BayesDensity.jl

BayesDensity.jl is a Julia package for nonparametric univariate Bayesian density estimation. It offers a unified interface to a variety of density estimators developed in the statistical literature, and supports posterior inference via both Markov chain Monte Carlo (MCMC) and variational inference methods. Moreover, the package is designed to be extensible, allowing new estimators to make use of its built-in methods for posterior inference without requiring additional boilerplate code.

Installation

The BayesDensity.jl package is part of the Julia general registry, and can as such easily be installed via the default package manager:

using Pkg
Pkg.add("BayesDensity")

Alternatively, it is possible to install each of the Bayesian density estimators implemented in this package separately. For instance, the histogram smoother estimator can be downloaded as follows:

Pkg.add("BayesDensityHistSmoother")

If you encounter any problems during the installation process, we encourage you to open an issue in this repository!

Quick start

To get started, we illustrate the basic use of the package by fitting a histogram smoother to a two-component mixture of normal densities:

using BayesDensity, Distributions, Random
rng = Random.Xoshiro(1) # for reproducibility

# Simulate some data:
d_true = MixtureModel([Normal(-0.2, 0.25), Normal(0.5, 0.15)], [0.4, 0.6])
x = rand(rng, d_true, 1000)

# Create a histogram smoother model object:
hs = HistSmoother(x)

Having specified a model for the data, we can perform posterior inference through Markov chain Monte Carlo methods or variational Bayes:

mcmc_fit = sample(rng, hs, 5000; n_burnin=1000) # MCMC
vi_fit, info = varinf(hs)                       # VI

The resulting fitted model objects can be used to compute posterior quantities of interest such as the posterior median of the density evaluated at given point(s) t through median(mcmc_fit, t). Additionally, the package also provides convenience plotting functions through its Makie.jl and Plots.jl extensions, making it easy to visualize the density estimates. For instance, one can easily plot the posterior mean, along with a 95% credible interval with Makie as follows:

using CairoMakie
plot(mcmc_fit) # Based on MCMC
plot(vi_fit)   # Based on VI

For a more thorough introduction to the API and the capabilities of the package, we refer the interested reader to the documentation.

Supported versions

This package makes use of the workspaces feature introduced in Julia 1.12. As a result, this package currently supports release 1.12.0 and newer ones. In the future, the plan is to support the Long-Term Support (LTS) release and newer versions, but only after the version of the LTS release exceeds 1.12.0.

The package is continuously tested via CI on the latest stable Julia 1.12 release as well as Julia pre releases (i.e. upcoming versions in their pre-release stage). This helps ensure compatibility with future Julia versions while maintaining stability on the current stable release.