# 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.
2. Stephen P. Kachmar and Kimberly Blair (2007). "Counseling Across the Life Span" Jocelyn Gregoire and Christin Jungers The Counselor's Companion: What Every Beginning Counselor Needs to Know, Routledge.
3. Walter W. Piegorsch and A. John Bailer (2005). "Quantitative Risk Assessment with Stimulus–Response Data" Analyzing environmental data, John Wiley and Sons.
4. Geoffrey W. Hoffmann (1988). "Neurons with hysteresis?" Rodney Cotterill Computer simulation in brain science, Cambridge University Press.
5. Teodor Rus (1993). Systems methodology for software, World Scientific.

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