MCMCLogDensityProblems.jl: Vectorised Log Density Targets for MCMC

This package contains common target distributions in Bayesian inference, with vectorised log-density and gradient evaluation supported.

A minimal example

target = Banana()               # the banana distribution

x = randn(dim(target))          # size(x) is (2,)
@info logpdf(target, x)         # -433.1
@info logpdf_grad(target, x)    # (-433.1, [646.1, 129.8])

x = hcat(x, x)                  # size(x) is (2, 2)
@info logpdf(target, x)         # [-433.1, -433.1]
@info logpdf_grad(target, x)    # ([-433.1, -433.1], [646.1 646.1; 129.8 129.8])

A note on the gradient interface

All targets support logpdf_grad(target, x::VecOrMat), which returns a tuple of log-densities and their gradients. The gradient in most cases (if I didn't hand-code them) is computed via ReverseDiff.jl, which compiles a tape for the gradient. Thus, if you were to call the gradient multiple times, you can potentially save the compilation time by avoiding calling logpdf_grad directly, but instead

gradfunc = gen_logpdf_grad(target, x)
gradfunc(x) # 1st time
gradfunc(x) # 2nd time
            # ...

Also note that gen_logpdf_grad still expects the second argument x::Union{AbstractVector, AbstractMatrix} to correctly dispatch on vectorised mode or not.

Targets included

• Banana distribution: Banana()

  

• Multivariate diagonal Gaussian: HighDimGaussian(dim)

  

• Mixture of Gaussians

  • One dimensional mixture of gaussians: OneDimGaussianMixtures()

  

  • Two dimensional mixture of gaussians: TwoDimGaussianMixtures()

  

• Spiral distribution: Spiral(n_gaussians, σ)

  

• Neal's funnel: Funnel()

  

• Logistic regression on the German credit dataset

• Log-Gaussian Cox point process on the Finnish pine saplings dataset

  • Dataset raw

    

  • Dataset processed

    Note that the visualisations above are not the posterior but rather just datasets.