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Bayesian inference with probabilistic programming.


Turing models are easy to read and write — models work the way you write them.


Turing supports models with discrete parameters and stochastic control flow. Specify complex models quickly and easily.


Turing is modular, written fully in Julia, and can be modified to suit your needs.


Turing is fast.

Hello World in Turing — Linear Gaussian Model

Turing's modelling syntax allows you to specify a model quickly and easily. Straightforward models can be expressed in the same way as complex, hierarchical models with stochastic control flow.

Quick Start

@model function demo(x, y)
# Assumptions
σ2 ~ InverseGamma(2, 3)
σ = sqrt(σ2)
μ ~ Normal(0, σ)

# Observations
x ~ Normal(μ, σ)
y ~ Normal(μ, σ)

Advanced Markov Chain Monte Carlo Samplers

Turing provides Hamiltonian Monte Carlo sampling for differentiable posterior distributions, Particle MCMC sampling for complex posterior distributions involving discrete variables and stochastic control flow, and Gibbs sampling which combines particle MCMC, HMC and many other MCMC algorithms.


Interoperable With Deep Learning Libraries

Turing supports Julia's Flux package for automatic differentiation. Combine Turing and Flux to construct probabilistic variants of traditional machine learning models.

Bayesian Neural Network Tutorial

Bayesian Neural Network Tutorial


Join the Turing community to contribute, learn, and get your questions answered.


Report bugs, request features, discuss statistical applications/theory, and more.

Go to GitHub

Turing.jl Discourse

Browse and join discussions on Turing.

Go to Turing.jl Discourse


Discuss advanced topics. Request access here.

Go to Slack


Explore a rich ecosystem of libraries, tools, and more to support development.


Robust, modular and efficient implementation of advanced Hamiltonian Monte Carlo algorithms.

Go to AdvancedHMC


Chain types and utility functions for MCMC simulations.

Go to MCMCChains


Automatic transformations for constrained random variables.

Go to Bijectors