Slice Sampling Algorithms in Julia

This package implements slice sampling algorithms accessible through the AbstractMCMC interface. For general usage, please refer to here.

Implemented Algorithms

Univariate Slice Sampling Algorithms

• Univariate slice sampling (Slice) algorithms by R. Neal ¹:
  • Fixed window (Slice)
  • stepping-out window adaptation (SliceSteppingOut)
  • doubling-out window adaptation (SliceDoublingOut)

Meta Multivariate Samplers for Augmenting Univariate Samplers

• Random permutation coordinate-wise Gibbs sampling² (RandPermGibbs)
• Hit-and-run sampling³ (HitAndRun)

Multivariate Slice Sampling Algorithms

• Latent slice sampling (LSS) by Li and Walker⁴ (LatentSlice)
• Gibbsian polar slice sampling (GPSS) by P. Schär, M. Habeck, and D. Rudolf⁵ (GibbsPolarSlice)

Example with Turing Models

This package supports the Turing probabilistic programming framework:

using Distributions
using Turing
using SliceSampling

@model function demo()
    s ~ InverseGamma(3, 3)
    m ~ Normal(0, sqrt(s))
end

sampler   = RandPermGibbs(SliceSteppingOut(2.))
n_samples = 10000
model     = demo()
sample(model, externalsampler(sampler), n_samples)

The following slice samplers can also be used as a conditional sampler in Turing.Experimental.Gibbs sampler:

• For multidimensional variables:
  • RandPermGibbs
  • HitAndRun
• For unidimensional variables:
  • Slice
  • SliceSteppingOut
  • SliceDoublingOut

See the following example:

using Distributions
using Turing
using SliceSampling

@model function simple_choice(xs)
    p ~ Beta(2, 2)
    z ~ Bernoulli(p)
    for i in 1:length(xs)
        if z == 1
            xs[i] ~ Normal(0, 1)
        else
            xs[i] ~ Normal(2, 1)
        end
    end
end

sampler = Turing.Experimental.Gibbs(
    (
        p = externalsampler(SliceSteppingOut(2.0)),
        z = PG(20, :z)
    )
)

n_samples = 1000
model     = simple_choice([1.5, 2.0, 0.3])
sample(model, sampler, n_samples)

Footnotes

1. Neal, R. M. (2003). Slice sampling. The annals of statistics, 31(3), 705-767. ↩

2. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, (6). ↩

3. Bélisle, C. J., Romeijn, H. E., & Smith, R. L. (1993). Hit-and-run algorithms for generating multivariate distributions. Mathematics of Operations Research, 18(2), 255-266. ↩

4. Li, Y., & Walker, S. G. (2023). A latent slice sampling algorithm. Computational Statistics & Data Analysis, 179, 107652. ↩

5. Schär, P., Habeck, M., & Rudolf, D. (2023, July). Gibbsian polar slice sampling. In International Conference on Machine Learning. ↩