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R로 배우는 다변량 확률 분포

중급기술 수준

업데이트됨 2025. 5.

다변량 데이터를 분석, 그래프화, 모델링하는 법을 배워보세요.

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RProbability & Statistics

4시간

15 동영상

50 연습 문제

3,900 XP

8,783

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여러 변수를 포함하는 데이터를 다룰 때, 우리는 다변량 통계를 사용해 변수 간의 관계를 분석하는 데 관심을 갖습니다. 이 강의에서는 이러한 데이터셋을 분석하는 다양한 방법을 배웁니다. 다변량 정규분포, 다변량 t분포, 그리고 여러 다변량 왜도 분포를 포함한 주요 다변량 확률 분포를 학습합니다. 이후 주성분 분석(PCA)과 다차원 척도법(MDS)을 활용해 고차원 데이터를 더 적은 차원으로 표현하는 기법도 소개합니다.

선수 조건

Foundations of Probability in R

1

Reading and plotting multivariate data

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.

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

3D plotting techniques

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.

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

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.

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

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.

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

Congratulations

R로 배우는 다변량 확률 분포

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