# Multivariate Probability Distributions in R

Learn to analyze, plot, and model multivariate data.

4 Hours15 Videos51 Exercises

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## Course Description

When working with data that contains many variables, we are often interested in studying the relationship between these variables using multivariate statistics. In this course, you'll learn ways to analyze these datasets. You will also learn about common multivariate probability distributions, including the multivariate normal, the multivariate-t, and some multivariate skew distributions. You will then be introduced to techniques for representing high dimensional data in fewer dimensions, including principal component analysis (PCA) and multidimensional scaling (MDS).
1. 1

### Reading and plotting multivariate data

Free

In this introduction to multivariate data, you will learn how to read and summarize it. You will learn how to summarize multivariate data using descriptive statistics, such as the mean vector, variance-covariance, and correlation matrices. You'll then explore plotting techniques to provide insights into multivariate data.

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Specifying datatypes for columns
100 xp
Mean vector and variance-covariance matrix
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Calculating the mean vector
100 xp
Calculating the variance-covariance matrix
100 xp
Calculating the correlation matrix
100 xp
Plotting multivariate data
50 xp
Pairs plot using base graphics and lattice
100 xp
Plotting multivariate data using ggplot
100 xp
3D plotting techniques
100 xp
2. 2

### Multivariate Normal Distribution

This chapter will introduce you to the most important and widely used multivariate probability distribution, the multivariate normal. You will learn how to generate random samples from a multivariate normal distribution and how to calculate and plot the densities and probabilities under this distribution. You will also learn how to test if a dataset follows multivariate normality.

3. 3

### Other Multivariate Distributions

This chapter introduces a host of probability distributions to model non-normal data. In particular, you will be introduced to multivariate t-distributions, which can model heavier tails and are a generalization of the univariate Student's t-distribution. You will be introduced to various skew distributions, which are specifically designed to model data that are right or left skewed.

4. 4

### Principal Component Analysis and Multidimensional Scaling

In the final chapter, you will be introduced to techniques for analyzing high dimensional data, including principal component analysis (PCA) and multidimensional scaling (MDS). You will also learn to implement these techniques by analyzing data.

Datasets

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Collaborators  Surajit Ray

Senior Lecturer in Statistics, University of Glasgow

Surajit is a Professor of Statistics at the University of Glasgow's School of Mathematics & Statistics. His research interests are in the area of model selection, the theory and geometry of mixture models, and functional data analysis. He is especially interested in challenges presented by "large magnitude", both in the dimension of data vectors and in the number of vectors. He is the author of the R-package Modalclust. He is also a founder board member and instructor for the Online MSc in Data Analytics at the University of Glasgow.
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