slide3 bme adat_2015
TRANSCRIPT
session#3 Divényi János @divenyi.janos
b.socrative.com
Student login into room BMEADAT
QUESTION
DATA
ANALYSIS
PRESENTATION
QUESTION
DATA
QUESTION
DATA
ANALYSIS
How to find answersto relevant questions
using data
http://boredbug.com/wp-content/uploads/2015/08/onesecondbeforedisaster.jpg
http://www.webpages.uidaho.edu/ed571/571-Modules/M3/Sampling_Design-Funny.gif
QUESTION
DATA
ANALYSIS
How doesa new piece of
information
affects
what we knowabout the world?
ww
w.b
igs
toc
kp
ho
to.c
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P(A|B)
conditional probability
probability that A occurs given than B has occurred
Explained Visually
Problem #1
Mr. Jones has two children. The older child is a boy. What is the
probability that both children are boys?
Problem #1
Mr. Jones has two children. The older child is a boy. What is the
probability that both children are boys?
1/2
Problem #2
Mr. Smith has two children.At least one of them is a boy. What is the probability that both children are boys?
Problem #2
Mr. Smith has two children.At least one of them is a boy. What is the probability that both children are boys?
1/3
Problem #3
Mr. Gardner has two children. At least one of them is a boy born on Tuesday. What is the
probability that both children are boys?
Problem #3
Mr. Gardner has two children. At least one of them is a boy born on Tuesday. What is the
probability that both children are boys?
13/27
https://xkcd.com/795/
How doesa new piece of
information
affects
what we knowabout the world?
ww
w.b
igs
toc
kp
ho
to.c
om
Down syndrome screening
Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
Down if positive?
Down if positive?
Down if positive?
Down if positive?
P(+, Down) / (P(+, Down) + P(+, not Down))
Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
P(+, Down) / (P(+, Down) + P(+, not Down))
Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
P(+, Down) / (P(+, Down) + P(+, not Down))
0.83*0.0025 / (0.83*0.0025 + 0.047*0.9975)
Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
Down if positive 0.0424
P(+, Down) / (P(+, Down) + P(+, not Down))
0.83*0.0025 / (0.83*0.0025 + 0.047*0.9975)
Unconditional risk 1:400 = 0.0025
Discovery rate 0.83
False positive rate 0.047
Down if positive 0.0424
P(+, Down) / (P(+, Down) + P(+, not Down))
0.83*0.0025 / (0.83*0.0025 + 0.047*0.9975)
Bayes’ Theorem
P(B|A) = P(A|B) ∙ P(B)
P(A)
P(B|A) =P(A|B) ∙ P(B)
P(A|B) ∙ P(B) + P(A|not B) ∙ P(not B)
1% prevalence
99% accurate test
positive result means risk of
Simplistic example
1% prevalence
99% accurate test
positive result means risk of
50%
Simplistic example
In 1999 Sally Clark was accused for murdering her2 children after she sequentially claimed thatthey died in sudden infant death syndrome (SIDS).
The probability of SIDS is 1 in 8500.
In 1999 Sally Clark was accused for murdering her2 children after she sequentially claimed thatthey died in sudden infant death syndrome (SIDS).
The probability of SIDS is 1 in 8500.
1. If you were the judgewhat other probabilityyou would want to know?
2. Would you convict her?
In 1999 Sally Clark was accused for murdering her2 children after she sequentially claimed thatthey died in sudden infant death syndrome (SIDS).
The probability of SIDS is 1 in 8500.
1. If you were the judgewhat other probabilityyou would want to know?
2. Would you convict her?
3. Do you think she was convicted?
