slide3 bme adat_2015

session#3 Divényi János @divenyi.janos

b.socrative.com

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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

om

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?