## 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; J. A. 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 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).

## 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, the estimated parameters across tasks should be consistent (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, the estimated parameters should be consistent across criteria (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.