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Statistics, Operations Research (OR), Actuarial Finance, etc. Machine Learning (ML) and Statistics are closely related fields, so do check out the AI.md page for ML packages.

ACTUARIAL SCIENCE

Econometrics

  • copula.jl :: Julia Copula package implements the gaussian AR1 copula.
  • DynamicFactorModels.jl :: Dynamic Factor Models for Julia.
  • Dynare.jl :: This package aims at bringing to Julia some of the algorithms incorporated in Dynare, a platform for solving dynamic economic models.
  • GARCH.jl :: Generalized Autoregressive Conditional Heteroskedastic (GARCH) models for Julia.
  • Jconometrics.jl :: MATLAB to Julia port of Spatial Econometrics.
  • julia_timeseries :: Time-series analysis functions for Julia.
  • Loss.jl :: General functions for estimating loss functions inspired by Kaggle's release of code for many common metrics.
  • QuantEcon.jl :: This package collects code for quantitative economic modeling. It is currently comprised of two main parts: 1. A toolbox of routines useful when doing economics and 2. Implementations of types and solution methods for common economic models.
    • Quantitative economic modelling lecture series in Julia language, designed and written by Thomas J. Sargent and John Stachurski, that is freely available as a PDF file too.
  • RuinProbability.jl :: For calculating the ruin probability with real data under different claims models.
  • SolveDSGE :: The package contains a variety of methods for solving Dynamic Stochastic General Equilibrium (DSGE) models to first- or second-order accuracy. It will be of most interest to macro-economists, but others may find the routines for reordering the complex Schur form and the generalized complex Schur form useful.

Finance

  • AssetMgmt.jl :: Asset Management.
  • BigFinance.jl :: Analysis of high frequency quantitative data.
  • BusinessDays.jl :: A highly optimized Business Days calculator written in Julia language. Also known as Working Days calculator.
  • EodData.jl :: Julia package for connecting to the EodData.com XML Web Service.
  • FinMarkets.jl :: Describe and model financial markets objects using Julia.
  • FRED.jl :: Package to read from the St. Louis Federal Reserve Bank API.
  • Ito.jl :: An open source toolkit for financial computing in Julia.
  • LibTrading.jl :: A wrapper for the libtrading library, an "open source API for high-performance, low-latency trading applications".
  • MCInsurance.jl :: This Julia package provides multi-period Monte Carlo simulations for life insurance.
  • OpenFiscaCore.jl :: A port of OpenFisca-Core to Julia. This is the core module of OpenFisca, without GUI or country-specific code & data.
  • OpenFiscaFrance.jl :: A port of OpenFisca-France to Julia, containing the formulas and parameters of the french tax-benefit system.
  • Quandl.jl :: Julia api to Quandl open source financial, economic and social datasets.
  • SDE.jl :: Simulation and inference for Ito processes and diffusions.
  • stockMonitor.jl :: A module which constantly collects and performs analyses the stock market.
  • TradingSystem.jl :: Quantitative trading framework in Julia.
  • WorldBankDataTd.jl :: Accessing World Bank Data.
  • ZVSimulator.jl :: The ZVSimulator package provides a framework for assessing the zero variance (ZV) principle for Monte Carlo or random sampling via simulation.

Org-JuliaQuant

  • FinancialBlotter.jl :: Financial Instruments and Accounting in Julia.
  • FinanceStats.jl :: An experimental sandbox of functions that implement common statistical methods in finance.
  • Grist.jl :: Financial blotter.
  • Timestamps.jl :: Immutable timestamped values.
  • TradeModels.jl :: Modeling the allocation of resources to markets based on the restraints of objective functions.
  • TradingLogic.jl :: An attempt at a unified framework in Julia language for both event-driven backtesting and live trading. This package utilizes reactive programming elements implemented in Reactive.jl.
Learning Resources

