Statistical model: Difference between revisions

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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 [[stimulation|stimulus]], for example one administered by a researcher.
 
==Fields of application==
 
Stimulus–response models are applied in international relations,<ref>
{{cite book
  | title = What causes war?: an introduction to theories of international conflict
| chapter = International Interaction: Stimulus–Response Theory and Arms Races
| author = Greg Cashman
| publisher = Lexington Books
| year = 2000
| isbn = 978-0-7391-0112-4
| pages = 160–192
| url = http://books.google.com/books?id=I9xIfeijGhMC&pg=PA167&dq=stimulus-response-model+statistical#v=onepage&q=stimulus-response-model%20statistical&f=false
}}</ref>  
[[:en:Neuropsychological_test|psychology]],<ref>
{{cite book
| title = The Counselor's Companion: What Every Beginning Counselor Needs to Know
| editor = Jocelyn Gregoire and Christin Jungers
| chapter = Counseling Across the Life Span
| author = Stephen P. Kachmar and Kimberly Blair
| publisher = Routledge
| year = 2007
| isbn = 978-0-8058-5684-2
| page = 143
| url = http://books.google.com/books?id=5V9nvsKeBgIC&pg=RA1-PA143&dq=stimulus-response-model++behavior#v=onepage&q=stimulus-response-model%20%20behavior&f=false
}}</ref>
risk assessment,<ref>
{{cite book
| title = Analyzing environmental data
| chapter = Quantitative Risk Assessment with Stimulus–Response Data
| author = Walter W. Piegorsch and A. John Bailer
| publisher = John Wiley and Sons
| year = 2005
| isbn = 978-0-470-84836-4
| pages = 171–214
| url = http://books.google.com/books?id=FrNv8AwkoKgC&pg=PA172&dq=stimulus-response-model+statistical#v=onepage&q=stimulus-response-model%20statistical&f=false
}}</ref>
[[:en:Neuroscience|neuroscience]],<ref>
{{cite book
| title = Computer simulation in brain science
| chapter = Neurons with hysteresis?
| author = Geoffrey W. Hoffmann
| editor = Rodney Cotterill
| publisher = Cambridge University Press
| year = 1988
| isbn = 978-0-521-34179-0
| pages = 74–87
| url = http://books.google.com/books?id=B6nfz--ePEEC&pg=PA79&dq=stimulus-response++neuron#v=onepage&q=stimulus-response%20%20neuron&f=false
}}</ref>
neurally-inspired system design,<ref>
{{cite book
| title = Systems methodology for software
| author = Teodor Rus
| publisher = World Scientific
| year = 1993
| isbn = 978-981-02-1254-4
| page = 12
| url = http://books.google.com/books?id=l7o31p-6dlAC&pg=PA12&dq=stimulus-response-model++neuron#v=onepage&q=stimulus-response-model%20%20neuron&f=false
}}</ref>
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|date=August 2009}}
 
: <math>E(Y) = f(x)</math>
 
A common simplification assumed for such functions is linear, thus we expect to see a relationship like
 
: <math>E(Y) = \alpha + \beta x.</math>
 
[[Statistical theory]] for [[linear model]]s has been well developed for more than fifty years, and a standard form of analysis called [[linear regression]] has been developed.
 
==References==
 
<references/>
 
{{DEFAULTSORT:Stimulus-Response Model}}
[[Category:Behavioral concepts]]
[[Category:Specific models]]
 
 
{{statistics-stub}}

Revision as of 01:01, 1 February 2014

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:Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

E(Y)=f(x)

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

E(Y)=α+βx.

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. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  2. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  3. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  4. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  5. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534


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