Probability and Statistics

• Wikipedia: Probability.
• Julia stats organization.

Resources

• StatsWithJuliaBook : a collection of all 200+ code blocks contained in the book: Statistics with Julia: Fundamentals for Data Science, Machine Learning and Artificial Intelligence
• ISLR.jl : Julia version of “An Introduction to Statistical Learning: With Applications in R”.

Probabilistic programming

Wikipedia: Probabilistic programming

• Gen.jl : Probabilistic programming with programmable inference.
• Mitosis.jl : Automatic probabilistic programming for scientific machine learning and dynamical models.
• Omega.jl :  Causal, Higher-Order, Probabilistic Programming.
• RollingFunctions.jl : Roll a function over data, run a statistic along a weighted data window.
• Soss.jl : Probabilistic programming via source rewriting.
• Stan.jl : A Julia wrapper for the Stan language.
• Stheno.jl : Probabilistic programming with Gaussian processes in Julia.
• Turing.jl : A Turing complete probabilistic programming language.

Stochastic process

Wikipedia: Stochastic process

• Pigeons.jl :  Sampling from intractable distributions, with support for distributed and parallel methods.

Markov Logic Network

Wikipedia: Markov Logic Network

• HMMBase.jl : A lightweight abstraction for hidden Markov models (HMM) in Julia.
• ParticleFilters.jl : Simple particle filter implementation in Julia - works with POMDPs.jl models or others.
• POMDPs.jl : A Julia framework for solving Markov decision processes. Its support tool is POMDPToolbox.jl

Gaussian

• GaussianMixtures.jl : Julia modules for Gaussian Mixture Models.
• GaussianProcesses.jl : A Julia package for Gaussian Processes.

Bayesian

• BayesNets.jl : Bayesian Networks for Julia.
• KissABC.jl : Pure julia implementation of Multiple Affine Invariant Sampling for efficient Approximate Bayesian Computation (ABC).
• RxInfer.jl : Julia package for automated Bayesian inference on a factor graph with reactive message passing.

Statistic Regression analysis

Wikipedia: Regression analysis

• CurveFit.jl : Simple least squares and curve fitting functions. JuliaCon 2025
• FixedEffectModels.jl : Fast estimation of linear models with IV and high dimensional categorical variables.
• GLM.jl : Linear models (LM) and generalized linear models (GLM).
• GLMNet.jl : Julia wrapper for glmnet, fitting Lasso/ElasticNet GLM models.
• KissSmoothing.jl : Easily smooth your data with a denoise() function.
• LARS.jl : Least angle regression.
• Lasso.jl : Lasso solvers for linear and generalized linear models.
• LinearFitXYerrors.jl : Linear Regression with errors in both X and Y, correlated or not, confidence intervals and plots.
• LinearRegressionKit.jl: Linear Regression for Julia.
• Loess.jl : is a loess implementation based on the fast kd-tree based approximation algorithm, a space-partitioning data structure for organizing points in a k-dimensional space.
• LsqFit.jl : Simple curve fitting functionality from Optim.jl has been moved into its own package.
• MixedModels.jl : A Julia package for fitting (statistical) mixed-effects models.
• MixedModelsSmallSample.jl : inference adjustments for MixedModels.jl. JuliaCon 2025
• NonNegLeastSquares.jl : Some nonnegative least squares solvers in Julia.
• QuantileRegressions.jl : Quantile regression in Julia.
• Smoothers.jl : a collection of smoothing heuristics, models and smoothing related applications.
• SparseRegression.jl : Statistical Models with Regularization in Pure Julia.
• Survival.jl : A Julia package for performing survival analysis.

Density estimation

Wikipedia: Density_estimation

• AverageShiftedHistograms.jl : David Scott’s Average Shifted Histogram (ASH) density estimation.
• KernelDensity.jl : Kernel density estimators for continuous variable
• MultiKDE.jl : Multivariate kernel density estimation.

