Post on 28-Feb-2018
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7/25/2019 All Models Are Right
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All Models are Right
... most are useless
Thaddeus Tarpey
Wright State University
thaddeus.tarpey@wright.edu
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:thaddeus.tarpey@wright.edumailto:thaddeus.tarpey@wright.edu7/25/2019 All Models Are Right
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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.
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