| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6022 | Statistics II | Fall | 3 | 0 | 3 | 12 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | Tr |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Prof. Dr. İRİNİ DİMİTRİYADİS |
| 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. |
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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. |
| 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. |
| 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. | ||
| Course Notes: | 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. |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | 6 | % 20 |
| Presentation | % 0 | |
| Project | 2 | % 30 |
| Seminar | % 0 | |
| Midterms | % 20 | |
| Preliminary Jury | % 0 | |
| Final | % 30 | |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 40 | |
| PERCENTAGE OF FINAL WORK | % 60 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 0 | 0 | 0 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 2 | 24 | 48 |
| Homework Assignments | 6 | 10 | 60 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 1 | 24 | 24 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 26 | 26 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |