Statistical inference
Summary
Inference from the particular to the general based on probability models is central to the statistical method. This course gives a graduate-level introduction of the main ideas of statistical inference.
Content
Formalisation of inferential problems. Frequentist, Bayesian and design-based inference. Parametrisation. Quick overview of point and interval estimation, and of testing. Bias/variance tradeoff. Pivots and evidence functions. Role of approximation.
Exponential family models.
Principles of statistics: conditioning, sufficiency, etc.
Significance testing, its implementation and applications. Multiple hypothesis testing. Effect of selection.
Likelihood inference and associated statistics (maximum likelihood estimator, likelihood ratio statistic). Varieties of likelihood (conditional, marginal, partial, empirical, etc.). Issues arising in high dmensions. Misspecification, efficiency, robustness.
Data and sampling problems (truncation, censoring, etc.).
Shrinkage estimation.
Elements of Bayesian inference; choice of prior and related issues.
Predictive inference and its assessment.
Keywords
Statistical inference; calibration; data; decision theory; evidence; likelihood inference.
Learning Prerequisites
Required courses
Courses on basic probability and statistics (e.g., MATH-240, MATH-230) and a first course on the linear model (e.g., MATH-341).
Important concepts to start the course
Basic statistical background.
Learning Outcomes
By the end of the course, the student must be able to:
- Formulate a statistical model suitable for a given situation
- Analyze the properties of a statistical inference procedure
- Assess / Evaluate the adequacy of a statistical formulation
- Assess / Evaluate the evidence for a statistical hypothesis
Transversal skills
- Assess one's own level of skill acquisition, and plan their on-going learning goals.
- Continue to work through difficulties or initial failure to find optimal solutions.
- Demonstrate a capacity for creativity.
- Demonstrate the capacity for critical thinking
Teaching methods
Slides and board
Expected student activities
Attending lectures and exercise sessions; interacting in class; solving problem sheets.
Assessment methods
Final exam and possibly an optional mid-term exam.
Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.
Supervision
| Office hours | No |
| Assistants | Yes |
| Forum | Yes |
Resources
Virtual desktop infrastructure (VDI)
No
Bibliography
Cox, D. R. (2006) Principles of Statistical Inference
Cox, D. R. and Hinkley, D. V. (1974) Theoretical Statistics
Davison, A. C. Statistical Models
Ressources en bibliothèque
Notes/Handbook
Will be provided on Moodle.
Moodle Link
Prerequisite for
MATH-524
In the programs
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Statistical inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Statistical inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Statistical inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Statistical inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Statistical inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Statistical inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Statistical inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: mandatory
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Statistical inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: mandatory
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Statistical inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional