Signal Detection Theory and ROC-analysis

2IFC assume Bernoulli counter Bernoulli distributions Bernoulli trials binomial distribution chi-square distributions chi-square ROCs constant cutoff decision axis decision goal decision rule density functions distribution function equal prior probabilities equal-variance equation example expected value false-alarm rate family of ROCs fixed gamma distributions gamma observer gamma ROCs Gaussian geometric distribution given hit rate increases integral isocriterion contour L(xo likelihood ratio likelihood-ratio observer max-P max-P(C monotone likelihood-ratio family n-distribution N-N ROC negative binomial distribution negative diagonal negative exponential distributions Neyman-Pearson observer noise normal distributions observation interval P(sn P(Yn P(Ysn pair of distributions Poisson counting Poisson distribution Poisson observer Poisson process power-law ROC prior probabilities probability distributions proper decision variable proper ROC psychometric functions psychophysics random variable ROCs based say yes shows signal detection theory slope sn-trials square-root law straight-line segments strictly monotone Swets tion transformation λη μεη μη ση