Multivariate Probability Distributions in R

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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).

Multivariate Probability Distributions in R

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.

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.

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.

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.

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Reading and plotting multivariate data
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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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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.
View Chapter Details Play Chapter Now
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.
View Chapter Details Play Chapter Now
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.
View Chapter Details Play Chapter Now

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Surajit Ray

Senior Lecturer in Statistics, University of Glasgow

Surajit is a Reader in 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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Probability and Distributions with R

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Chester Ismay
Nick Solomon
Amy Peterson

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Multivariate Probability Distributions in R

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Loved by learners at thousands of top companies:

Course Description

Reading and plotting multivariate data

Reading multivariate data

Reading multivariate data using read.table

Specifying datatypes for columns

Mean vector and variance-covariance matrix

Calculating the mean vector

Calculating the variance-covariance matrix

Calculating the correlation matrix

Plotting multivariate data

Pairs plot using base graphics and lattice

Plotting multivariate data using ggplot

3D plotting techniques

Other Multivariate Distributions

Other common Multivariate distributions

Generate samples from multivariate t-distribution

Identify the distribution

Density and cumulative density for multivariate-t

Density of multivariate t-distribution

Cumulative distributions and quantiles of t

Comparing normal and t probabilities

Multivariate skewed distributions

Drawing samples from skew distributions

Plotting and testing of skewed-densities

Examine skewness from contour plot

Parameter estimation for multivariate skew-normals

Multivariate Normal Distribution

Multivariate normal distribution

Samples from multivariate normal distributions

Identify the distribution of a normal sample

Density of a multivariate normal distribution

Calculating the density of multivariate normal

Calculating dmvnorm over a grid

Cumulative Distribution and Inverse CDF

Using the pmvnorm function

Calculating probability contours using qmvnorm

Checking normality of multivariate data

Graphical tests for multivariate normality

Numerical tests for multivariate normality

Test multivariate normality by wine type

Principal Component Analysis and Multidimensional Scaling

Principal Component Analysis

Number of PCs for the state.x77 dataset

Using the princomp function

Choosing the number of components

Calculating the proportion of variation explained

Choosing the number of PCs

Number of components explaining 95% variation

Number of PCs using scree plot

Interpreting PCA attributes

Loadings and scores for the PCs

Visualizing PCA using the factoextra library

Multi-dimensional scaling

Multidimensional scaling in two dimensions

Multidimensional scaling in three dimensions

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