Course Unit Code | Course Unit Title | Type of Course | Year | Semester | ECTS |

BİS601 | Statistical Inference | 927001 | 1 | 2 | 6 |

Level of Course Unit

Second Cycle

Objectives of the Course

The theory of statistics deals in principle with the general concepts underlying all aspects of suchwork and from this perspective the formal theory of statistical inference is but a part of that full theory.
Much of the theory is concerned with indicating the uncertainty involved in the conclusions of statistical analyses, and with assessing the relative merits of different methods of analysis, and it is important even at a very applied level to have some understanding of the strengths and limitations of such discussions.

Name of Lecturer(s)

Learning Outcomes

- Distribution Functions and Probability Functions, Some Important Discrete Random variables, Some Important Continuous Random Variables
- Expectation, Properties of Expectations, Moment Generating Functions, Checking Assumptions
- Fundamental Concepts in Inference . Point Estimation, Confidence Sets, The Method of Moments, Maximum Likelihood . Properties of Maximum Likelihood Estimators
- The Bayesian Method, Bayes Estimators, Bayesian Testing, Bootstrap Variance Estimation

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

Language of Instruction

Work Placement(s)

None

Course Contents

Weekly Detailed Course Contents

Week | Theoretical | Practice | Laboratory |

1. | Role of formal theory of inference | ||

2. | Formulation of objectives, Point estimation | ||

3. | Two broad approaches to statistical inference | ||

4. | Some concepts and simple applications, Likelihood, Sufficiency, Exponential family, Simple frequentist discussion | ||

5. | Significance tests, Simple significance test, One- and two-sided tests, Relation with acceptance and rejection, | ||

6. | Formulation of alternatives and test statistics, Relation with interval estimation, Interpretation of significance tests | ||

7. | Some more general frequentist developments | ||

8. | Bayesian testing, Personalistic probability | ||

9. | Statistical implementation of Bayesian analysis | ||

10. | Asymptotic theory, Multidimensional parameter, Nuisance parameters | ||

11. | Aspects of maximum likelihood, information matrix | ||

12. | Modified likelihoods | ||

13. | Some applications | ||

14. | Some applications | ||

15. |

Assessment Methods and Criteria

Term (or Year) Learning Activities | Quantity | Weight (%) |

Midterm Examination | 1 | 0 |

Makeup Examination | 1 | 0 |

Practice | 14 | 60 |

Tutorial | 5 | 10 |

Problem Solving | 8 | 10 |

Discussion | 6 | 10 |

Question-Answer | 6 | 5 |

Homework | 2 | 5 |

SUM | 1070 | |

End Of Term (or Year) Learning Activities | Quantity | Weight (%) |

Final Examination | 1 | 100 |

SUM | 100 | |

Term (or Year) Learning Activities | 40 | |

End Of Term (or Year) Learning Activities | 60 | |

SUM | 100 |

Workload Calculation

Activities | Quantity | Time(hours) | Total Workload(hours) |

Midterm Examination | 1 | 1 | 1 |

Final Examination | 1 | 1 | 1 |

Makeup Examination | 1 | 1 | 1 |

Attending Lectures | 14 | 3 | 42 |

Practice | 14 | 3 | 42 |

Problem Solving | 6 | 5 | 30 |

Discussion | 6 | 4 | 24 |

Homework | 2 | 5 | 10 |

SUM | 151 |