Setting up Pluto.jl

Pluto is nice as you can prototype pretty fast.

Important

Pluto.jl has its own dependency management included!

If you want to add packages that are not registered, you have to activate your own environment. For example

using Pkg
Pkg.activate(mktempdir())
Pkg.add("/path/to/your/package/CoolPackage")
Pkg.add(url="https://github.com/username/MyPackage.jl")

using CoolPackage,MyPackage

To run pluto in the first place use:

]add Pluto
Pluto.run()

Task 1: Visualize some statistic properties

1. Data

Generate 500 normally distributed samples

Tip

You might want to make your results reproducible by fixing some seeds for the random generators. The two most common random generators used in julia are Random.MersenneTwister and StableRNGs.StableRNG - For this execrise I would recommend the latter (even though MersenneTwister is much more common to be used), thus run:

using StableRNGs
randn(StableRNG(1),100)

to get 100 random numbers.

Scale the random numbers to fullfill std(x) ≈ 10

functionize it

Next wrap that code in a function simulate which takes two arguments, a random seed and the number of samples

2. cumulative mean

Calculate the cumulative mean of a single simulation. save it to a variable

Note that there is no cummean function, but clever element-wise division in combination with cumsum should lead you there - or you just use a loop 🤷

click to show solution

cumsum(x) ./ (1:length(x))

3. Plotting!

Now for your first plot. Use a scatter plot¹ to visualize the cummulative mean output, if you do not generate a Figure() + ax = f[1,1] = Axis(f) manually, you can get it back by the scatter call. f,ax,s = scatter(). This is helpful as we later want to extend the Axis and Figure with other plot elements

Use hlines! to add a horizontal line at your “true” value

4. Subplot

simulate repeatedly

Let’s simulate 1000x datasets, each with a different seed, and take the mean over all simulated values

click to show tip

An easy way to call a function many times is to broadcast it on an array created e.g. via 1:1000 - you could also use map to do it, but I don’t think it is as clear :)

click to show solution

simulate.(1:1000,nmax)

Mean it

calculate the mean of each simulation

click to show solution

using Statistics
mean.(simulate.(1:1000,nmax))

# or 
sum.(...) ./ nmax

Add it as a subplot

We want to add a histogram of the 1000 means to the plot.

Add a new Axis to f[1,2]
use it to plot the histogram of the means via hist! - don’t forget to change the direction=:x to flip the histogram
link the axes using linkaxes

5. Prettify it

There are some simple tricks to make a plot look nicer:

remove the “box” using `hidespines!(ax,:r,:t)
resize the right sub-plot to be smaller colsize! and Relative(X)
hide the x-grid (type ax.+ TAB to find all possible attributes)
hide the xlabels + xticks + bottomspine from the right subplot
add two Labels (A) and (B) to the plot
Bonus: use color to color the cummulative sum samples according to how many samples went into that sum. colormap=:Reds looks good to me!

Bonus: Click for more fancy labels

You can create a slightly fancier label by adding a circle around it :)

    Label(f[1,2,TopLeft()],"B",padding=[0,0,5,0])
    Label(f[1,2,TopLeft()],"⭕",padding=[0,0,8,0],fontsize=30)

Task 2: Interactivity!

Using the Pluto.jl reactive backend, changing a value in some cell will automatically update all other cells - including plots.

We can use Sliders instead of fixing the parameters of the simulation

A slider is defined like this:

@bind yourVarName PlutoUI.Slider(from:to) # from:step:to is optional, step by def 1

Adding interactivity via sliders

Define a slider that controls the number of samples from 1:500
Define a second slider that adds a constant offset to all values of the simulation simulation
make sure to fix the x/y-limits to get a nice looking plot :-)

Bonus: Advanced slider management

After understanding the slightly awkward syntax, the following gives a nice collection of Sliders, Checkboxes, Widgets etc. with at the same time being drag-and-dropable and in a sidebar. Neat!

using PlutoExtras

PlutoExtras.BondTable([
    PlutoExtras.@BondsList "Sliders" let 
        "name A" = @bind(varA,PlutoUI.Slider(1:500))
        "name B" = @bind(varB, PlutoUI.Slider(-5:5))
    end
    ])

Task 3: AlgebraOfGraphics

For this task we need a dataset, and I choose the US EGG dataset for it’s simplicity for you.

to load the data, use the following code

using DataFrames, HTTP, CSV
# dataset via https://github.com/rfordatascience/tidytuesday/tree/master
df = CSV.read(download("https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2023/2023-04-11/egg-production.csv"),DataFrame)

If you dislike Pluto.jl

If you dont like to use Pluto.jl, you can of course switch back to VSCode. Then you have to create a new environment and add the packages you use before.

🥚 vs. 🗓

Visualize the number of eggs against the year

Tip

To get a first overview, first(df) , describe(df) and names(df) are typically helpful

Split them up

Next split them up, choose color and col and choose reasonable columns from the dataset

Rotate the labels

Use the trick from the handout to modify a plot after it was generated: Rotate the x-label ticks by some 30°

:::callout-tip instead of rotating each axis manually, you can also replace the draw command in your pipeline with an anonymous function. This allows you to specify additional arguments e.g. to the axis, for all “sub”-plots

... |> x-> draw(x;axis=(;xlims = (-3,2)))

1: Note the ; before xlims, this enforces that a NamedTuple is created

Footnotes

after a using CairoMakie↩︎