🔖 Probability and Statistics in Julia


See also

Probabilistic programming

📖 Probabilistic programming

  • Gen.jl :: Probabilistic programming with programmable inference.
  • Omega.jl :: Causal, Higher-Order, Probabilistic Programming.
  • 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

📖 Stochastic process


Markov Logic Network

  • POMDPs.jl :: A Julia framework for solving Markov decision processes.
  • POMDPToolbox.jl :: Support tools for solving POMDPs.
  • HMMBase.jl :: A lightweight abstraction for hidden Markov models (HMM) in Julia.



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Statistic Regression analysis

Regression analysis

  • CurveFit.jl :: Simple least squares and curve fitting functions.
  • FixedEffectModels.jl :: Fast estimation of linear models with IV and high dimensional categorical variables.
  • GLM.jl :: Linear models (LM) and generalized linear models (GLM).
  • Isotonic.jl :: This implements several algorithms for isotonic regression in Julia. (No Project.toml)
  • LARS.jl :: Least angle regression.
  • Lasso.jl :: Lasso solvers for linear and generalized linear models.
  • MixedModels.jl :: A Julia package for fitting (statistical) mixed-effects models.
  • NonNegLeastSquares.jl :: Some nonnegative least squares solvers in Julia.
  • QuantileRegression.jl :: Quantile regression in Julia.
  • SparseRegression.jl :: Statistical Models with Regularization in Pure Julia.
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  • 🏚️ FLSA.jl :: Computing the Fused LASSO Signal Approximator to denoise data.
  • 🏚️ ParallelSparseRegression.jl :: A Julia library for parallel sparse regression, that implements solvers for regression problems including least squares, ridge regression, LASSO, non-negative least squares, and elastic net; and proposes to add fast methods to obtain regularization paths.
  • 🏚️ Regression.jl :: Algorithms for regression analysis (e.g. linear regression and logistic regression).

Density estimation




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



  • GeoStats.jl :: High-performance geostatistical algorithms in Julia.
  • GeoStatsImages.jl :: Training images for geostastical simulation.
  • GslibIO.jl :: Utilities to read/write extended GSLIB files in Julia.

Time series

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 : an easy to use Julia implementation.
  • 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.
  • 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.
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  • 🏚️ SmoothingKernels.jl :: Smoothing kernels for use in kernel regression and kernel density estimation.

Online algorithm


  • CoDa.jl :: Compositional Data Analysis in Julia



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  • 🏚️ CauseMap.jl :: An implementation of Convergent Cross Mapping (CCM), a method for causal inference in non-linear dynamics systems, written in Julia.


  • Bootstrap.jl :: Bootstrapping is a widely applicable technique for statistical estimation, especially in the absence of closed-form solutions.
  • GeneralizedSampling.jl :: Generalized Sampling in Julia.
  • Jackknife.jl :: Jackknife resampling and estimation in Julia.
  • Jags.jl :: Julia package for using Just another Gibbs sampler.
  • MonteCarloMeasurements.jl :: Uncertainty propagation by Monte-Carlo sampling: Real numbers with uncertainty represented by particle clouds.
  • RecombinatorKMeans.jl :: An implementation of the recombinator-k-means method.
  • StableDQMC.jl :: Numerical stabilization routines for determinant quantum Monte Carlo.
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  • 🏚️ PSIS.jl :: Pareto smoothed importance sampling (PSIS) and PSIS leave-one-out cross-validation for Julia.


  • HypothesisTests.jl :: T-tests, Wilcoxon rank sum (Mann-Whitney U), signed rank, and circular statistics in Julia.
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  • 🏚️ RobustStats.jl :: A collection of robust statistical tests based on the R package WRS (R-Forge repository) by Rand Wilcox.


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  • 🏚️ CTDE.jl :: Continuous time, discrete event system in Julia.
  • 🏚️ DirichletProcessMixtures.jl :: This package implements Dirichlet Process Mixture Models in Julia using variational inference for truncated stick-breaking representation of Dirichlet Process.
  • 🏚️ FactorModels.jl :: Factor models or diffusion index models.
  • 🏚️ JointMoments.jl :: Tensors and statistics for joint central moments.
  • 🏚️ KernSmooth.jl :: A direct port of the R package KernSmooth, (v2.23-10.), carrying an unlimited license.
  • 🏚️ PowerLaws.jl :: A Julia package for power laws distributions.
  • 🏚️ PValueAdjust.jl :: P-value adjustment methods for multiple testing correction.

  1. Julia.jl is under COPYRIGHT © 2012-Now SVAKSHA, dual-licensed for the data (ODbL-v1.0+) and the software (AGPLv3+), respectively. ↩︎