MATH-562 / 5 credits

Teacher: Davison Anthony Christopher

Language: English

## Summary

Inference from the particular to the general based on probability models is central to the statistical method. This course gives a graduate-level account 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

Bayesian inference; calibration; data; decision theory; evidence; likelihood inference.

## 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

Slides and board

## Expected student activities

Attending lectures and problem classes; interacting in class; tackling problem sheets.

## Assessment methods

Final exam. Maybe a mid-term test.

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

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

## Notes/Handbook

Will be provided on Moodle.

## In the programs

• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Statistical inference
• Lecture: 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
• Lecture: 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
• Lecture: 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
• Lecture: 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
• Lecture: 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
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional

## Related courses

Results from graphsearch.epfl.ch.