Bayesian Statistics

0. RefreshR

_{Dominique Makowski}
_{^{D.Makowski@sussex.ac.uk}}

Follow the slides

https://github.com/DominiqueMakowski/teaching
- 👉 Lecture 0

The Environment

Setup

Make sure you have R and RStudio on your computer
- Why local installation? Independence, flexibility, and power
Follow the instruction on Canvas (in /Module Information)
If you have any problem, let me know

Vocabulary

R = programming language
RStudio = the “editor” that we use to work with R
Posit = The company that created R Studio and that provides cloud services (used to be called RStudio)
Posit cloud = The online version of RStudio
Quarto = Used to be called R Markdown. A system to combine code, text, and code output into nice documents (similar to Jupyter)
Markdown = A simple syntax to *format* text used on **internet**

Panels

Source (text editor)
Console (interactive)
Environment (objects)
Files (navigate)

Creating New Document

You can interact with code inside code chunks

Options

Remove “editor” (or replace visual with source)
- editor: source
Select “Chunk Output in Console”

Interacting

Create a new document (file)
- .R (R script) or .qmd (quarto document)
Write some code in the script
Run the code
- Click somewhere on the same line that you want to execute
- Or select the code that you want to execute
- Hit Ctrl+Enter

2 + 2

[1] 4

Programming Concepts

Classes

In R, each thing has a class (type)
- Numeric (aka integers and floats; numbers)
- Character (aka string; text)
- Logical (aka booleans; TRUE/FALSE)
  - Note: TRUE and FALSE are equivalent to 1 and 0
  - Try: TRUE + TRUE
- Factors (aka categorical; e.g. experimental conditions)
- Comments (with hash #, CTRL + SHIFT + C)
- “Functions” (ends with (); e.g. mean())
- Many more…
You can check the class of an object with class()
You can access a function’s documentation with ?mean or clicking on the function and pressing F1

Types

# Number
3
# Character "quotations"
"text"
# Logical
TRUE

Check class

x <- 3
class(x)

[1] "numeric"

Vectors vs. Lists (1)

A vector is a “list” of elements of the same class, indexed by their position
In R, most operations are by default vectorized (i.e., applied to each element of the vector)
Create and concatenate vectors with the combine function c()

# Vector
x <- c(0, 1, 2)
x + 3

[1] 3 4 5

c(x, 3)

[1] 0 1 2 3

Warning

R starts counting at 1, not 0.

x[2]

[1] 1

Vectors vs. Lists (2)

A list is a container of named elements of any kind, indexed by their name
The order of things doesn’t matter (unlike in a vector)
We can extract elements via their names (instead of via their index)

mylist <- list(var1 = "some text", var2 = 30, var3 = x)
mylist$var3 # = mylist[["var3"]]

[1] 0 1 2

Warning

mylist[] returns a list, while mylist[[]] returns the element itself

You can also merge lists with c()

mylist2 <- list(var4 = "some other text")
c(mylist, mylist2)

$var1
[1] "some text"

$var2
[1] 30

$var3
[1] 0 1 2

$var4
[1] "some other text"

Pipes

Pipe: |>, with CTRL + SHIFT + M
- If old pipe %>%: Tools -> Global Options -> Code -> Native Pipe Operator
Puts the previous “stuff” as the first argument of the next function

4 |> sqrt()  # equivalent to

[1] 2

sqrt(4)

[1] 2

Pipes are useful to chain operations in a Human-readable way (“do this then this then this”)

result <- 4 |>
  sqrt() |>
  c(1, 0) |>
  as.character()

result

[1] "2" "1" "0"

DataFrames

A data frame is a collection of vectors of the same length (i.e. a table)
Each vector is a column of the data frame
Each column can have a different class (e.g., numeric, character, logical, etc.)

# Create a data frame
df <- data.frame(
  var1 = c(1, 2, 3),
  var2 = c("a", "b", "c"),
  var3 = c(TRUE, FALSE, TRUE)
)

A few “example” dataframes are directly available in base R, e.g., mtcars, iris

Tip

You can view the first rows of a data frame with head()

head(iris)

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

Packages

Install packages with install.packages()

install.packages("tidyverse")
install.packages("easystats")

tidyverse¹ and easystats² are actually collections of packages
Load packages with library()
- This simply makes the functions of the package available in the current session
- You can still call functions from packages that are not loaded by explicitly mentioning the package name pkg::fun()

Tip

It is good practice to explicitly mention a function’s package when using it, e.g. dplyr::select(), especially when using less popular functions.

