PM599: INTRODUCTION TO THE THEORY OF STATISTICS PART 1 Fall 2012
PM599 – SYLLABUS
DIVISION OF BIOSTATISTICS
DEPARTMENT OF PREVENTIVE MEDICINE
KECK SCHOOL OF MEDICINE
UNIVERSITY OF SOUTHERN CALIFORNIA
Instructor:
Juan Pablo Lewinger, Ph.D., Assistant Professor
Division of Biostatistics
2001 Soto St., second floor, Suite 202U
(323) 442-1932
E-mail: [email protected]
Office Hours: By appointment
Teaching Assistant: TBA
E-mail:
Office hours:
Sessions schedule:
TBA
Room:
TBA
Units:
3
Course content
This course is a rigorous non-measure theoretic introduction to probability theory with an
emphasis on the results and methods that are most relevant to statistical inference. It replaces
PM522, which will not be taught in 2012. In subsequent years this course will be taught as
PM522a. PM599/522a should be taken in sequence with PM522b. PM999/522a will cover
probability and PM522b will cover statistical inference. These two courses form the core
statistical-theory of the Biostatistics program, providing a sound theoretical basis for
understanding applied statistical methods and pursuing more advanced Theory. The sequence
PM522a-b is required for all the Biostatistics PhD tracks and it is also open to quantitatively
oriented students in Epidemiology and other population-based sciences. A detail list of the topics
is given below.
Course objectives
 To acquire skill in the basic computations involving probabilities and to develop probabilistic
thinking
 To gain probabilistic intuition and understanding with the aid of computer-based simulation
and visualization.
PM599: INTRODUCTION TO THE THEORY OF STATISTICS PART 1 Fall 2012


To become familiar with common parametric families of distributions and their applications.
To understand the key probability theory results that are fundamental to statistical inference.
Method of instruction
This course will emphasize active learning. Students will be expected to study the relevant
textbook sections and complete a short online quiz ahead of each session. Lectures will be given
by Dr. Lewinger to review, clarify, provide context, and illustrate the topics covered each week.
A substantial amount of class time will be devoted to problem solving and group discussion.
Assessment
Weekly homework assignments requiring calculations/derivations and/or conducting small
simulation/visualization exercises in R or Mathematica; A final project requiring a more
involved extension or applications of a topic covered in class or and additional topic; A final
exam; Short online weekly quizzes; Class participation.
Grade
Online quizzes (10%); Seven (7) homework assignments (7% each, 49% total); Final Exam
(35%); Class participation (6%);
Required Textbook:
Statistical Inference, 2nd Ed. [CB]
Casella G, Berger RL. Wadsworth & Brooks, 2002
Additional References:
1. Introduction to the Theory of Statistics, 3rd Ed.
Mood AM, Graybill FA, Boes DC. Mcraw-Hill, 1974
2. Mathematical Statistics: Basic Ideas and Selected Topics
Bickel PJ, Doksum KA. Holden-Day, 1977
3. Mathematical Statistics and Data Analysis, 3rd Ed.
Rice JA. Thomson-Brooks/Cole, 2007
4. A Course in Mathematical Statistics, 2nd Ed.
Roussas GR. Academic Press, 1997
Prerequisites
College-level Calculus and Linear Algebra are the recommended preparation.
Schedule
Times and locations TBA, 3 hours per week
A detailed list of topics follows.
PM599: INTRODUCTION TO THE THEORY OF STATISTICS PART 1 Fall 2012
Week 1.
Week 2.
Basic counting and combinatorics; Probability on Finite Sample Spaces; Basic set
theory; Sigma algebras; General Probability Spaces. Assignment 1 out.
Random Variables. Independence; Conditional Probability. Cumulative
Distribution Functions. Density and Probability Mass function.
Week 3.
Transformation of Random variables. Expectation. Properties of Expectation.
Assignment 1 Due. Assignment 2 out.
Week 4.
Variance and Higher Order Moments. Moment Generating Function. Markov,
Chebyshev and Jensen inequalities.
Week 5.
Common Families of discrete Distributions: Bernoulli; Binomial; Poisson;
Geometric; Hyper-Geometric. Assignment 2 Due. Assignment 3 out
Week 6.
Common families of continuous distributions: Uniform, Normal, Exponential,
Gamma, Beta; Location and scale families; Exponential Families.
Week 7.
Random Vectors; Joint Probability Distribution Function; Covariance and
correlation. Cauchy-Schwartz inequality. Assignment 3 Due. Assignment 4 out
Week 8.
Conditional probability and conditional expectation. Properties and applications.
Week 9.
Common multivariate Distributions. Multinomial; Multivariate Normal; Dirichlet
Distribution. Assignment 4 Due. Assignment 5 out
Week 10. Random Samples; Chi-Square, t, and F distributions; Order Statistics.
Week 11. Modes of Convergence: Convergence in Distribution; Convergence in
Probability, Almost Sure convergence, Convergence in Lp; Relationships between
modes of convergence. Examples and counterexamples. Assignment 5 Due.
Assignment 6 out.
Week 12. Central Limit Theorem; Slutsky’s Theorem. Delta Method.
Week 13. Law of Large Numbers (LLN); Monte Carlo method. Assignment 6 Due.
Assignment 7 out.
Week 14. Generating Random Variables: Inverse probability method; Alias method;
Accept/ Reject Method;
Week 15. Importance Sampling; Markov Chains; Metropolis Algorithm. Assignment 7 Due.
PM599: INTRODUCTION TO THE THEORY OF STATISTICS PART 1 Fall 2012
STATEMENT FOR STUDENTS WITH DISABILITIES:
Any student requesting academic accommodations based on a disability is required to register
with Disability Services and Programs (DSP) each semester. A letter of verification for approved
accommodations can be obtained from DSP. Please be sure the letter is delivered to me (or to
TA) as early in the semester as possible. DSP is located in STU 301 and is open 8:30 a.m.–5:00
p.m., Monday through Friday. The phone number for DSP is (213) 740-0776.
STATEMENT ON ACADEMIC INTEGRITY:
USC seeks to maintain an optimal learning environment. General principles of academic honesty
include the concept of respect for the intellectual property of others, the expectation that
individual work will be submitted unless otherwise allowed by an instructor, and the obligations
both to protect one’s own academic work from misuse by others as well as to avoid using
another’s work as one’s own. All students are expected to understand and abide by these
principles. Scampus, the Student Guidebook, contains the Student Conduct Code in Section
11.00, while the recommended sanctions are located in Appendix A: http://webapp.usc.edu/scampus/gov/. Students will be referred to the Office of Student Judicial Affairs and
Community Standards for further review, should there be any suspicion of academic dishonesty.
The Review process can be found at: http://www.usc.edu/student-affairs/SJACS/.