View
2
Download
0
Category
Preview:
Citation preview
EC40 2-(2018/19) LT
BAYES 'RULE ,
SIZE,
FD2RAGVIR MISSES - HIS - EC402-STUDENTS NOTES ?
Bayes' IIIe PARTI :
Rta ' R,
I WISH I WAS IN YourSH02 CLASSES 4 YEARS AGO !
- Say there is a RARE disease.
RARE : = 16 of pop has it
-
Say there is a DECENT test.
DECENT := 902 of the timethe test gets it
I ,right ,
- Yougo
to the doctor and oh no ! The test is positive!
- Q : Shouldyou be worried ?
At: Doctor says"
umm.
. .
sorry ,the test is correct
90% of the time.
Yes, Say bye . bye to
yourwife Landcat ) .
"
Al : Statisticiansays
" Doctors are idiots"
let see why . - -
D: went that you have disease" II:=:= 'IIPIG .
Then, PlD) = 0.01 PCDC ) = 0.99
1¥:*:: :The Idiot) doctor is pointing to PHD) and Pff D) .
He's a well -
defined idiot because :
lityou did NOT ask him" I've got the disease
.
What's the probability I
test positive ? "
④ you asked him" I've tested positive .
what's the probability I Ive
got the disease ? "
Let's ask the statistician to analyse . . .
Say there are 1000 people :
1000
%10 990
%Hi
③ I 1997 891
You knowyou are in one the 2 boxes - i. e. you
tested +.
What's the pub . you are in the red box?¥¥ DIFFERENCE
Ans :
9/(9+99)= 91 , of
a 102 I not 902 ) .
Go enjoy your life (and get a secondopinion) !
This is basically Bayes' rule
.
You don't need to draw
trees if youknow Bayes ' rule :
P1D nt ) =P + ) PE ) ID) P1D) →
defijfh.gs
⇒ PIDH ) = PHD ) PCD )( twice )
TFpT⇒→ Bayes
' rule !
We are"
reversingthe conditioning
"
=P HD) PCD ) → Bayes 't LOTP
PHD PIHDYPDIY
Pig numbers ⇒, I . . , . ,
=
. o.ua In
PARTI : But I'M NOT IN 5h02,
I'M IN EC40 2
- Think of Ho : D' ( You are
healthy) .
4 4- Reject the is a
"
discovery" I You discovered you have
a disease. )
- The size of the test is P( + I5) = 0 . I
- The False positive or
"
false discovery rate "
is P f) fie. 99/(9+99) false positive
proportion of all
the rejected hypotheses)Obviously ,
FDR = I - p @ It)= PAIDc) p④y/ PH4P @
+ PG1N)p%)'
In other words FDR = I - Pf¥p④PK1D) PP1-1PH
=I -
Gag =
IT99So it all lies together .
sizeBo Hombre :
"
444+1f- Pff 5)
The two are linked byBayes ' rule which allows us to
iiacse the conditioning" to
get what we actually want.
I DISAGREE.
THIS IS NOT
/ COMPATIBLEWITH # )
- If them is
true all
discoveryis false .FDR⇒.
99/99 .
¥PG15 ) the false
positives
PINKYya )
are dominatingthe total
proportion ofdiscoveries
because the disease is so 1108 )rare 4%1 that must people are L
healthy llotottmetto 's ) !
Recommended