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 ) !