1. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 1 Outline Questions, Comments? Quiz next Tuesday Take roll Example of Quiz Results Lecture

2. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 2 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

3. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 3 Bayesian make assumptions about distributions, gather data, revise assumption Traditional Hypothesize about facts, gather data, make a conclusion

4. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 4

5. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 5

6. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 6 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?

7. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 7 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

8. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 8 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?

9. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 9 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

10. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 10 Confirmation of beliefs

11. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 11 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?

12. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 12 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%

13. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 13 Monte Hall

14. Session 2 University of Southern California ISE500 Thursday, August 28, 2014 Geza P. Bottlik Page 14 Monte Hall only 14/42 switched