Feature Request: Easy Fan Plots

[ParadaCarleton]

A fan-plot is a visually-appealing way to display many confidence (or credible) intervals at once. This makes it easier to look at the uncertainty as a continuous whole, which helps counter bad habits like discounting any values that fall outside a 95% confidence interval. Here's a good example of a fan plot:

It'd be great if these were easier to make!

[asinghvi17]

Could you post some code of how you deal with it right now? To my perspective this seems appropriate:

# example code from https://makie.juliaplots.org/stable/examples/plotting_functions/band/#:~:text=color%20%3D%20%3Ared)%0A%0Af-,using%20Statistics,-using%20CairoMakie%0A%0Af
f = Figure()
Axis(f[1, 1])

n, m = 100, 101
t = range(0, 1, length=m)
X = cumsum(randn(n, m), dims = 2)
X = X .- X[:, 1]
μ = vec(mean(X, dims=1)) # mean
lines!(t, μ)              # plot mean line
σ = vec(std(X, dims=1))  # stddev

# end example code
# plot decreasing "confidence intervals" - replace this with real confint calculations
for i in 1:4 # sigma/i
    band!(t, μ + σ ./ i, μ - σ ./ i, color = (:red, 0.3))
end
f

Basically, this "stacks" transparency so that each succeeding layer appears more and more opaque. Thus we go from outside (large width) to inside (small width).

[ParadaCarleton]

Could you post some code of how you deal with it right now? To my perspective this seems appropriate:

# example code from https://makie.juliaplots.org/stable/examples/plotting_functions/band/#:~:text=color%20%3D%20%3Ared)%0A%0Af-,using%20Statistics,-using%20CairoMakie%0A%0Af
f = Figure()
Axis(f[1, 1])

n, m = 100, 101
t = range(0, 1, length=m)
X = cumsum(randn(n, m), dims = 2)
X = X .- X[:, 1]
μ = vec(mean(X, dims=1)) # mean
lines!(t, μ)              # plot mean line
σ = vec(std(X, dims=1))  # stddev

# end example code
# plot decreasing "confidence intervals" - replace this with real confint calculations
for i in 1:4 # sigma/i
    band!(t, μ + σ ./ i, μ - σ ./ i, color = (:red, 0.3))
end
f

Basically, this "stacks" transparency so that each succeeding layer appears more and more opaque. Thus we go from outside (large width) to inside (small width).

Oh wow, that's great! Maybe this should be in a tutorial?

[ParadaCarleton]

Actually, thinking about it, this kind of stacking might be a problem for users who also want to create a legend; is there a way to add one to make it clear what each color represents?

[asinghvi17]

Hmm, that's a good point. In the legend each plot would be displayed at an equal transparency.

One could certainly create a custom legend element instead of the automatic one, with the same stacking behaviour (by stacking PolyElement or similar).

[jkrumbiegel]

You can also precompute the colors you get here by stacking with alpha by blending red with white in different ratios. That would then look correct in the legend automatically.

[ParadaCarleton]

Another comment: continuous fan plots can be a big improvement on ones that show only a handful of intervals. Examples can be found here.

[asinghvi17]

This kind of thing should be easily doable with surface. Consider the following code (yes, a little long :D): Viridis colormap :rainbow_bgyr_35_85_c72_n256 colormap

# Fan plot replication

using KernelDensity, Trapz
# construct data
xs = LinRange(0, 1, 100)

y_data = [randn(1000) .* (1+x) .+ x^2 .+ x * 0.3 for x in xs]

# helper functions

function cumtrapz(x, y)
    return [trapz(@view(x[begin:i]), @view(y[begin:i])) for i in axes(x, 1)]
end

function grid_kde(data, N = 100; min_cutoff=0.05)
    k = KernelDensity.kde(data)
    ct = cumtrapz(k.x, k.density)
    minind = findfirst(>(min_cutoff), ct)
    maxind = findlast(<(1-min_cutoff), ct)
    xs = LinRange(k.x[minind], k.x[maxind], N)  
    return (xs, pdf.(Ref(InterpKDE(k)), xs))
end

# process data to extract "distributions"
N = 200
x_vals = zeros(N, length(xs))
y_vals = zeros(N, length(xs))
y_colors = zeros(N, length(xs))

for i in 1:length(xs)
    x_vals[:, i] .= xs[i]
    y_vals[:, i], y_colors[:, i] = grid_kde(y_data[i], N; min_cutoff = 0.01)
    # uncomment the following if you do not want absolute coloring
    # y_colors[:, i] ./= maximum(@view(y_colors[:, i]))
end

fig = Figure()
ax = Axis(fig[1, 1])
plt = surface!(ax, x_vals, y_vals; color = y_colors, shading = false)
fig

[asinghvi17]

Here's an interesting plot I made with this (to try and see a continuous confidence interval):

[ffreyer]

Is this something we want to support as a plot type or something that users should do on their own (i.e. document in BeautifulMakie or here as a more complex usage example)?

[asinghvi17]

Probably something users can do on their own, though I'd like to leave the issue open for documentation in that case. The recipe is super specific.

[aplavin]

A basic version of a discrete fan plot is easy to achieve with generic functions and recipes already: Hard to see any potential way for improvement here...

Btw, even more convenient with multiplot (experimental) from MakieExtra: