This R package provides a header-only C++ implementation of Adaptive Rejection Metropolis Sampling (ARMS), along with R packages for the same purpose. The C++ implementation is not tied to R and can be used outside the context of this package.
This package is in CRAN, so it can be installed with
install.packages('armspp')
Adaptive Rejection Metropolis Sampling (ARMS) is a Markov chain Monte Carlo based algorithm to sample from a univariate target distribution specified by its (potentially unnormalised) log density. The algorithm constructs a rejection distribution based on piecewise linear functions that envelop the log density of the target. For distributions with log concave density functions, this envelope is used directly, and usually results in a very efficient sampler. For distributions that are not log concave, or have unknown log concavity, an extra Metropolis Hastings accept/reject step is used to correct for any mismatch between the proposal density and the target. This sometimes results in a sampler with good convergence properties.
Here is a simple (and somewhat useless) example, sampling from a standard normal distribution:
samples <- arms(
1000, dnorm, -1000, 1000, metropolis = FALSE, arguments = list(log = TRUE)
)
hist(samples, freq = FALSE, br = 20)
curve(dnorm(x), min(samples), max(samples), col = 'red', add = TRUE)
We set metropolis = FALSE because the normal density is known to be log concave.
Here is a more complicated example, sampling from a mixture of normals:
dnormmixture <- function(x) {
parts <- log(c(0.4, 0.6)) + dnorm(x, mean = c(-1, 4), log = TRUE)
log(sum(exp(parts - max(parts)))) + max(parts)
}
samples <- arms(1000, dnormmixture, -1000, 1000)
hist(samples, freq = FALSE)
Now we leave the metropolis parameter at its default value TRUE, because we know that a mixture of normals density is not log concave (though it is piecewise log concave).
The code is released under the MIT license.