BENCHMARKS

Preprocessor

OPERATIONS RESEARCH

  • CGRASP.jl :: Continuous Greedy Randomized Adaptive Search Procedure (CGRASP), in Julia.
  • CSDP.jl :: Julia wrapper for the CSDP semidefinite programming solver.
  • CutPools.jl :: Pools of cutting planes for JuMP models.
  • jlSimplex :: Proof-of-concept implementation of the (dual) simplex algorithm for linear programming in Julia.
  • jobshop :: The Jobshop (Open Shop Scheduling Problem (OSSP)) problem is solved with evolutionary strategies in Julia.
  • MinFinder.jl :: The MinFinder algorithm to find all the minima for a differentiable function inside a bounded domain.
  • OptimizationServices.jl :: Julia interface to COIN-OR Optimization Services. This Julia package is intended to be an interface between MathProgBase.jl and COIN-OR Optimization Services (OS), translating between the Julia-expression-tree MathProgBase format for nonlinear objective and constraint functions and the Optimization Services instance Language (OSiL) XML-based optimization problem interchange format.
  • Predictors.jl
  • Ranking.jl :: Tools for ranking in Julia.
  • RationalSimplex.jl :: Pure Julia implementation of the simplex algorithm.
  • SemidefiniteProgramming.jl :: This package provides a Julia interface for low-level modeling of semidefinite programming problems and for solving semidefinite programs with solvers such as SDPA and CSDP.
  • TrafficAssignment.jl :: A package for traffic assignment that loads the network data and finds the user equilibrium traffic pattern.
  • VRP :: Vehicle Routing Problem (VRP) is a combinatorial optimization and integer programming problem.
Resources
  • ORSoftwareTools2014 :: This is the repository for code/examples/instructions for the MIT course 15.S60 "Software Tools for Operations Research".
  • DG2012Tutorial.jl :: Simple examples of SGD-style computations in Julia.

Optimization

  • ampl.jl :: Julia interface to the AMPL Solver Library (ASL).
  • AMPLMathProgInterface.jl :: Wrapper for MathProgBase.jl {see the JuliaOpt section below}.
  • BARON.jl :: A wrapper for the BARON mixed-integer nonlinear programming solver.
  • BlackBoxOptim.jl :: An experimental, work-in-progress global optimization framework for Julia, supporting both multi- and single-objective optimization problems, focused on (meta-)heuristic/stochastic algorithms (DE, PSO, CMA-ES etc).
  • BLOM.jl :: A Julia port of the Berkeley Library for Optimization Modeling (Work-In-Progress).
  • CPLEX.jl :: The CPLEX.jl package provides an interface for using IBM's CPLEX Optimizer™ from the Julia language. You cannot use CPLEX.jl without having purchased and installed a copy of CPLEX Optimizer™ from IBM. This package is available free of charge and in no way replaces or alters any functionality of IBM's CPLEX Optimizer product.
  • CUTEst.jl :: Julia interface for CUTEst.
  • DDUS.jl :: Data-driven Uncertainty Sets for the JuMPeR framework.
  • ECOS.jl :: Julia wrapper for the ECOS SOCP solver.
  • GeneticAlgorithms.jl :: is a lightweight framework that simplifies the process of creating genetic algorithms and running them in parallel.
  • IProfile :: Preferably, use IProfile in Base packages to profile your code, which contains an "instrumenting profiler" for the Julia language. And, ReadTheDocs
  • JuliaCMAES :: CMA-ES port - a mix of the original minimal MATLAB implementation (purecmaes.m) and the full one (cmaes.m).
  • JuMP.jl :: Modelling language for Linear, Integer, and Quadratic Programming.
    • Resources::JuMP::
    • JuMPSupplement :: Repository containing supplementary materials and code for "JuMP: A Modeling Language for Mathematical Optimization" by I. Dunning, J. Huchette, and M. Lubin.
  • JuMPeR.jl :: Julia for Mathematical Programming (JuMP) extension for Robust optimization.
  • JuMPStoch.jl :: A stochastic optimization framework for JuMP.
  • Junquo.jl :: stands for "JUlia Nonconvex QUadratically constrained quadratic program Optimizer", a (mixed-integer) nonconvex quadratically constrained quadratic program (QCQP) solver.
  • LossFuns.jl :: An implementation of loss functions for empirical risk minimization.
  • LSQ.jl :: is a library that makes it easy to formulate and solve least-squares optimization problems with linear equality constraints.
  • Memoize.jl :: Easy memoization for Julia.
  • MOpt.jl :: Parallel derivative-free Moment Optimization for Julia.
  • NEOS.jl :: A Julia interface for the NEOS Optimisation Server.
  • NLTester :: Code for benchmarks comparing AMPL, Julia, and YALMIP (MATLAB) for nonlinear modeling.
  • PerfPlot.jl :: Performance Profile Plot.
  • pikaia.jl :: Genetic Algorithms (GA's).
  • Polyopt.jl :: Julia package for polynomial optimization using semidefinite programming, with some presentation notebooks of an optimization package.
  • Proximal.jl :: Translation of Parikh and Boyd code for proximal algorithms.
  • Quadprog.jl :: A wrapper around Ipopt.jl to solve quadratic programming problems. This package provides the function quadprog which calls the Ipopt.jl library for Interior Point Nonlinear Optimization.
  • QuickCheck.jl :: is listed in METADATA and based on QuickCheck specification-based randomized tester for Julia.
  • scheduleCrew.jl.
  • SCIP.jl by @mlubin :: An optimization software for mixed-integer programs.
  • SCIP.jl by @ryanjoneil :: A Julia interface to the SCIP solver.
  • SCS.jl :: Julia Wrapper for SCS (https://github.com/cvxgrp/scs).
  • SGDOptim.jl :: A julia package for Stochastic Gradient Descent.
  • SGD.jl by @johnmyleswhite :: Fit models using SGD in Julia.
  • SGDDemo.jl :: Stochastic Gradient Descent (SGD) predictive models for large data sets in Julia.
  • SGD2.jl :: Stochastic gradient descent, a draft of new methods for SGD calculations.
  • simplex.jl :: Practice project program that performs the simplex algorithm.

