MAT6022 Statistics IIBahçeşehir UniversityDegree Programs MATHEMATICS (TURKISH, PHD)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
MATHEMATICS (TURKISH, PHD)
PhD TR-NQF-HE: Level 8 QF-EHEA: Third Cycle EQF-LLL: Level 8

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT6022 Statistics II Spring 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. İRİNİ DİMİTRİYADİS
Recommended Optional Program Components: The use of statistical packages.
Course Objectives: The purpose of the course is to give the student who has a basic knowledge of probability and statistics, a further understanding of the general concepts putting emphasis on theoretical issues.

Learning Outcomes

The students who have succeeded in this course;
The student who completes this course will have a theoretical background on the basic subjects under Statistics, will be able to analyze and interpret statistical data, will know about estimators and their properties, will be able to apply hypothesis tests, linear regression and variance anlysis and non parametric tests in problem solving.

Course Content

Short review of probability. Statistical estimation, point estimators and their properties, confidence intervals, hypothesis tests, properties of tests, non parametric estimatimation, linear regression and variance analysis, simulation.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Review of probability. Discrete and continuous probability disrtributions, expected value, variance and higher moments, moment generating and probability generating functions.
2) Estimation, statistical inference, prior and posterior distributions, conjugate prior distributions, random sums.
3) Bayes estimators, loss functions, maximum likelihood estimators, moment matching.
4) Properties of point estimators. Unbiasedness, consistency,efficiency of an estimator. Sufficiency statistics. The Cramer Rao theorem. Properties of Maximum Likelihood estimators.
5) Sampling distributions of estimators, confidence intervals, unbiased estimators of the mean and the variance.Fisher information matrix.
6) Testing hypotheses. Uniformely most powerful tests. One sided and two sided tests. Likelihood ratio tests.
7) Testing the difference between two means, the F distribution, Bayes test procedures.
8) Categorical data and nonparametric methods. Tests of goodness of fit, contingency tables, tests of homogeneity, robust estimation, sign and rank tests.
9) Nonparametric tests continued. Order statistics.
10) Linear Statistical models: method of least squres, single and multivariable regression.
11) Linear regression continued. Forward addition and backward elimination methods in regression.Correlation. A complete example.
12) Analysis of variance.
13) Simulation; simulating specific distributions, Markov chains, Markov chain Monte Carlo.
14) Application examples of statistical inference.

Sources

Course Notes / Textbooks: Morris H. DeGroot, Mark, J., Schervish, Probability and Statistics, Thirf edition, 2002, Addison, Wiley
References: Robert W. Keener, Theoretical Statistics, Topics for a Core Course, Springer Texts in Statistics.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 6 % 20
Project 2 % 30
Total % 50
PERCENTAGE OF SEMESTER WORK % 20
PERCENTAGE OF FINAL WORK % 30
Total % 50

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Project 2 24 48
Homework Assignments 6 10 60
Midterms 1 24 24
Final 1 26 26
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution