留学生辅导 p ← – cscodehelp代写

p ←
(
weather – – Weather)

=
|%÷:)
8 Weather €
{sung , cloudy
sung)=
on
rainy,
– – if

Joint Probability Tables
Consider the joint probability table for the three binary variables P , Q and R: p 9p
qqqq r 0.002 0.328 r 0.231 0.036
P÷{ . c -Trenn, King’s College London
0.008 0.182 0.169 0.044
CalculatePp q,r| pq ̈Ppp,q,rq.
0008=0.004339
%÷÷

0.55
2

Bayes’ Rule
You have two cookie jars in front of you. Both cookie jars contain vanilla and chocolate cookies, but in different proportions.
You’re blindfolded and told to pick a cookie at random from one of the two jars.
After picking, you’re told that you selected a vanilla cookie. What is the probability
that you picked the cookie from the first jar?
c -Trenn, King’s College London 3

Bayes’ Rule
You’re blindfolded and told to pick a cookie at random from one of the two jars. After picking, you’re told that you selected a vanilla cookie. What is the probability that you picked the cookie from the first jar?
c -Trenn, King’s College London 4

Bayes’ Rule
=P 174
You’re blindfolded and told to pick a cookie at random from one of the two jars. After picking, you’re told that you selected a vanilla cookie. What is the probability that you picked the cookie from the first jar?
J indicator variable that we picked from the first jar V indicator variable that we picked a vanilla cookie
=PCVb)P#
pain =P”¥¥”‘=p%•÷mÉ¥*G¥-
c -Trenn, King’s College London
=1¥,⇒= Is
5

Bayes’ Rule
You’re blindfolded and told to pick a cookie at random from one of the two jars. After picking, you’re told that you selected a vanilla cookie. What is the probability that you picked the cookie from the first jar?
J indicator variable that we picked from the first jar
V indicator variable that we picked a vanilla cookie
PpJ|V q “ PpV |JqPpJq “ 0.6 P pV q
c -Trenn, King’s College London 6

Surgery Medication
78% (273/350)
83% (289/350)
c -Trenn, King’s College London
7

Surgery Medication
93% (81/87) 73% (192/263)
87% (234/270) 69% (55/80)
small tumour large tumour
c -Trenn, King’s College London
8

00
small tumour large tumour total
Surgery Medication 93% (81/87) 87% (234/270)
73% (192/263) 69% (55/80)
78% (273/350)
83% (289/350)
¥-50
-0.93
+0.73-32%1=0.78
c -Trenn, King’s College London
9

Surgery Medication
93% (81/87) 73% (192/263)
87% (234/270) 69% (55/80)
78% (273/350)
83% (289/350)
small tumour
large tumour
total
The sizes of the groups are very different. Small tumour cases are mostly treated with medication. Large tumours with surgery.
Success rate depends on (confounding) variable size! Large tumours have a small success rate.
In short, medication appears incorrectly to be more successful, because of the bias in the treatment. But surgery is actually the better option!
c -Trenn, King’s College London 10