Special Topics in Probability (MAE838)
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General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
ΜΑΕ838 |
| Semester |
8 |
| Course Title |
Special Topics in Statistics |
| Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
| Course Type |
Special Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The course’s objective is to introduce students to the limiting behaviour of sequences of random variables for various types of data which are independent but not necessarily identically distributed. Particular emphasis is given to the strong law of large numbers and the central limit theorem under these conditions. The starting point is the basic concepts and terminology of probability theory in combination with measure theory. Particular emphasis is given in measuring the accuracy of the approximations offered by the specific central limit theorems, i.e. Berry-Esseen bounds, etc) as well as alternative and more accurate approximations: Edgeworth expansions, saddle point approximations. |
|---|---|
| General Competences |
|
Syllabus
The concepts of Sigma Algebra, measure, measurable functions and Lebesgue integral. Applications of convergence of random variables: variance stabilizing transformations, bias correction, symmetry transformations and applications in Statistics. Bounds for sums of random variables (not necessarily i.i.d.). Generalizations of the Strong Law of Large Numbers on non-i.i.d. observations. Generalizations of the central limit theorem to non independent / non i.i.d. observations. Accuracy of central limit theorems: Berry-Esseen bounds, Edgeworth expansions, Saddle point approximations.
Teaching and Learning Methods - Evaluation
| Delivery |
Classroom (face-to-face) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
Final written exam. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Ένα δεύτερο μάθημα στις πιθανότητες, Δ. Χελιώτης, Εκδόσεις Κάλλιπος
- K.B. Athreya and S.N. Lahiri, Measure Theory and Probability Theory, Springer (2006), υλικό από κεφ. 8 και 11.
- Petrov, Limit Theorems of Probability Theory: Sequences of Independent Random Variables, Oxford University Press (1995) (υλικό κυρίως από εδώ).
- Billingsley, Probability and Measure, Wiley (1995), υλικό από κεφ. 22 και 27.