Julia: Multivariate Normal Distribution – Alicia’s Side Projects

Plot of multivariate normal distribution.

Simple Multivariate Normal Distribution

Define the distribution

μ = [0.0, 0.0]  # Means
Σ = [1.0 0.0; 0.0 1.0]  # Covariance matrix--off diagonal 0.0, directions uncorrelated.
mv_gaussian = MvNormal(μ, Σ);  # ; To suppress output from cell

Plot the PDF as a countour plot

# Create a grid of points for the x and y axes
xs = range(start=-3, stop=3, length=100)
ys = range(start=-3, stop=3, length=100)

# Compute the PDF values over the grid
zs = [pdf(mv_gaussian, [x, y]) for x in xs, y in ys]

fig = Figure(resolution = (775, 700))
ax = Axis(fig[1, 1])
contour_plot = CairoMakie.contour!(ax, xs, ys, zs, levels=20, colormap=:viridis, linewidth = 3)
Colorbar(fig[1, 2], limits=(0, maximum(zs)), colormap=:viridis, flipaxis=false, size=50)
fig

┌ Warning: Found `resolution` in the theme when creating a `Scene`. The `resolution` keyword for `Scene`s and `Figure`s has been deprecated. Use `Figure(; size = ...` or `Scene(; size = ...)` instead, which better reflects that this is a unitless size and not a pixel resolution. The key could also come from `set_theme!` calls or related theming functions.
└ @ Makie ~/.julia/packages/Makie/ux0Te/src/scenes.jl:238

Plot 10,000 random samples as a histogram

samples = rand(mv_gaussian, 100000)
x_samples = samples[1, :]
y_samples = samples[2, :]

histogram2d(x_samples, y_samples, nbins=(100, 100), colormap=:viridis, normalize=true, size=(700, 600))