Foundations of Probability and Mathematical Statistics: A Scientific Computing Approach
Semester Taught - Spring
This course is a fast-paced introduction to calculus-based probability and statistics aimed at graduate students in engineering and quantitative life sciences. It covers the essentials of STA5325 and STA5328 in a single semester making use of calculus and basic scientific computing to gain understanding about fundamental results and methods of probability and statistics. Successful completion of the course will enable one to take graduate-level courses in statistics, biostatistics, operations research and computer science. Whenever possible, the course prioritizes development of intuition behind statistical methods via scientific computing and simulation experiments rather than formal derivations and justification of the procedures. R will be the preferred statistical computing environment of choice; Matlab will also be allowed.
Successful completion of this course (or a sequence STA5325/5328) will be a prerequisite for students wishing to take any of my future topics courses.
- solid knowledge of calculus of multiple variables;
- experience reading and writing simple computer programs in a scripting language (ideally, in R); basic knowledge of scientific computing (e.g., ABE 5643C for ABE students);
- intro undergraduate statistics; a recent first graduate statistical methods class (such as ALS5932 or STA6166) is preferred
- learn essentials of calculus-based probability theory with an aid of computer experiments
- apply the knowledge of probability to understand fundamental principles, methods and results of mathematical statistics
- integrate knowledge of probability, statistics and scientific computing to make exact and simulation-based inference in a modern computing environment
Office: Room 239 Rogers Hall
Class Materials Required
Lecture notes and readings will be posted on course page. R and R Studio environments are available free of charge.
We shall cover most topics in the course text (please check out the table of contents).
Tentative list of topics
- Basic Probability: random events, calculus of probability.
- Discrete Random Variables and Their Probability Distributions.
- Continuous Random Variables and Their Probability Distributions.
- Multivariate Probability Distributions.
- Functions of Random Variables.
- Sampling Distributions and the Central Limit Theorem.
- Point and Interval Estimation.
- Properties of Point Estimators and Methods of Estimation.
- Hypothesis Testing.
- Linear Models and Estimation by Least Squares.
Attendance and participation in class is expected. Make-ups are not allowed except for documented health, family emergency or work reasons; details of make-ups – to be arranged with the instructor in advance of the event.
|Three exams||60%, weighted equally|
|(two prelims and the final – potentially, take-home)|
|(problem sets, potentially graded through quizzes, TBA in advance)|
All students admitted to the University of Florida have signed a statement of academic honesty committing themselves to be honest in all academic work and understanding that failure to comply with this commitment will result in disciplinary action. This statement is a reminder to uphold your obligation as a UF student and to be honest in all work submitted and exams taken in this course and all others.
Accommodation for Students with Disabilities
Students requesting classroom accommodation must first register with the Dean of Students Office. That office will provide the student with documentation that he/she must provide to the course instructor when requesting accommodation.
Use of Library, Personal References, PC Programs and Electronic Databases
These items are university property and should be utilized with other users in mind. Never remove, mark, modify nor deface resources that do not belong to you. If you're in the habit of underlining text, do it only on your personal copy. It is inconsiderate, costly to others, and dishonest to use common references otherwise.
All faculty, staff and students of the University are required and expected to obey the laws and legal agreements governing software use. Failure to do so can lead to monetary damages and/or criminal penalties for the individual violator. Because such violations are also against University policies and rules, disciplinary action will be taken as appropriate. We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honesty and integrity.
UF Counseling Services
Resources are available on-campus for students having personal problems or lacking clear career and academic goals which interfere with their academic performance. These resources include:
- University Counseling Center, 301 Peabody Hall, 392-1575, personal and career counseling;
- Student Mental Health, Student Health Care Center, 392-1171, personal counseling;
- Center for Sexual Assault/Abuse Recovery and Education (CARE), Student Health Care Center, 392-1161, sexual assault counseling;
- Career Resource Center, Reitz Union, 392-1601, career development assistance and counseling.