# Stimulus–response model

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The stimulus–response model is a characterization of a statistical unit (such as a neuron) as a black box model, predicting a quantitative response to a quantitative stimulus, for example one administered by a researcher.

## Fields of application

Stimulus–response models are applied in international relations,[1] psychology,[2] risk assessment,[3] neuroscience,[4] neurally-inspired system design,[5] and many other fields.

## Mathematical formulation

The object of a stimulus–response model is to establish a mathematical function that describes the relation f between the stimulus x and the expected value (or other measure of location) of the response Y:[citation needed]

$E(Y) = f(x)$

A common simplification assumed for such functions is linear, thus we expect to see a relationship like

$E(Y) = \alpha + \beta x.$

Statistical theory for linear models has been well developed for more than fifty years, and a standard form of analysis called linear regression has been developed.

## References

1. ^ Greg Cashman (2000). "International Interaction: Stimulus–Response Theory and Arms Races". What causes war?: an introduction to theories of international conflict. Lexington Books. pp. 160–192. ISBN 978-0-7391-0112-4.
2. ^ Stephen P. Kachmar and Kimberly Blair (2007). "Counseling Across the Life Span". In Jocelyn Gregoire and Christin Jungers. The Counselor's Companion: What Every Beginning Counselor Needs to Know. Routledge. p. 143. ISBN 978-0-8058-5684-2.
3. ^ Walter W. Piegorsch and A. John Bailer (2005). "Quantitative Risk Assessment with Stimulus–Response Data". Analyzing environmental data. John Wiley and Sons. pp. 171–214. ISBN 978-0-470-84836-4.
4. ^ Geoffrey W. Hoffmann (1988). "Neurons with hysteresis?". In Rodney Cotterill. Computer simulation in brain science. Cambridge University Press. pp. 74–87. ISBN 978-0-521-34179-0.
5. ^ Teodor Rus (1993). Systems methodology for software. World Scientific. p. 12. ISBN 978-981-02-1254-4.