Computational Statistics (MAE836)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	ΜΑΕ836
Semester	8
Course Title	Computational Statistics
Independent Teaching Activities	Lectures-Laboratory (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	Students completing this course should be able to: Apply the most common methods of computational statistics generate random numbers from discrete and continuous distributions use R and other statistical software to perform statistical analysis use different methods to solve an optimization problem.
General Competences	Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism.

Syllabus

Using R the following topics will be discussed: Generation of random numbers from discrete and continuous distributions. Monte Carlo integration. Using simulation techniques to visualize classical results of statistical inference via simulated data (asymptotic normality of mean, power of a test etc). Density Estimation and Applications (Kernel density estimation). Methods of Resampling ς (Jackknife και Bootstrap). Numerical maximization techniques (Newton-Raphson, Fisher scoring, expectation-maximization [EM]).

Teaching and Learning Methods - Evaluation

Delivery	Classroom (face-to-face)
Use of Information and Communications Technology	-
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:

• Davison, A. C., Hinkley, D. V., Bootstrap methods and their application. Cambridge University Press 1997.
• Rizzo, M. L., Statistical computing with R. Chapman & Hall/CRC 2007.
• Robert, C. P., Casella, G., Introducing Monte Carlo methods with R. Springer Verlag 2009