session 2 university of southern california ise500 thursday, august 28, 2014 geza p. bottlik page 1...

Session 2University of Southern California

ISE500 Thursday, August 28, 2014

Geza P. Bottlik

Outline

• Questions, Comments?

• Quiz next Tuesday

• Take roll

• Example of Quiz Results

• Lecture



Geza P. Bottlik

What are we going to learn and apply?

Acquiring data

Analyzing data

Organizing data

Making inferences and drawing conclusions

Presenting results

How people make decisions and the traps they fall into

Using traditional and Bayesian analysis



Geza P. Bottlik

Bayesian

make assumptions about distributions, gather data, revise assumption

Traditional

Hypothesize about facts, gather data, make a conclusion



Geza P. Bottlik



Geza P. Bottlik

Two bags with green and white chips – the value of a sample

Bag A has 70 green chips, 30 white chips

Bag B has 30 green chips, 70 white chips

What is the chance that you can correctly identify which bag is which without taking out any chips?

Suppose I pick a bag at random and then pick 12 chips from it, one at a time, each time replacing the chip and mixing up the bag. I find that 8 chips are green.

What is the probability that it is the bag with 70 green chips?



Geza P. Bottlik

Two bags with green and white chips

Bag A has 70 green chips, 30 white chips

Bag B has 30 green chips, 70 white chips

What is the chance that you can correctly identify which bag is which without taking out any chips? 50%

Suppose I pick a bag at random and then pick 12 chips from it, one at a time, each time replacing the chip and mixing up the bag. I find that 8 chips are green.

What is the probability that it is the bag with 70 green chips?

If it is the green bag .7^8*.3^4 = 0.00047

If it is the white bag .3^8*.7^4 = 0.000016

Probability that it is the green bag =

= 0.00047/(0.00047+0.000016) = 96.7% Class answers 80,60,67,85,75,70,67

Odds =96.7/3.3 = 29.6



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Is the population of Iceland greater then 1,500,000?

Is the population of California less than 20,000,000?

Is the area of Cyprus greater than 100,000 km^2?



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Anchoring

Is the population of Iceland greater then 1,500,000? 9/42 Yes

329,807

Is the population of California less than 20,000,000? 11/42 Yes

39,309,017

Is the total area of Cyprus greater than 100,000 km^2? 12/42 Yes

9251



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Confirmation of beliefs



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Base rates

The occurrence of Tuberculosis (TB) in the US is 4.6/100,000

If we test a person at random with one of the traditional test, the effectiveness of the test can be described as follows:

3% of the time a person without the disease will test positive

10% of the time a person who has the disease will test negative

If a person is chosen at random from the population and tests positive, what is the probability that he/she has the disease?



Geza P. Bottlik

Base rates

The occurrence of Tuberculosis (TB) in the US is 4.6/100,000

If we test a person at random with one of the traditional test, the effectiveness of the test can be described as follows:

3% of the time a person without the disease will test positive

10% of the time a person who has the disease will test negative

If a person is chosen at random from the population and tests positive, what is the probability that he/she has the disease?

0.14% correct. Class answers 98%,91%,97%,95%,93%,90%

Before the test is was 0.0046%

The test said 90%



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Monte Hall



Geza P. Bottlik

Monte Hall only 14/42 switched

session 2 university of southern california ise500 thursday, august 28, 2014 geza p. bottlik page 1...

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