Signal Detection Theory and Psychophysics - Andrei Gorea

SDT: THE STANDARD MODELOptimal criteria“One very desirable objective, were it possible, would be to maximize p(S|s) whileminimizing p(S|n). A (…) weaker, but feasible, objective is to maximize the quantity{p(S|s) – p(S|n)}where is a constant, > 0. This is a reasonable goal, since it is achieved whenwhen p(S|s) is large and p(S|n) is small. The parameter establishes the relativeimportance of these two objectives in the sense that when p(S|s) is increased by anamount , then p(S|n) should increase by no more than / for the change to bedesirable.” (Green & Swets, 1966, p 20)The optimal given payoffs isβ opt =V CR + V FA p(n)V H + V omiss p(s)Where V is the value of the payoffs. When the payoffs (gains & costs) are balanced,the eq. above reduces toβ opt = p(n)p(s)