All Models Are Right

download All Models Are Right

of 9

Transcript of All Models Are Right

  • 7/25/2019 All Models Are Right

    1/9

    All Models are Right

    ... most are useless

    Thaddeus Tarpey

    Wright State University

    [email protected]

    George Box's Quote

    George Boxs !uote"

    All Models are Wrong, some are useful"

    This quote is useful ... but wrong.

    #ere is an extended $uote"

    ... The fat that the !olnomial is an a!!roximation does not neessaril detrat from its usefulness

    beause all models are approximations. #ssentiall, all models are wrong, but some are useful.

    $owe%er, the a!!roximate nature of the model must alwas be borne in mind."

    From the book: Empirical Model-Building and Response Surfaces (1!"# p $%$ b' Box and

    raper)

    Models are Approximations %an approximations &e wrong'

    & ()*+ *his is +R,.& ()*+ is not wrong

    Stay (ositive

    When teahing, wh fous on the negati%e as!et of Box's quote)

    - lass, toda / will introdue regression models. -h, and b the wa, all these models arewrong."

    )nstead"

    - lass, toda we will introdue regression models whih an be %er useful a!!roximations to

    the truth."

    *alla+y o, Rei,i+ation

    0alla of 1eifiation) When an abstration 2the model3 is treated as if it were a real onrete entit. The falla of reifiation is ommitted o%er and o%er, e%en b statistiians, who belie%e a !artiular

    model re!resents the truth ... instead of an a!!roximation. The model is not wrong but treating the model as the absolute truth 2i.e. reifiation3 is wrong.

    A -ress A suit A Model

    /f a dress or suit fits niel, it is useful.../f the model fits the data niel, it an be a useful a!!roximation to the truth.

    /oes this model make me look fat0

    /o dear

    ), we /ust twea0 the language a &it

    )n the simple linear regression model

    Saying"

    Assume 4 is normal" is almost alwas wrong.

    Saying"

    Assume 4 is a!!roximatel normal" will often be aurate.

    A !uote

    (aul 1elleman writes"

    A model for data, no matter how elegant or orretl deri%ed, must be disarded or re%ised if it

    does not fit the data or when new or better data are found and it fails to fi them."

    mailto:[email protected]:[email protected]
  • 7/25/2019 All Models Are Right

    2/9

    From 2*ruth# amn *ruth# and Statistics in the 3ournal of Statistical Education# %44!)

    1ellemans $uote is use,ul ... &ut not always

    5ewton's 6nd 7aw of Motion 0 ma hasn't been disarded...

    ... e%en though it has been re%ised due to#instein's s!eial theor of relati%it

    0 ma is still a useful a!!roximation...aslong as ou don't go too fast.

  • 7/25/2019 All Models Are Right

    3/9

  • 7/25/2019 All Models Are Right

    4/9

  • 7/25/2019 All Models Are Right

    5/9

  • 7/25/2019 All Models Are Right

    6/9

  • 7/25/2019 All Models Are Right

    7/9

  • 7/25/2019 All Models Are Right

    8/9

  • 7/25/2019 All Models Are Right

    9/9