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Turing.jl

Bayesian inference with probabilistic programming.

Intuitive

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

General-purpose

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

Modular

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

High-performance

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)
end

News feed

Google Summer of Code 2022 — February 17, 2022
Google Summer of Code 2021 — February 10, 2021
Google Summer of Code 2020 — September 11, 2020
Replication study: Estimating number of infections and impact of NPIs on COVID-19 in European countries (Imperial Report 13) — May 14, 2020
Turing's Blog — December 14, 2019

News

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.

Samplers

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

Ecosystem

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

AdvancedHMC

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

MCMCChains

Chain types and utility functions for MCMC simulations.

Bijectors

Automatic transformations for constrained random variables.