# 🔖 Probability and Statistics in Julia

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## 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

### Markovian

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.

### Bayesian

WIP or may not work

## 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.
WIP or may not work
• 🏚️ 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

Density_estimation

## Multivariate

Multivariate

• 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).

## Geostatistics

Geostatistics

• 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.
WIP or may not work
• 🏚️ SmoothingKernels.jl :: Smoothing kernels for use in kernel regression and kernel density estimation.

## COMPOSITIONAL

• CoDa.jl :: Compositional Data Analysis in Julia

## Causal

WIP or may not work
• 🏚️ CauseMap.jl :: An implementation of Convergent Cross Mapping (CCM), a method for causal inference in non-linear dynamics systems, written in Julia.

## Sampling

• 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.
WIP or may not work
• 🏚️ PSIS.jl :: Pareto smoothed importance sampling (PSIS) and PSIS leave-one-out cross-validation for Julia.

## Tests

• HypothesisTests.jl :: T-tests, Wilcoxon rank sum (Mann-Whitney U), signed rank, and circular statistics in Julia.
WIP or may not work
• 🏚️ RobustStats.jl :: A collection of robust statistical tests based on the R package WRS (R-Forge repository) by Rand Wilcox.

## Unclassified

• BloomFilters.jl :: are a probabilistic data structur e that can be used to test the inclusion and exclusion of items in a list. (No `Project.toml`)
• Civecm.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.
• Distributions.jl :: Probability distributions in Julia.
• 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.
• PortHamiltonian.jl :: Port-Hamiltonian systems in Julia. (No `Project.toml`)
• RankAggregation.jl :: Rank aggregation in Julia.
• Rmath.jl :: Archive of functions that emulate R’s d-p-q-r functions for probability distributions.
• StatsBase.jl :: Basic statistics.
• TopicModels.jl :: TopicModels for Julia.
WIP or may not work
• 🏚️ 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.