Multivariate

Wikipedia: Multivariate statistics

• LowRankModels.jl : modeling and fitting generalized low rank models.
• ManifoldLearning.jl : manifold learning and non-linear dimensionality reduction.
• MultivariateStats.jl : multivariate data analysis (e.g. dimension reduction).

Time series

Wikipedia: Time series

• BasisFunctionExpansions.jl : Basis Function Expansions for Julia.
• ControlSystemIdentification.jl : System Identification for LTI systems, compatible with ControlSystems.jl.
• DCCA.jl : Detrended cross-correlations coefficient analysis.
• DependentBootstrap.jl : A module that implements several varieties of the dependent statistical bootstrap as well as the corresponding block-length selection procedures.
• LPVSpectral.jl : Least-squares (sparse) spectral estimation and (sparse) LPV spectral decomposition.
• MessyTimeSeries.jl : Time series analysis compatible with incomplete data.
• PerronFrobenius.jl : Estimating the transfer operator (Perron Frobenius operator) and invariant measures from time series.
• Temporal.jl : Flexible and efficient time series class & methods for the Julia language.
• TimeSeries.jl : Time-series toolkit for Julia.

Online algorithm

• OnlineStats.jl : Online algorithms for statistics.

Compositional Data Analysis

Wikipedia: Compositional Data Analysis

• CoDa.jl : Compositional Data Analysis in Julia. Inspired by R compositions package.

Extreme value theory

Wikipedia: Extreme value theory

• ExtremeStats.jl : analysing and estimating extreme value distributions.

Sampling

• Bootstrap.jl : Bootstrapping is a widely applicable technique for statistical estimation, especially in the absence of closed-form solutions.
• Distributions.jl : Probability distributions in Julia.
• EllipticalSliceSampling.jl : elliptical slice sampling in the Julia language. JuliaCon 2021 video
• GeneralizedSampling.jl : Generalized Sampling in Julia.
• Jackknife.jl : Jackknife resampling and estimation in Julia.
• Jags.jl : Julia package for using Just another Gibbs sampler.
• RecombinatorKMeans.jl : An implementation of the recombinator-k-means method.
• StableDQMC.jl : Numerical stabilization routines for determinant quantum Monte Carlo.

Statistical tests

• HypothesisTests.jl : T-tests, Wilcoxon rank sum (Mann-Whitney U), signed rank, and circular statistics in Julia.
• PowerAnalyses.jl : Statistical power (power = 1 - β) analyses, where β is Type II error (false negative).

Misc

• AdaGram.jl : Adaptive Skip-gram implementation.
• BloomFilters.jl : are a probabilistic data structure that can be used to test the inclusion and exclusion of items in a list.
• Cointegration.jl : Cointegration in Vector Error Correction Models in Julia.
• ConjugatePriors.jl : A package to support conjugate prior distributions.
• CovarianceMatrices.jl : Covariance Matrix Estimation in Julia.
• DiscriminantAnalysis.jl : A package for linear and quadratic regularized Discriminant Analysis.
• Distances.jl :  A Julia package for evaluating distances(metrics) between vectors.
• Divergences.jl : A Julia package for evaluating divergences.
• FeldtLib.jl : Misc julia code that have not yet found its home in a package…
• FreqTables.jl : Frequency tables.
• GaussDCA.jl : Multivariate Gaussian Direct Coupling Analysis for residue contact prediction in protein families. paper
• NMF.jl : Factorizing a non-negative matrix X into the product of two lower rank matrices W and H, such that WH optimally approximates X.
• RankAggregation.jl : Rank aggregation in Julia.
• Rmath.jl : Archive of functions that emulate R’s d-p-q-r functions for probability distributions.
• ROC.jl : Receiver Operating Characteristic (ROC) Curve.
• StatsBase.jl : Basic statistics.
• TopicModels.jl : Topic Models are Bayesian, hierarchical mixture models of discrete data.
• TSne.jl : T-SNE visualisation technique.