Genetic Programming

  • CGP.jl :: Cartesian Genetic Programming (CGP) implemented in Julia.
  • GaussDCA.jl :: Multivariate Gaussian Direct Coupling Analysis for residue contact prediction in protein families.
  • InformedDifferentialEvolution.jl :: Implementation of Differential Evolution with optional custom predictors.
  • ParallelGenocop.jl :: Parallel implementation of Genocop - a genetic algorithm for numerical optimization problems with linear constraints.

Org-JuliaOpt

An umbrella group for Julia-based optimization-related projects, with its own mailing list at Google groups.

  • Cbc.jl :: Julia interface to the mixed-integer linear programming solver Cbc via the CoinMP C library.
  • Convex.jl :: a Julia library for mathematical programming that makes it easy to formulate and fast to solve nonlinear convex optimization problems. It can use (nearly) any solver that complies with the MathProgBase interface, including Mosek, Gurobi, ECOS, SCS, and GLPK.
  • GLPKMathProgInterface.jl :: Interface between the GLPK.jl wrapper and MathProgBase.jl.
  • Gurobi.jl :: is a Julia interface for the Gurobi Optimizer, a commercial optimization solver for a variety of mathematical programming problems, including linear programming (LP), quadratic programming (QP), quadratically constrained programming (QCP), mixed integer linear programming (MILP), mixed-integer quadratic programming (MIQP), and mixed-integer quadratically constrained programming (MIQCP).
  • Ipopt.jl :: is a Julia interface to the Ipopt nonlinear solver.
  • KNITRO.jl :: This package provides an interface for using the KNITRO solver from the Julia language, which can only be used after having purchased and installed a copy of KNITRO from Ziena Optimization.
  • LsqFit.jl :: Simple curve fitting functionality from Optim.jl has been moved into its own package.
  • MathProgBase.jl :: Solver-independent functions (incl. linprog and mixintprog) and low-level interface for Mathematical Programming.
  • Mosek.jl :: Interface to the Mosek solver in Julia.
  • NLopt.jl :: Package to call the NLopt nonlinear-optimization library from the Julia language.
  • Optim.jl :: A basic optimization algorithms implementation.

Regression Analysis

  • FLSA.jl :: Computing the Fused LASSO Signal Approximator.
  • HD.jl :: High-dimensional tools.
  • Lasso.jl :: Lasso solvers for linear and generalized linear models.
  • 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.
  • OutOfSampleBootstrap.jl :: Regression model validation (out-of-sample) statistics.
Resources

