown in MAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State Univ Maximum entropy psychophysics y is inferred. Table I shows the joint probabilities of signals and responses. In Table 2, these are divided by the row marginals to give the conditional probabilities of responding “A” or “B” given the stimulus value.Although here viewed as a symmetric discrimination, the origin of CSDT was in dete Maximum entropy psychophysics ction tasks, where Su was the background, or noise stimulus. This gave rise to the terminology of Correct Rejection (CR) for responses in the R,Sa celMaximum entropy psychophysics
l, and Misses (M) for responses in the R-.Sy, cell.+ + Tables 2 & 3 about here ++Table 2 describes the performance from the perspective of an experimeMAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State Univ Maximum entropy psychophysics the applications of SDT, we are usually given the response--the verdicts of radiologists, juries, and children who cry "wolf’- and wish to know the probability that a signal was in fact present. This requires dividing the cells in Table 1 by their columnMAXENT ROC 5marginals, yielding Table 3. One m Maximum entropy psychophysics ay go between Tables 2 & 3 by using Bayes’ theorem to convert the arguments of a conditional probability. Table 3 is more user-friendly, in that consuMaximum entropy psychophysics
mers of SDT analyses are seldom given the state of nature, and wish to evaluate that state, not characterize the detector. The impact of these differeMAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State Univ Maximum entropy psychophysics conventional Table 2, but only 1% by Table 3. No matter how Table I is conditionalized it has two degrees of freedom, and no evaluation of a discrimination is complete without reporting both accuracy of affirmatives and accuracy of negatives. Table 3 is often more convenient for information-theoret Maximum entropy psychophysics ic analyses.CSDT invokes normal discriminal processes to translate the probabilities in Table 2 into the two measures of theoretical interest (d.’ andMaximum entropy psychophysics
C). Other distributions are reviewed by Egan (1975). The data are often consistent with these assumptions. However, the discriminal processes are nevMAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State Univ Maximum entropy psychophysics means and standard deviations of signal and noise distributions, and the location of the criterion. These overendowed distributions are then slimmed down by stipulating an origin and unit for the perceptual abcissae. The origin is set either at the mean of the first percept, or halfway between the Maximum entropy psychophysics means of the two percepts (as inferred from the data). The unit—the standard deviation—is set to1.0. This leaves the scale value of the second stimuluMaximum entropy psychophysics
s, d.' and the MAXENT ROC 6 location of the criterion, c, as the recovered parameters that re-present the information found in the hit and false alarmMAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State Univ Maximum entropy psychophysics Macmillan and Creelman (1991.Equation2.2) include the factor 1/2 so that the range of the bias statistic is the same as that of 1E- For the data in Table 2, £ = -(0.385 -0.675) = 0.29. As shown in Figure I. the criterion is slightly above the mean of the percepts, indicating a conservative criterion Maximum entropy psychophysics : The observer is more likely to reject a marginal perception as noise than to accept it as a signal.CSDT was a trail breaking innovation. Now standinMaximum entropy psychophysics
g near the summit, a glance back shows that CSDT did not pick out the most direct route to the goal OÍ representing discrimination performance. Too muMAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State Univ Maximum entropy psychophysics a condign sense of parsimony. Macmillan and Creelman (1996) reviewed these alternatives in an article whose title hedged “nonparametric”, because the measures reviewed either made subtle assumptions of underlying distributions or mechanisms--or were at least consistent with such distributions.SuhsHD Maximum entropy psychophysics ipiisin__PsychophysicsIt this paper we make assumptions about mechanisms and distributions in incremental fashion, in the style of Brooks (1991). whoMaximum entropy psychophysics
coined the term subsumption architecture to describe such a bottom-upMAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State UnivMAXENT ROC 1Running head: MINIMAL SDTBits of the ROC:Signal Detection as Information TransmissionPeter R. Killeen & Thomas J. TaylorArizona State UnivGọi ngay
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