A Monte Carlo Markov Chain sampler that makes use of gradient information. Proposed by Livingstone et al. (2021)
The adaptative preconditioning is based on Andrieu and Thoms (2008), Algorithm 4 in Section 5. For details see Algorithm 7.2 of the supporting information of Livingstone et al. (2021).
] add BarkerMCMC
See the documentation for all arguments.
using BarkerMCMC
# --- Target distribution
function log_p_rosebruck_2d(x; k=1/200)
-k*(100*(x[2] - x[1]^2)^2 + (1 - x[1])^2)
end
function ∇log_p_rosebruck_2d(x; k=1/200)
[-2*k*(200*x[1]^3 - 200*x[1]*x[2] + x[1] -1), # d/dx[1]
-200*k*(x[2] - x[1]^2)] # d/dx[2]
end
# --- Sampling
# see `?barker_mcmc` for all options
res = barker_mcmc(log_p_rosebruck_2d,
∇log_p_rosebruck_2d,
[5.0, 5.0];
n_iter = 1_000,
target_acceptance_rate=0.4)
res.samples
res.log_p
# --- Result
# acceptance rate
length(unique(res.samples[:,1])) / size(res.samples, 1)
# You may want to use `MCMCChains.jl` for plots and diagonstics
# (must be installed separately)
using MCMCChains
using StatsPlots
chain = Chains(res.samples, [:x1, :x2])
chains[200:10:end] # remove burn-in and thinning
plot(chains)
meanplot(chain)
histogram(chain)
autocorplot(chain)
corner(chain)Andrieu, C., Thoms, J., 2008. A tutorial on adaptive MCMC. Statistics and computing 18, 343–373.
Livingstone, S., Zanella, G., 2021. The Barker proposal: Combining robustness and efficiency in gradient-based MCMC. Journal of the Royal Statistical Society: Series B (Statistical Methodology). https://doi.org/10.1111/rssb.12482 (see https://github.com/gzanella/barker for the R code used)