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Kai Xu edited this page Jul 3, 2018 · 19 revisions

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Several models are benchmarked against Stan with HMC sampler for 2,000 iterations.


Model Turing Stan Ratio
Bernoulli Model 0.55 0.021 26.2
School 8 1.2 0.05 24.0
100,000D Gaussian 351.4 80.31 4.38
Kid 6.9 2.1 3.29
Latent Dirichlet Allocation 156.8 205.3 0.76
Mixture of Categorical 16.6 10.9 1.52
Naive Bayes 630.4 37.27 16.91
Hidden Markov Model 274.97 21.85 12.58
Stochastic Volatility 12.04 0.5769 20.87


Numbers here are inference time in second - smaller number indicates better performance.


Numbers are highly dependent on models and size of data. For different models, Turing.jl is generally 3 ~ 30 times slower than Stan. For the same model, when the size of data increases, the gap between Turing and Stan becomes very small.


Turing.jl is currently using ForwardDiff.jl for automatic differentiation, which is believed to be the main reason of slowness of Turing.jl. This AD backend will be replaced by a reverse-mode AD implementation when Julia has a mature one.


New benchmark based on ReverseDiff.jl. Note when data or model is very small, the constant overhead of Turing.jl makes the ratio very large.


  • Commit: f4ca7bfc8a63e5a6825ec272e7dffed7be623b31
  • Hardware: MacBook Pro (Retina, 13-inch, Late 2013),
    • Processor: 2.4 GHz Intel Core i5,
    • Memory: 8 GB 1600 MHz DDR3
    • Graphics: Intel Iris 1536 MB (not used)



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