Annealed Leap-Point Sampler (ALPS)

The Annealed Leap-Point Sampler (ALPS) is an R package for Markov chain Monte Carlo (MCMC) sampling from multimodal posterior distributions. Standard MCMC algorithms (e.g. random-walk Metropolis, HMC) mix poorly when the target has multiple well-separated modes because local proposals cannot bridge the low-density regions between them.

ALPS overcomes this by combining two strategies:

• Annealing (raising the density to powers β > 1) concentrates and sharpens each mode, making it locally Gaussian. This is the opposite of traditional "parallel tempering" (which flattens the density with β < 1).
• Mode-jumping independence sampler moves, guided by Laplace approximations at each discovered mode, allow the chain to jump directly between modes.

The result is an algorithm whose mixing time scales as O(d), compared to exponential scaling for standard tempering approaches.

Note: ALPS is being prepared for submission to CRAN. Until version 1.0.0, the user-facing API (argument names, the format of the `centres` list, and the structure of returned objects) may change without deprecation. The code used for the published paper is archived as this release, v0.3-5