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Introduction Mathematical Statistics


Admission requirements

Introduction to probability theory
Analysis 1 (both not mandatory)


Mathematical statistics focuses on modelling random experiments and analysing data using probability models. In this course we discuss the basic concepts of estimators, tests and confidence intervals. We address general principles to derive them and to examine their quality.

Amongst others, moment estimators, maximum likelihood estimators, Wald intervals, the Neyman-Pearson lemma, exponential families, monotone likelihood ratios, linear regression and an introduction to Bayesian statistics are covered. Here we build on the basic concepts from the introduction to probability theory.

Some concrete statistical procedures are also discussed. Furthermore basic skills in the statistical programming language R are taught by software exercises.

Course Objectives

The ability to determine parametric models using general principles:

  • estimators (method of moments, maximum likelihood estimation, Bayes estimators)

  • confidence intervals (based on pivots, Wald intervals and Baysian confidence regions)
    and evaluate these, as well as given estimators and confidence regions based on various optimality criteria, including MSE, bias, UMVU.


The schedule for the course can be found on MyTimeTable.

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different

Mode of instruction

Lectures tutorials and homework

Assessment method

The final grade consists of homework (20%) and a written (retake) exam (80%). To pass the course, the grade for the (retake) exam should be at least 5 and the (unrounded) weighted average of the two partial grades at least 5.5. No minimum grade is required for the homework in order to take the exam or to pass the course. The homework counts as a practical and there is no retake for it.

Reading list

Fetsje Bijma, Marianne Jonker, Aad van der Vaart: An Introduction to Mathematical Statistics. Amsterdam University Press 2017.


From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ's on MyStudymap can be found here.


See the Brightspace page