STATISTICS

  • AdaGram.jl :: Adaptive Skip-gram implementation.
  • AD_StatTest-julia :: An implementation of the Anderson Darling statistical test for exponential or Rayleigh distributions in Julia.
  • ApproXD.jl :: B-splines and linear high-dimensional approximators in multiple dimensions for Julia.
  • ASH.jl :: David Scott's Average Shifted Histogram density estimation.
  • BasicSpace.jl :: A port of the R "basicspace" package to Julia.
  • Bootstrap.jl :: Bootstrapping is a widely applicable technique for statistical estimation, especially in the absence of closed-form solutions.
  • Causality.jl :: A Julia Package for Causal Inference.
  • CauseMap.jl :: An implementation of Convergent Cross Mapping (CCM), a method for causal inference in non-linear dynamics systems, written in Julia.
  • Civecm.jl :: Cointegration in Vector Error Correction Models in Julia.
  • ConditionalRandomFields.jl :: Scalable Conditional Random Fields code for Julia.
  • ConjugatePriors.jl :: Closed form expressions for conjugate priors in Julia.
  • CRBM.jl :: Conditional RBMs package.
  • CrossDecomposition.jl :: Canonical-Correlation Analysis (CCA).
  • CTDE.jl :: Continuous time, discrete event system in Julia.
  • CurveFit.jl :: Simple least squares and curve fitting functions.
  • JointMoments.jl :: Tensors and statistics for joint central moments.
  • DA.jl :: A package for linear and quadratic regularized Discriminant Analysis.
  • DiscreteFactor.jl :: Discrete factor and its operations in Probabilistic Graphical Models.
  • DiscreteInference.jl :: Viterbi algorithm.
  • DiscriminantAnalysis.jl :: Methods for discriminant analysis, in Julia.
  • Divergences.jl :: A Julia package for evaluating divergences.
  • DPMM.jl :: Dirichlet Process Mixture Models in Julia.
  • DirichletProcessMixtures.jl :: This package implements Dirichlet Process Mixture Models in Julia using variational inference for truncated stick-breaking representation of Dirichlet Process.
  • Earth.jl :: is the wrapper for the stand-alone version of R's earth package. The Earth package in R for Multivariate Adaptive Regression Splines (MARS), a form of regression analysis.
  • FactorModels.jl :: Factor models or diffusion index models.
  • FeldtLib.jl :: Comparing two set of samples (empirical distributions)Baumgartner-Weis-Schindler statistic and tests.
  • FixedEffectModels.jl :: Linear models with instrumental variables and/or high dimensional fixed effects
  • Hotspot.jl :: Hotspot modeling.
  • HyperLogLog.jl :: A simple HyperLogLog implementation in Julia.
  • HypothesisTests.jl :: T-tests, Wilcoxon rank sum (Mann-Whitney U), signed rank, and circular statistics in Julia.
  • Isotonic.jl :: This implements several algorithms for isotonic regression in Julia.
  • ITC.jl :: Code for modeling intertemporal choice in Julia.
  • JAGS.jl :: A Julia interface to JAGS, to provide a shared library as an interface between Julia and JAGS - Just another Gibbs sampler.
  • Jags.jl :: Julia package for using Just another Gibbs sampler.
  • KernSmooth.jl :: A direct port of the R package KernSmooth, (v2.23-10.), carrying an unlimited license.
  • KLDivergence.jl :: KL-divergence estimation in Julia.
  • LARS.jl :: Least angle regression.
  • 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.
  • MixedModels.jl :: A Julia package for fitting (statistical) mixed-effects models.
  • MixtureModels.jl :: A Julia package for probabilistic mixture models.
  • MultivariateAnalysis.jl :: A Julia package for multivariate data analysis (e.g. dimension reduction).
  • NaiveBayes.jl :: Simple Naive Bayes implementation in Julia.
  • NullableArrays.jl :: Prototype of the new JuliaStats NullableArrays package designed to replace DataArrays.jl.
  • NURBS.jl :: A Julia package for manipulating NURBS objects (curves, surfaces, volumes, etc.).
  • NHST.jl :: Null hypothesis significance tests.
  • Pandas.jl :: A Julia front-end to Python's Pandas package.
  • pgm.jl :: Another probabilistic graphical model repo.
  • PGM0.jl :: A bottom-up approach to probabilistic graphical models.
  • ProbabilisticModeling.jl :: A BUGS-like language for describing probabilistic models in Julia.
  • ProbTopicModels.jl :: Probabilistic topic models.
  • PValueAdjust.jl :: P-value adjustment methods for multiple testing correction.
  • QuantileRegression.jl :: Quantile regression in the Julia language.
  • Queries :: Composable queries for Julia DataFrames.
  • RandomProcesses.jl :: Random processes (CRP, CRT) in Julia.
  • RBM.jl
  • Resampling.jl :: Tools for resampling data.
  • Ridge.jl :: Ridge regression and classification.
  • Rmath.jl :: Archive of functions that emulate R's d-p-q-r functions for probability distributions.
  • RunningStats.jl :: Julia translation of John D. Cook's code for running moment statistics and univariate regressions.
  • SDP.jl by @trthatcher :: Statistical Data Processing.
  • SimpleRL.jl :: A bare-bones package for simulating RL models and estimating them from behavioral data.
  • SpecialFunctions.jl :: Functions for AMOS, a statistical software package for structural equation modeling, produced by SPSS.
  • TopicModels.jl :: TopicModels for Julia.
  • Turing.jl :: A Turing complete probabilistic programming language embedded in Julia.
  • VCOV.jl :: Build StatusHeteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation for Julia.
  • VStatistic.jl :: Implements the v-statistic, a measure that compares the estimation accuracy of the ordinary least squares estimator against a random benchmark.
Resources

Org-JuliaStats.

