Decision Theory - Bayesian Theory (MAE731A)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	ΜΑΕ731
Semester	7
Course Title	Decision Theory - Bayesian Theory
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

This course consists of two modules: the Decision Theory and Bayes Theory. The Decision Theory deals with problems of decision-making. Object of Statistical Decision Theory is decisions about unknown numerical quantities (parameters) by utilizing the presence of statistical knowledge. The aim of the course is the evaluation of the performance of the estimators subject to properties such as the unbiasedness, sufficiency, consistency etc. The second part of the course gives an introduction to Bayesian statistical approach. At the end of the course the student should be able to compare Bayes and classical approaches and evaluate the "performance" of different estimators by using various criteria.

General Competences

Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism

Syllabus

Decision Theory: decision function, loss function, risk function, admissible and minimax estimators; Bayesian inference: Bayes estimators, Bayes confidence intervals, minimax and Bayes tests.

Teaching and Learning Methods - Evaluation

Delivery	Classroom (face-to-face)
Use of Information and Communications Technology	Use of ICT in communication with students
Teaching Methods	Activity Semester Workload Lectures 39 Working independently 78 Exercises-Homeworks 33 Course total 150
Student Performance Evaluation	Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course.

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. Additionally:

• Berger, J.O. (1985) Statistical decision theory and Bayesian analysis. Springer.
• Bernardo J. M. & Smith A. F. M., (1994). Bayesian Theory, Wiley, London.
• Κ. Φερεντίνος (2005). Εκθετική οικογένεια κατανομών Θεωρία Bayes, Πανεπιστημιακές Παραδόσεις.