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Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| STATISTICS (MASTER) (WITH THESIS) | |
| Code | ISB573 |
| Name | Bayesian Statistical Inference |
| Term | 2026-2027 Academic Year |
| Term | Fall |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Dr. Öğr. Üyesi İsmet BİRBİÇER |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
The objective of the course is to provide students with a solid understanding of Bayesian approaches and skills in computational inference.
Course Content
The Bayesian perspective in statstics, prior and posterior distributions, predictive distributions, fundamental decision theory, measurement of model performance, posterior convergence, and probabilistic programming.
Course Precondition
None
Resources
Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman and Hall/CRC.
Notes
Clyde, M., Çetinkaya-Rundel, M., Rundel, C., Banks, D., & Chai, C. An Introduction to Bayesian Thinking: A Companion to the Statistics with R Course. GitHub Pages.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Distinguishes the differences between Bayesian and classical statistical approaches. |
| LO02 | Determines posterior distributions by using prior distributions with different structures. |
| LO03 | Applies multiparameter and hierarchical models to real-world problems. |
| LO04 | Explain the working principles of Monte Carlo methods. |
| LO05 | Applies Bayesian models using R and Stan programming languages. |
| LO06 | Evaluates the performance of the generated models. |
| LO07 | Applies Bayesian hypothesis testing. |
| LO08 | Evaluates the goodness of fit of the fitted model. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Have in-depth theoretical and practical knowledge about Probability and Statistics | 2 |
| PLO02 | Bilgi - Kuramsal, Olgusal | They have the knowledge to make doctoral plans in the field of statistics. | 1 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Has comprehensive knowledge about analysis and modeling methods used in statistics. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has comprehensive knowledge of methods used in statistics. | 2 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Make scientific research on Mathematics, Probability and Statistics. | 1 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Indicates statistical problems, develops methods to solve. | 2 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply innovative methods to analyze statistical problems. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Designs and applies the problems faced in the field of analytical modeling and experimental researches. | 1 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Access to information and do research about the source. | 2 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Develops solution approaches in complex situations and takes responsibility. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Has the confidence to take responsibility. | |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | They demonstrate being aware of the new and developing practices. | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | He/She constantly renews himself/herself in statistics and related fields. | 1 |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Communicate in Turkish and English verbally and in writing. | |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Transmits the processes and results of their studies clearly in written and oral form in national and international environments. | |
| PLO16 | Yetkinlikler - Öğrenme Yetkinliği | It considers the social, scientific and ethical values in the collection, processing, use, interpretation and announcement stages of data and in all professional activities. | |
| PLO17 | Yetkinlikler - Öğrenme Yetkinliği | Uses the hardware and software required for statistical applications. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction and basic concepts | Review of lecture notes | Öğretim Yöntemleri: Anlatım |
| 2 | One parameter models | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 3 | Determining the prior distribution and its characteristics. | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 4 | Multi-parameter models | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Asymptotic properties of posterior distributions | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 6 | Hierarchical models | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 7 | Model review and improvement | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 8 | Mid-Term Exam | - | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Model comparison and hypothesis testing | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 10 | Bayesian decision theory | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 11 | Markov Chain Monte Carlo methods | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | Metropolis-Hastings algorithm | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 13 | Gibbs algorithm | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 14 | Regression models | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 15 | Generalized linear models | Review of lecture notes | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 16 | Term Exams | - | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | - | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 2 | 10 | 20 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 140 | ||
| Total Workload / 25 (h) | 5,60 | ||
| ECTS | 6 ECTS | ||