rmcmc - Robust Markov Chain Monte Carlo Methods
Functions for simulating Markov chains using the Barker
proposal to compute Markov chain Monte Carlo (MCMC) estimates
of expectations with respect to a target distribution on a
real-valued vector space. The Barker proposal, described in
Livingstone and Zanella (2022) <doi:10.1111/rssb.12482>, is a
gradient-based MCMC algorithm inspired by the Barker
accept-reject rule. It combines the robustness of simpler MCMC
schemes, such as random-walk Metropolis, with the efficiency of
gradient-based methods, such as the Metropolis adjusted
Langevin algorithm. The key function provided by the package is
sample_chain(), which allows sampling a Markov chain with a
specified target distribution as its stationary distribution.
The chain is sampled by generating proposals and accepting or
rejecting them using a Metropolis-Hasting acceptance rule.
During an initial warm-up stage, the parameters of the proposal
distribution can be adapted, with adapters available to both:
tune the scale of the proposals by coercing the average
acceptance rate to a target value; tune the shape of the
proposals to match covariance estimates under the target
distribution. As well as the default Barker proposal, the
package also provides implementations of alternative proposal
distributions, such as (Gaussian) random walk and Langevin
proposals. Optionally, if 'BridgeStan's R interface
<https://roualdes.github.io/bridgestan/latest/languages/r.html>,
available on GitHub <https://github.com/roualdes/bridgestan>,
is installed, then 'BridgeStan' can be used to specify the
target distribution to sample from.
