STP 421 – Probability
Spring 2015
Instructor: Dr. Jay Taylor, office: PSA 447; phone:
9652641; email: jetaylo6@asu.edu
Time: Tuesdays and
Thursdays 3:004:15
Location: PSA 203
Office
Hours: Wednesdays 1:003:00 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 measuretheoretic 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, universitysanctioned activities), in which case you need to contact me as soon as possible to arrange a makeup 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; LuriaDelbruck (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 χ^{2} 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 