# Multivariate Statistics

Course
2023-2024

Introduction to probability theory
Introduction mathematical statistics

## Description

In multivariate statistics we observe multiple measurements for each individual observation. This can be vital signs like heart rate, blood pressure and respiratory rate of a patient or household expenditures for housing, food, education and entertainment. A focus lies on finding and modelling dependencies between these individual variables so that we can gain insights into the underlying mechanics.

A particular challenge is posed by the case where the dimension of the observations is large. Nowadays collecting data is much cheaper than in the past so that working with huge data sets is not unusual any more. We will tackle this problem among others by means of dimension reduction. Graphical tools will help us to understand and visualize the structure of big and complex data sets.

Often we can not assume that all observations are homogeneous and follow the same probability model. In this case we want to discover groups within the data set and classify observations into them.

## Course Objectives

After the course, students can select and fit an appropriate (possibly advanced) statistical model to a multivariate data set. They can also handle very large data sets for example through tools of dimension reduction. Students can visualize multivariate data sets and interpret fundamental plots like biplots and dendrograms. If the application of parametric models is questionable, basic knowledge of asymptotic statistics enables to carry out basic non-parametric analysis like two-sample tests. Students will gain advanced knowledge of the statistical software R, especially within the field of multivariate analysis.

## Timetable

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 timetables into one. This video explains how to do this.

## 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.

• Anderson, Theodore W. (2003). An introduction to Multivariate Statistical Analysis. John Wiley & Sons.

• Härdle, Wolfgang K. and Simar Leopold (2003) Applied multivariate Statistical Analysis. Springer.

## Registration

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.

## Contact

See the Brightspace page

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