1. 1 Probability Scott Matthews Courses: 12-706 / 19-702/ 73-359 Lecture 15 - 10/19/2005

2. 12-706 and 73-3592 Admin Issues  HW 4, Project 1 due today  Lecture  Wednesday: First Project Ideas

3. 12-706 and 73-3593 Conditional Probability  “Probability (P) that A occurs conditional on B occurring”  Also referred to as “P of A given B”  Joint Probability: P(A and B)  Recall Venn diagram from chapter - finding portion of “Dow Jones Up” circle where “Stock Price Up” occurs.

4. 12-706 and 73-3594 Total Probability  Alternatively..  Probability of an event occuring alone is combination of all possible joint outcomes with another event  Given n mutually exclusive events (A 1..A n ) whose probabilities sum to 1:

5. 12-706 and 73-3595 Another Conditional Example  Example of Probability of having passed HW 1 and HW 2 (assume pass=75%).

6. 12-706 and 73-3596 Subjective Probabilities (Chap 8)  Main Idea: We all have to make personal judgments (and decisions) in the face of uncertainty (Granger Morgan’s career)  These personal judgments are subjective  Subjective judgments of uncertainty can be made in terms of probability  Examples: “My house will not be destroyed by a hurricane.” “The Pirates will have a winning record (ever).” “Driving after I have 2 drinks is safe”.

7. 12-706 and 73-3597 Outcomes and Events  Event: something about which we are uncertain  Outcome: result of uncertain event  Subjectively: once event (eg coin flip) has occurred, what is our judgment on outcome?  Represents degree of belief of outcome  Long-run frequencies, etc. irrelevant  Example: Steelers* play AFC championship game at home. I Tivo it instead of watching live. I assume before watching that they will lose.  *Insert Cubs, Astros, etc. as needed (Sox removed 2005)

8. 12-706 and 73-3598 Next Steps  Goal is capturing the uncertainty/ biases/ etc. in these judgments  Might need to quantify verbal expressions (e.g., remote, likely, non-negligible..)  Example: if I say there is a “negligible” chance of anyone failing this class, what probability do you assume?  What if I say “non-negligible chance that someone will fail”?

9. 12-706 and 73-3599 Merging of Theories  Science has known that “objective” and “subjective” factors existed for a long time  Only more recently did we realize we could represent subjective as probabilities  But inherently all of these subjective decisions can be ordered by decision tree  Where we have a gamble or bet between what we know and what we think we know  Clemen uses the basketball game gamble example  We would keep adjusting payoffs until optimal

10. 12-706 and 73-35910 Probability Wheel  Mechanism for formalizing our thoughts on probabilities of comparative lotteries  You select the area of the pie chart where until you’re indifferent between the two lotteries  Quick 2-person exercise. Then we’ll discuss p-values.

11. 12-706 and 73-35911 Heuristics and Biases  Heuristics are rules of thumb  Which do we use in life?  Representativeness (fit category)  Availability (seen it before, fits memory)  Anchoring/Adjusting (common base point)  Motivational Bias (perverse incentives)

12. 12-706 and 73-35912 Continuous Distributions  Similar to above, but we need to do it a few times.  E.g., try to get 5%, 50%, 95% points on distribution

13. 12-706 and 73-35913 Projects  Groups of 3-4, others need permission  Must have a “real” client (e.g., Brad/Don)  “Core model” must be more than just cashflows (Decision Anal, MCDM, Monte Carlo, Cost- Effectiveness, etc.)  Will have peer evaluations on effort/etc.  Final product is a report of 15 pages  Appendices, etc outside of 15 are ok  Follow Writing Rubric (see syllabus)  Next Wed: Initial Groups, project outline with purpose, data sources, model, tasks (1 page)