# Decision Theory - Bayesian Theory (MAE731A)

### General

School School of Science Department of Mathematics Undergraduate ΜΑΕ731A 7 Decision Theory - Bayesian Theory Lectures (Weekly Teaching Hours: 3, Credits: 6) Special Background - Greek Yes (in English, reading Course) 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. 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
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. Books and other resources, not provided by Eudoxus:

• Berger, J.O. (1985) Statistical decision theory and Bayesian analysis. Springer.
• Bernardo J. M. & Smith A. F. M., (1994). Bayesian Theory, Wiley, London.
• Congdon, P. (2007), Bayesian Statistical Modelling, Willey.
• Κ. Φερεντίνος (2005). Εκθετική οικογένεια κατανομών Θεωρία Bayes, Πανεπιστημιακές Παραδόσεις.