Data Analysis and Statistical Thinking
1
Introduction
2
Getting Started with Data Analysis
3
Probability Part 1
3.1
Today’s programme
3.2
The Bernoulli distribution: tossing a coin
3.3
Adding up coin tosses
3.4
The expectation
3.5
Our first probability mass function
3.6
The variance
4
Probability Part 2
5
Probability Catch-up
5.1
Discrete distributions
5.1.1
Poisson distribution
5.1.2
Geometric distribution
5.1.3
Sampling from arbitrary distributions
5.2
The Normal distribution and the Central Limit Theorem
5.3
The exponential distribution
6
Linear Models
6.1
Fitting a simple linear regression
6.2
Interpreting a simple linear regression
6.3
Simulating data from a linear model
7
Properties of Estimators and Hypothesis Testing
7.1
Properties of point estimators
7.2
Obtaining confidence intervals
7.3
Hypothesis testing
8
Likelihood-based inference
8.1
Meteorite data
8.2
Simple linear regression
9
Bayesian Inference
9.1
Using Bayes’ rule: Covid-19
9.2
First foray into Bayesian inference
9.3
Conjugate prior, Rejection sampling and MCMC*
9.4
Bayesian point estimates and credible intervals
9.4.1
Point estimates
9.4.2
Credible intervals
10
Classification
11
Model Assessment
12
Resampling
12.1
The bootstrap
12.2
Permutation test
12.3
Extra: A ready-made permutation test
12.4
Extra: A two-category permutation test
12.5
Permutation recap
12.6
Validation
12.7
Cross-validation
13
Mixed Models
14
Ordination
14.1
Libraries and Data
14.2
Principal component analysis (PCA)
14.3
PCA under the hood
14.4
Principal components as explanatory variables
14.5
NMDS
15
Clustering
15.1
Libraries and Data
15.2
Distances
15.3
K-means clustering
16
REcoStats: Linear Models
16.1
Fitting a simple linear regression
16.2
Interpreting a simple linear regression
16.3
Simulating data from a linear model
16.4
Hypothesis testing and permutation testing
16.5
A ready-made permutation test
16.6
A two-category permutation test
16.7
Permutation recap
References
Published with bookdown
Data Analysis and Statistical Thinking: An R Workbook
Chapter 13
Mixed Models