ggplot basics (1)

ggplot2 is the main R package for data visualization
It is based on the Grammar of Graphics _{^{(Wilkinson, 2005)}}
The main function is ggplot()
1. Takes a data frame as first argument
2. Followed by a mapping of variables to aesthetic characteristics (x, y, color, shape, etc.)
3. We can then add layers to the plot with +
Note: In ggplot (and most tidyverse) packages, variables are not quoted (x=Sepal.Length, not x="Sepal.Length")
- This is not typically the case (in other packages and languages)

library(tidyverse)

ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width)) +
  geom_point() +
  geom_density_2d() +
  theme_classic()

ggplot basics (2)

The arguments passed to ggplot() are inherited by the layers
One can specify different data & aesthetics for each layer

ggplot() +
  geom_point(data=iris, aes(x = Sepal.Length, y = Sepal.Width)) +
  geom_density_2d(data=iris, aes(x = Sepal.Length, y = Sepal.Width)) +
  theme_classic()

ggplot basics (3)

Aside from aesthetics and data, other arguments can be used to customize the plot

ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width)) +
  geom_point(color="yellow", size=4, shape="triangle") +
  geom_density_2d(color="red") +
  see::theme_abyss()  # Package in easystats

ggplot basics (4)

Warning

Misnomer: do NOT confuse arguments that are “aesthetics” in aes() (i.e., map variable names to aesthetic features) with arguments that control the appearance of the plot (not in aes())

ggplot(iris) +
  geom_point(aes(x = Sepal.Length,
                 y = Sepal.Width,
                 color="blue"))

ggplot(iris) +
  geom_point(aes(x = Sepal.Length,
                 y = Sepal.Width),
             color="blue")

ggplot basics (5)

The appearance of aesthetic mappings can be controlled with scale_*()

iris |>
  ggplot(aes(x = Sepal.Length, y = Sepal.Width, color=Species)) +
  geom_point(size=3) +
  scale_color_manual(values=list(setosa="orange",
                                 versicolor="purple",
                                 virginica="green")) +
  see::theme_abyss()

For loops

For loops are used to iterate over a sequence of values

myvec <- c("Tom", "Dom", "Harry")
for(x in myvec){
  print(x)
}

[1] "Tom"
[1] "Dom"
[1] "Harry"

It is convenient to iterate over sequences of numbers, e.g., 1:10

for(i in 1:10){
  print(i)
}

[1] 1
[1] 2
[1] 3
[1] 4
[1] 5
[1] 6
[1] 7
[1] 8
[1] 9
[1] 10

It is useful to initialize an empty list to then store some result at each iteration

myseq <- c()  # Initialize empty vector
for(i in 1:10){
  # Take 10 random elements from this list 
  newvector <- sample(c(1, 2, 3), 10, replace = TRUE) 
  # Compute mean
  mu <- mean(newvector)
  # Append to myseq
  myseq <- c(myseq, mu)
}
myseq

 [1] 1.7 2.1 1.8 1.8 2.7 2.2 1.6 1.9 2.2 1.9

Functions

Functions are self-contained factories
- They take some variables in (through arguments)
- They return some output

# Define a new function
do_an_addition <- function(x, y) {
  result <- x + y
  return(result)  
}

# Call the function
result <- do_an_addition(x=2, y=3)
result

[1] 5

Quizz Time

1 + "1" returns an error. Why?
What’s the difference between c() and list()?
In ggplot, aesthetics refer to visual customization (e.g., change the color of all points)
A pipe takes the output of the previous function as the first argument of the next
What will True * 3 return?
What will TRUE / 10 return?
I do ggplot(iris, aes(x="Sepal.Length", y="Petal.Length")) but it throws an error. Why?
I do ggplot(iris, aes(x=Sepal.Length, y=Petal.length)) but it throws an error. Why?
I am running mutate(data, x = 3) but it says Error in mutate(x) : could not find function "mutate". Why?
What is the problem with the following:

do_a_multiplication <- function(numbers) {
  result <- x * y
  return(result)  
}

The End _{^{(for now)}}

Thank you!

Bayesian Statistics

Follow the slides

The Environment

Setup

Vocabulary

Panels

Creating New Document

Options

Interacting

Programming Concepts

Classes

Vectors vs. Lists (1)

Vectors vs. Lists (2)

Pipes

DataFrames

Packages

ggplot basics (1)

ggplot basics (2)

ggplot basics (3)

ggplot basics (4)

ggplot basics (5)

For loops

Functions

Quizz Time

The End (for now)

The End _{^{(for now)}}