# Computational Statistics (MAE836)

### General

School School of Science Department of Mathematics Undergraduate ΜΑΕ836 8 Computational Statistics Lectures-Laboratory (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 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. 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
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:

• 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