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Probability-Statistics.md

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§1. PROBABILITY

§1.1. Probabilistic Programming

  • DynamicPPL.jl :: Implementation of domain-specific language (DSL) for dynamic probabilistic programming
  • Gen.jl :: Probabilistic programming with programmable inference.
  • Omega.jl :: Causal, Higher-Order, Probabilistic Programming.
  • Soss.jl :: A library for probabilistic programming.
  • 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.

§1.2. STOCHASTICS

§1.2.1. Bayesian

§1.2.2. Gaussian

§1.2.3. Markovian

The 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 in Julia.

STATISTICS

REGRESSION

  • CovarianceMatrices.jl :: Covariance Matrix Estimation in Julia.
  • CurveFit.jl :: Simple least squares and curve fitting functions.
  • FixedEffectModels.jl :: Fast estimation of linear models with IV and high dimensional categorical variables.
  • FLSA.jl :: Computing the Fused LASSO Signal Approximator.
  • GLM.jl :: Linear models (LM) and generalized linear models (GLM).
  • Isotonic.jl :: This implements several algorithms for isotonic regression in Julia.
  • LARS.jl :: Least angle regression.
  • Lasso.jl :: Lasso solvers for linear and generalized linear models.
  • Metida.jl :: Julia package for fitting mixed-effects models with flexible random/repeated covariance structure.
  • MixedModels.jl :: A Julia package for fitting (statistical) mixed-effects models.
  • NonNegLeastSquares.jl :: Some nonnegative least squares solvers in Julia.
  • 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.
  • QuantileRegression.jl :: Quantile regression in Julia.
  • Regression.jl :: Algorithms for regression analysis (e.g. linear regression and logistic regression).
  • SparseRegression.jl :: Statistical Models with Regularization in Pure Julia.

DENSITIES

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).

SPATIAL

  • 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.

TEMPORAL

  • BasisFunctionExpansions.jl :: Basis Function Expansions for Julia.
  • ControlSystemIdentification.jl :: System Identification for LTI systems, compatible with ControlSystems.jl.
  • DependentBootstrap.jl :: A module that implements several varieties of the dependent statistical bootstrap as well as the corresponding block-length selection procedures.
  • DCCA.jl :: Detrended cross-correlations coefficient analysis : an easy to use Julia implementation.
  • 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.
  • SmoothingKernels.jl :: Smoothing kernels for use in kernel regression and kernel density estimation.
  • Temporal.jl :: Flexible and efficient time series class & methods for the Julia language.
  • TimeSeries.jl :: Time-series toolkit for Julia.

ONLINE

COMPOSITIONAL

  • CoDa.jl :: Compositional Data Analysis in Julia

EXTREMES

CAUSAL

  • 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.
  • PSIS.jl :: Pareto smoothed importance sampling (PSIS) and PSIS leave-one-out cross-validation for Julia.
  • RecombinatorKMeans.jl :: An implementation of the recombinator-k-means method.
  • StableDQMC.jl :: Numerical stabilization routines for determinant quantum Monte Carlo.

TESTS

  • HypothesisTests.jl :: T-tests, Wilcoxon rank sum (Mann-Whitney U), signed rank, and circular statistics in Julia.
  • 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 structure that can be used to test the inclusion and exclusion of items in a list.
  • AdaGram.jl :: Adaptive Skip-gram implementation.
  • Civecm.jl :: Cointegration in Vector Error Correction Models in Julia.
  • CTDE.jl :: Continuous time, discrete event system in Julia.
  • ConjugatePriors.jl :: A package to support conjugate prior distributions.
  • DiscriminantAnalysis.jl :: A package for linear and quadratic regularized Discriminant Analysis.
  • Divergences.jl :: A Julia package for evaluating divergences.
  • DirichletProcessMixtures.jl :: This package implements Dirichlet Process Mixture Models in Julia using variational inference for truncated stick-breaking representation of Dirichlet Process.
  • Distances.jl :: A Julia package for evaluating distances(metrics) between vectors.
  • Distributions.jl :: Probability distributions in Julia.
  • FactorModels.jl :: Factor models or diffusion index models.
  • FeldtLib.jl :: Comparing two set of samples (empirical distributions)Baumgartner-Weis-Schindler statistic and tests.
  • FreqTables.jl :: Frequency tables.
  • GaussDCA.jl :: Multivariate Gaussian Direct Coupling Analysis for residue contact prediction in protein families.
  • 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.
  • Rmath.jl :: Archive of functions that emulate R's d-p-q-r functions for probability distributions.
  • RankAggregation.jl :: Rank aggregation in Julia.
  • StatsBase.jl :: Basic statistics.
  • TopicModels.jl :: TopicModels for Julia.
  • PortHamiltonian.jl :: Port-Hamiltonian systems in Julia.