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.
The first jar contains 30 vanilla cookies and 10 chocolate cookies. The second jar contains 20 vanilla cookies and 20 chocolate cookies.
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
The first jar contains 30 vanilla cookies and 10 chocolate cookies. The second jar contains 20 vanilla cookies and 20 chocolate cookies.
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
The first jar contains 30 vanilla cookies and 10 chocolate cookies. The second jar contains 20 vanilla cookies and 20 chocolate cookies.
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
The first jar contains 30 vanilla cookies and 10 chocolate cookies. The second jar contains 20 vanilla cookies and 20 chocolate cookies.
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

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

Simpson’s Paradox
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

Simpson’s Paradox
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

Simpson’s Paradox
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

Simpson’s Paradox
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!
How could one design a study that would not have these problems?
c -Trenn, King’s College London 11