Stimulus–response model

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, psychology, risk assessment, neuroscience, neurally-inspired system design, 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:


 * $$E(Y) = f(x)$$

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.