Signal detection theory

General assumptions of the SDT framework

• The evidence used by the observer to make the decision can be represented by a single continous number \(x\) (Gold & Shadlen, 2007; Green & Swets, 1966; Swets, 1961).

  • Examples:
    • Ouput of a neuron

• \(x\) is a sample from a random variable \(X \in \mathcal{X}\) (Gold & Shadlen, 2007; Green & Swets, 1966).

• The decision rule \(d \in \mathcal{D}\) to choose and action \(a \in \mathcal{A}\) is established by using a simple criterium \(\beta\) on a decision variable \(W(x)\) (Gold & Shadlen, 2007; Green & Swets, 1966; Wickens, 2001).

• \(W(x)=\Lambda(x)\) for simple hypothesis tests. (Gold & Shadlen, 2007; Green & Swets, 1966; Kay, 1998; Wickens, 2001). This decision rule has good properties even when \(\beta\) iss not choose to produce optimal performance.

Not assumed

• No probalistic computation: the observer does not have access to the representation of uncertainty on a trial-by-trial basis (Ma, 2012).

Predictions

• Given an particular SDT model, some estimated parameters should be consistent across tasks (Green & Swets, 1966; Wickens, 2001).

  • For example under the equal variance normal model, \(\widehat{d'}\) should be the same independently on whether the task is Yes-No, Rating or 2AFC.

• Given an particular SDT model, some estimated parameters should be aproximately constant while the otherss vary (Green & Swets, 1966; Wickens, 2001).

  • For example under the equal variance normal model, \(\widehat{d'}\) should be the same independently on \(p_{FA}\) (Green & Swets, 1966; Wickens, 2001) .

References

Gold, J. I., & Shadlen, M. N. (2007). The neural basis of decision making. Annu. Rev. Neurosci., 30, 535–574.

Green, D., & Swets, J. (1966). Signal detection theory and psychophysics. 1966. New York, 888, 889.

Kay, S. M. (1998). Fundamentals of statistical signal processing, vol. II: Detection theory. Signal Processing. Upper Saddle River, NJ: Prentice Hall.

Ma, W. J. (2012). Organizing probabilistic models of perception. Trends in Cognitive Sciences, 16(10), 511–518.

Swets, J. A. (1961). Is there a sensory threshold. Science, 134(3473), 168–177.

Wickens, T. D. (2001). Elementary signal detection theory. Oxford University Press.