Probability and Statistics

• Wikipedia: Probability.
• Julia stats organization.

Resources

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

Probabilistic programming

Wikipedia: Probabilistic programming

• cscherrer/Soss.jl : Probabilistic programming via source rewriting.
• JuliaGaussianProcesses/Stheno.jl : Probabilistic programming with Gaussian processes in Julia.
• mschauer/Mitosis.jl : Automatic probabilistic programming for scientific machine learning and dynamical models.
• probcomp/Gen.jl : Probabilistic programming with programmable inference.
• StanJulia/Stan.jl : A Julia wrapper for the Stan language.
• TuringLang/Turing.jl : A Turing complete probabilistic programming language.
• zenna/Omega.jl : Causal, Higher-Order, Probabilistic Programming.

Stochastic process

Wikipedia: Stochastic process

Markov Logic Network

Wikipedia: Markov Logic Network

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

Gaussian

• davidavdav/GaussianMixtures.jl : Julia modules for Gaussian Mixture Models.
• STOR-i/GaussianProcesses.jl : A Julia package for Gaussian Processes.

Bayesian

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

Statistic Regression analysis

Wikipedia: Regression analysis

• ahwillia/NonNegLeastSquares.jl : Some nonnegative least squares solvers in Julia.
• FixedEffects/FixedEffectModels.jl : Fast estimation of linear models with IV and high dimensional categorical variables.
• francescoalemanno/KissSmoothing.jl : Easily smooth your data with a denoise() function.
• joshday/SparseRegression.jl : Statistical Models with Regularization in Pure Julia.
• JuliaStats/GLM.jl : Linear models (LM) and generalized linear models (GLM).
• JuliaStats/GLMNet.jl : Julia wrapper for glmnet, fitting Lasso/ElasticNet GLM models.
• JuliaStats/Lasso.jl : Lasso solvers for linear and generalized linear models.
• JuliaStats/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.
• JuliaStats/MixedModels.jl : A Julia package for fitting (statistical) mixed-effects models.
• JuliaStats/Survival.jl : A Julia package for performing survival analysis.
• pjabardo/CurveFit.jl : Simple least squares and curve fitting functions.
• pkofod/QuantileRegressions.jl : Quantile regression in Julia.
• rafael-guerra-www/LinearFitXYerrors.jl : Linear Regression with errors in both X and Y, correlated or not, confidence intervals and plots.
• simonster/LARS.jl : Least angle regression.
• viraltux/Smoothers.jl : a collection of smoothing heuristics, models and smoothing related applications.

Density estimation

Wikipedia: Density_estimation

• joshday/AverageShiftedHistograms.jl : David Scott's Average Shifted Histogram (ASH) density estimation.
• JuliaStats/KernelDensity.jl : Kernel density estimators for continuous variables.
• noilreed/MultiKDE.jl : Multivariate kernel density estimation.

Multivariate

Wikipedia: Multivariate statistics

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

Geostatistics

See earth-space-science.

Time series

Wikipedia: Time series

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

Online algorithm

• joshday/OnlineStats.jl : Online algorithms for statistics.

Compositional Data Analysis

Wikipedia: Compositional Data Analysis

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

Extreme value theory

Wikipedia: Extreme value theory

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

Sampling

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

Tests

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

Misc

• andreasnoack/Cointegration.jl : Cointegration in Vector Error Correction Models in Julia.
• carlobaldassi/GaussDCA.jl : Multivariate Gaussian Direct Coupling Analysis for residue contact prediction in protein families. paper
• diegozea/ROC.jl : Receiver Operating Characteristic (ROC) Curve.
• gragusa/CovarianceMatrices.jl : Covariance Matrix Estimation in Julia.
• gragusa/Divergences.jl : A Julia package for evaluating divergences.
• johnmyleswhite/BloomFilters.jl : are a probabilistic data structure that can be used to test the inclusion and exclusion of items in a list.
• JuliaML/RankAggregation.jl : Rank aggregation in Julia.
• JuliaStats/ConjugatePriors.jl : A package to support conjugate prior distributions.
• JuliaStats/Distances.jl : A Julia package for evaluating distances(metrics) between vectors.
• JuliaStats/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.
• JuliaStats/Rmath.jl : Archive of functions that emulate R's d-p-q-r functions for probability distributions.
• JuliaStats/StatsBase.jl : Basic statistics.
• lejon/TSne.jl : T-SNE visualisation technique.
• nalimilan/FreqTables.jl : Frequency tables.
• robertfeldt/FeldtLib.jl : Misc julia code that have not yet found its home in a package...
• sbos/AdaGram.jl : Adaptive Skip-gram implementation.
• slycoder/TopicModels.jl : Topic Models are Bayesian, hierarchical mixture models of discrete data.
• trthatcher/DiscriminantAnalysis.jl : A package for linear and quadratic regularized Discriminant Analysis.