STP 421 – Probability

Spring 2015

Instructor: Dr. Jay Taylor, office: PSA 447; phone: 965-2641; e-mail: jetaylo6@asu.edu
Time: Tuesdays and Thursdays 3:00-4:15
Location: PSA 203
Office Hours: Wednesdays 1:00-3:00 in PSA 447; alternatively make an appointment or just stop by my office.
Text (optional): Bayesian Logical Data Analysis for the Physical Sciences by Phil Gregory (Cambridge University Press, 2005).

Course Description: This course will provide an introduction to probability theory with a special emphasis on its application to Bayesian statistical inference. Topics covered will include measure-theoretic and subjective formulations of probability, random variables and probability distributions, conditional distributions, expectations, the strong law of large numbers and the central limit theorem, maximum entropy distributions, and Bayesian approaches to parameter estimation for linear and nonlinear models. By the end of the course, you should not only have an understanding of the core mathematical concepts of probability theory, but you will also be able to use these to address practical problems involving uncertainty in the natural and social sciences.

Attendance: Class attendance is not mandatory, but I strongly encourage you to come and participate. In particular, if you don't understand a concept, then please ask about it. Likewise, if you have something interesting to add to the discussion, please share it with the class. Attendance at exams is mandatory unless you have a legitimate excuse to be away (e.g., illness, university-sanctioned activities), in which case you need to contact me as soon as possible to arrange a make-up date.

Practice Exercises: These will be posted on the course web page at the following link, along with their solutions. Although optional, you are strongly encouraged to attempt these (either on your own or in groups) and check your answers against the posted solutions or discuss them with me during office hours. In particular, some of the problems that appear on the exams will be modeled after the practice exercises.

Grading: Grades will be based on two midterm exams (30% each) and a comprehensive final exam (40%). A score of 90% and above will guarantee an A, 75 – 89% will guarantee a B, 60 – 74% will guarantee a C, and 40 – 59% will guarantee a D.

ASU Policy on Academic Integrity: `Academic honesty is expected of all students in all examinations, papers, laboratory work, academic transactions and records. The possible sanctions include, but are not limited to, appropriate grade penalties, course failure (indicated on the transcript as a grade of E), course failure due to academic dishonesty (indicated on the transcript as a grade of XE), loss of registration privileges, disqualification and dismissal. For more information, see http://provost.asu.edu/academicintegrity.'

Final Exam: Tuesday, May 5, 2:30 – 4:20 in PSA 203.

Course notes: These are posted here. Some sections follow Gregory (2005) very closely, but other parts are completely independent of his book.


Date

Topic

Reading (from course notes)

13 Jan

Overview; frequentist and subjective formulations of probability

1.1 – 1.3

15 Jan

Deductive logic and plausible inference

2.1 – 2.2

20 Jan

Plausibility and probability: sum and product rules

2.3

22 Jan

Probability spaces and measures

3.1 – 3.2

27 Jan

Conditional Probabilities; The Law of Total Probability

3.3

29 Jan

Random variables and probability distributions

4.1

3 Feb

Discrete and continuous random variables

4.1

5 Feb

Expectations and moments

4.2

10 Feb

Assigning probabilities: count data and the binomial distribution

5.1

12 Feb

Assigning probabilities: rare events and the Poisson distribution

5.2; slides; Luria-Delbruck (1943)

17 Feb

Exam 1; solutions


19 Feb

Assigning probabilities: waiting times and lifespans

5.3

24 Feb

Assigning probabilities: random frequencies

5.4

26 Feb

Assigning probabilities: normal random variables

5.5

3 March

Transformations of random variables

5.6

5 March

Joint distributions and independent random variables

6.1 – 6.2

10 March

Spring Break – no class


12 March

Spring Break – no class


17 March

Conditional distributions

6.3

19 March

Conditional distributions

6.3

24 March

Expectations of sums and products

6.4

26 March

Covariance and correlation

6.5

31 March

The law of large numbers and the central limit theorem

6.6

2 April

Multivariate normal distributions

6.7

7 April

The χ2 and Student t distributions

6.8

9 April

Exam 2; solutions


14 April

Maximum entropy distributions: concepts

7.1 – 7.2

16 April

Maximum entropy distributions: computation and examples

7.3

21 April

Bayesian inference: estimating a mean with known variance

8.1

23 April

Bayesian inference: estimating a mean with unknown variance

8.1

28 April

Fisher Information and Jeffreys Priors

8.2; Gelman (2009)

30 April

Application: Genealogies and Coalescents

slides