MANOVABNPTest.jl

A Julia package that implements the Bayesian nonparametric (BNP) MANOVA model described in Gutiérrez et al. (2022).

Installation

Install with the Julia package manager Pkg:

# Press ']' to enter the Pkg REPL mode.
pkg> add https://github.com/igutierrezm/MANOVABNPTest.jl

or

julia> using Pkg; 
julia> Pkg.add(url = "https://github.com/igutierrezm/MANOVABNPTest.jl")

We recommend you create a Pkg environment for each project you use JuMP for, instead of adding lots of packages to the global environment. The Pkg manager documentation has more information on this topic. For example, if you want to install MANOVABNPTest.jl to use it in a project located at <dir>, you should install MANOVABNPTest.jl as follows:

julia> using Pkg; 
julia> Pkg.activate("<dir>")
julia> Pkg.add(url = "https://github.com/igutierrezm/MANOVABNPTest.jl")

Getting started

After installation, you can execute the hypothesis test by calling train(). This function has 3 main arguments: y (an N x D matrix of outcomes), x (an N-dimensional vector of group labels) and grid (an M-dimensional vector indicating M grid points for plotting purposes). You can also add a random number generator rng if desired. Here is a minimal example:

# Load the relevant datasets
using MANOVABNPTest
using Random

# Simulate (y, x, grid)
rng = MersenneTwister(1)
grid = collect(-3.0:0.1:3.0)
x = 1 .+ collect(0:99) .% 4
y = randn(rng, 100, 2)

# Fit the model
out = train(y, x, grid; rng);

The result is a named tuple with 2 DataFrames: hypotheses (containing the posterior probability of each hypothesis) and densities (containing the posterior predictive distribution over a cartesian product of the selected grid of points). Both dataframes are already in tidy format, so they are easy to use in combination with any ploting library that explotes the grammar of graphics, such as AlgebraOfGraphics.jl.

Using MANOVABNP.jl from R

R users can also use this package thanks to the R package JuliaConnectoR. Verify, install Julia.

Tip: We recommend installing Julia following these platform-specific instructions.

Next, make sure that JuliaConnectoR can call Julia:

Tip: The easiest way to ensure this is by adding Julia's bin/ folder to your PATH environment variable. This is also explained in detail in Julia's platform-specific instructions. It is important to understand that installing Julia is not enough, it must also be reachable from R.

Next, install JuliaConnectoR as usual:

install.packages("JuliaConnectoR")

Next, create/activate a Julia environment. For example, if your project is located as <dir>, you should create the environment as follows:

library(JuliaConnectoR)
Pkg <- juliaImport('Pkg')
Pkg$activate("<dir>")

Next, install MANOVABNPTest.jl as follows:

Pkg$add(url = "https://github.com/igutierrezm/MANOVABNPTest.jl")

Next, import the Julia packages MANOVABNPTest and Random as follows:

MANOVABNPTest <- juliaImport('MANOVABNPTest')
Random <- juliaImport('Random')

After this setup, we can execute our hypothesis test in R just as in Julia. Here is a minimal example:

set.seed(1)
y <- matrix(rnorm(200), 100, 2)
x <- as.integer(1 + 0:99 %% 4)
grid <- seq(-3, 3, by = 0.1)
rng <- Random$MersenneTwister(1L)
out <- MANOVABNPTest$train(y, x, grid, rng = rng)

Note that the result is a pointer to a Julia object. To collect the results, we can proceed as follows:

posterior_g <- data.frame(out$hypotheses) # p(gamma | y, x)
posterior_f <- data.frame(out$densities)  # p(y* | y, x)

Here is a glimpse the collected results

head(posterior_g, 3)
#   hypothesis   prob
# 1  [0, 0, 0] 0.7715
# 2  [1, 0, 0] 0.0055
# 3  [0, 1, 0] 0.2120

head(posterior_f, 3)
#   j var1 var2   y1 y2            f
# 1 1    1    2 -3.0 -3 2.802552e-05
# 2 1    1    2 -2.9 -3 3.213636e-05
# 3 1    1    2 -2.8 -3 3.708808e-05

As you can see, the results are already in tidy format, so they are easy to use in combination with any ploting library that explotes the grammar of graphics, such as ggplot2. However, the columns of inside the dataframe posterior_f are not easy to interpret. Here is the definition of each variable:

• f: The value of posterior predictive density when y[var1] == y1, y[var2] == y2 and x == j.
• j: The group indicator.
• var1, var2: Which outcomes are considered in this row.
• y1: The value of the variable with ID var1 considered in this row.
• y2: The value of the variable with ID var2 considered in this row.

Using this information, you can then plot each posible bivariate density.

Gallery

More elaborate examples are stored in extras/.

Notes

1. Currently, this package is a prototype. I'm planning to convert this prototype into a fully fledged package (including a proper documentation) during the following 6 months.

2. Currently, the package has been tested under Julia 1.5.3 and R 4.0.0. For full reproducibility, consider running this example in a Docker container generated from the Docker image generated by the file Dockerfile.