PAWL-Forced Simulated Tempering

In this short note, we show how the parallel adaptive Wang-Landau (PAWL) algorithm of Bornn et al. (2013) can be used to automate and improve simulated tempering algorithms. While Wang-Landau and other stochastic approximation methods have frequently been applied within the simulated tempering framework, this note demonstrates through a simple example the additional improvements brought about by parallelization, adaptive proposals and automated bin splitting. The central idea underlying Wang-Landau ([6]) and related algorithms is that instead of generating samples from a target density π, it is sometimes more efficient to instead sample a strategically biased density π. Algorithm 1 provides psuedo-code for the algorithm. Here c is a user-specified threshold.