Probabilistic Programming

  • OpenPP.jl :: Open Source Probabilistic Programming in Julia.
  • Sigma.jl :: A probabilistic programming environment implemented in Julia that allows you to specify probabilistic models as normal programs, and perform inference.
  • Stan.jl :: Julia package for using Stan, a probabilistic programming language for Bayesian inference written in C++, and licensed under the New BSD License. The Stan language is used to specify a Bayesian statistical model, which is an imperative declaration of the log probability density function.
  • Stochy.jl :: Probabilistic Programming in Julia.

Bayesian

  • ABCAuction :: Code for ABC, SMIL and CU-II estimation of a structural auction model.
  • ABCDistances.jl :: Performs approximate Bayesian computation (ABC) using various distance functions.
  • BayesianDataFusion.jl :: Implementation of data fusion methods.
  • BayesEstDiffusion.jl :: Code accompanying the paper Frank van der Meulen, Moritz Schauer: Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals : https://arxiv.org/abs/1406.4704
  • BayesModels.jl :: Tools and Building Blocks for Bayesian Modeling and Probabilistic Inference.
  • BayesNets.jl :: Bayesian Networks for Julia.
  • Bolstad2.jl :: Julia functions from W.M. Bolstad's "Understanding Computational Bayesian Statistics".
  • MCBN.jl :: Monte Carlo Bayesian averaging over Bayesian networks.
  • NestedSampling.jl :: Nested Sampling algorithms for Julia.
  • VarBayes.jl :: Variational Bayesian methods in Julia.

Gaussian

  • GP.jl :: Gaussian processes in Julia.
  • GaussianMixtures.jl :: Julia modules for Gaussian Mixture Models.
  • GaussQuadrature.jl :: Another package that generates the points and weights of the Gauss quadrature rules.
  • GaussianProcesses.jl :: A port of the Gaussian Processes toolkit to Julia.
  • NaiveBayes.jl :: The Gaussian Naive Bayes model in Julia.
  • Schauder.jl :: A graphical perspective on Gauss-Markov process priors and fast sparse Cholesky for hierarchically structured (generalized arrow) matrices.

Monte Carlo Method

  • Augur.jl :: Monte Carlo simulations, statistics and plotting tools for the Augur event consensus algorithm.
  • Church.jl :: Perform MCMC inference in complex, and simple, probabilistic models.
  • GeometricMCMC.jl :: Geometric MCMC algorithms and zero-variance (ZV) Monte Carlo Bayesian routines.
  • MCMC2.jl :: Alternative MCMC package design demo.
  • MCMCExampleRepository.jl :: Repository for MCMC Julia examples.
  • MCMCModels.jl :: Scratch space for hosting temporarily current model specification for MCMC inference.
  • SimpleMCMC.jl :: Small framework for MCMC sampling and maximization on user-defined models.

Statistical Tests

  • RobustStats.jl :: A collection of robust statistical tests based on the R package WRS (R-Forge repository) by Rand Wilcox.
  • StatTests.jl :: [A set of statistical tests for Julia.

[TimeSeries](https://en.wikipedia.org/wiki/Time_series] Analysis

  • DependentBootstrap :: A module that implements several varieties of the dependent statistical bootstrap as well as the corresponding block-length selection procedures.
  • KernelDensity.jl :: Kernel density estimators that can handle univariate and bivariate data, but only continuous variables.
  • KernelEstimator.jl :: The julia package for nonparametric density estimate and regression.
  • KernelStat :: A module for the Julia language for kernel-function based statistics.
  • KSVM.jl :: Kernel Support Vector Machine (SVM) written in Julia.
  • MarketTechnicals.jl :: Technical analysis of financial time series in Julia.
  • RARIMA :: An ARIMA (Autoregressive Integrated Moving Average) module for the Julia language that uses libraries from the R-language.
  • SmoothingKernels.jl :: Smoothing kernels for use in kernel regression and kernel density estimation.
  • TimeSeries.jl :: Time-series toolkit for Julia.
  • TimeModels.jl :: Modeling time series in Julia.

RESOURCES

Cookbooks

Slides

Videos