The Reverend Thomas Bayes (1702 - 1761)

Basic Information:
Lecture: Tu, Th 9:30 - 11:00am
Instructor:  Kent Johnson (learn more about Kent here; learn less about Kent here)
Office Hours/Location:  Wed. 11:00 - 11:55, SST 755
Course Password: ___________________________________________________________
When Kent has no class: Due to unavoidable professional conflicts, there will be no class on Thursday, May 5.

Required Readings: This course will be based on my lecture notes and a number of papers, all of which are available by clicking on the picture of Thomas Bayes above, or by clicking here. (Warning: the URL for the readings page is unstable; it will probably change over time. If you want to bookmark a page for this course, bookmark the main page, which you are currently viewing.)

Recommended Text: Michael Resnik 1987, Choices: An Introduction to Decision Theory; Minneapolis, MN: University of Minnesota Press. This book used to be required; my presentation of some of the basics of probability and utility still follow the corresponding sections of this book, at least to some extent. A copy of this book, along with M. Bergman, The Logic Book, is available on reserve at the Langson library.

Recitations:  You are required to attend at least one recitation each week. You needn't attend the same recitation you signed up for, and you needn't always attend the same recitation each week. Attending extra recitations one week cannot be substituted for missed recitations in some other week.

Test Dates:      Midterm:  Tuesday, May 3 (in class) [You will need a calculator for both the midterm and final.]
                         Final: Thursday, June 16, 8 - 10am

Student responsibilities. In this class, you are responsible for everything that you might be reasonably held responsible for, and I determine what counts as reasonable in this context. This includes, but is not limited to, announcements made in class, notices on this website, emails to you individually or as part of a class-wide distribution, and material present in assigned readings but not discussed in class.

Make-up policy. Alert! There are no make-up exams available for this course either before, during, or after the regularly scheduled exams. Please ensure that you are able to take the tests on the days listed above. Similarly, recitation sections cannot be made up. If you miss a week, you will not earn those points. Homework handed in after the due point will not be graded.

Grading. Your grade for the course will be based on a 1000 point scale.
Attendance at recitation sections: 200 points
Homework: 200 points
The midterm: 250 points
Final: 350 points

General remarks.Welcome to Inductive Logic. Our focus in this class will be on decision theory, especially some central elements of probability theory. We will investigate a number of methods designed to help us make better decisions given certain kinds of background information. The interesting thing about these methods is that they are quite general, and can aid us in the kinds of situations that we really care about. Here are two examples.

Love: Suppose you want to meet that special someone, who we'll call SS. You know that SS is either working at a certain restaurant, or else is in a study session in a large apartment building, so you only have time to check one of these places, and you think it is equally likely that SS is at either of them. If you go to the restaurant, there is a 50-50 chance of meeting SS, because half of the staff works in the kitchen, and thus are inaccessible to heartsick passers-by. If you go to the apartment building, you have only a one in four chance of finding SS, because the study session is being held at one of the four member's apartment, and you only know which apartment is SS's. The apartment is closer than the restaurant, so while you have only a 30% chance of getting to the restaurant before SS leaves, you have a 60% chance of getting to the apartment building before the study session is over.

• Where should you go?
• Where would you go if you found out that in fact there were 5 people in SS's study group? 6? 7?
• What if traffic to the restaurant is congested, and you only have a 20% chance of getting there in time?
• What if you also knew that of the twelve workers at the restaurant, only four of them would be working in the kitchen?
• Suppose the likelihood of SS being at the restaurant or the apartment was not 50-50. Could this likelihood change enough to make your reverse your original decision about where to go? If so, how much would it have to change to make you reverse your choice?

Money:  Two new companies are vying for your $1,000 investment (which must be made in one lump sum to Company A or Company B). in Company A, your $1,000 will buy you 1,000 shares of stock. There is an 20% chance of Company A's product not being approved by the FDA. If it is not approved, the company will fold, and you will lose all your money. If it is approved, then there is a 40% chance of obtaining exclusive export rights to the People's Republic of China, which would raise the price of stock to $100 a share. If that doesn't happen, domestic sales will still be enough to raise your stock to $65 a share. On the other hand, stock in Company B starts at $5 a share, and there is only a 40% chance that the company will not fold. If it doesn't, though, there is a 70% chance that Company B will be bought by Microsoft, and you will receive back $1,500 per share. If Microsoft does not buy the company, stocks are likely to hover around $100 a share.

• Should you invest in Company A or Company B?
• How much would the price of stock in Company B have to change to make you reverse your decision?
• If Company A's product is approved by the FDA, how much would the projected value of the stock have to change to make you reverse your decision?

Topics to be covered. Ideally, we will cover the following topics:

• Introduction to the probability calculus
• special attention to Bayes' Theorem
• The binomial coefficient and Bernoulli Trials
• Statistical Inference
• Null hypothesis testing (one- and two-tailed)
• Bayes' Theorem and null hypothesis testing
• Utility Theory
• Basic properties of random variables
• mean, variance, standard deviation, covariance, correlation
• The psychology of probabilistic judgement and decision-making

Studying Information.  In addition to doing the reading, which is itself conceptually difficult in places, it is crucial for you to work on practice exercises relevant to the reading. Similarly, it is important to have a writing instrument and paper nearby when you read the text, so that you can take notes and double check some of the calculations. Most importantly, you should make frequent use of the homework help and review sessions. Katherine and Kevin can supply you with detailed explanations of any material covered in class, answers to homework problems, etc. They will also have additional problems for you to practice on, if you want more.

Home