  Markov chain Monte Carlo (MCMC) methods are sampling methods that have become
a commonly used tool in statistics, for example to perform Monte Carlo
integration. As a consequence of the increase in computational power, many
variations of MCMC methods exist for generating samples from arbitrary,
possibly complex, target distributions. The performance of an MCMC method is
predominately governed by the choice of the so-called proposal distribution
used. In this paper, we introduce a new type of proposal distribution for the
use in MCMC methods that operates component-wise and with multiple trials per
iteration. Specifically, the novel class of proposal distributions, called
Plateau distributions, do not overlap, thus ensuring that the multiple trials
are drawn from different regions of the state space. Furthermore, the Plateau
proposal distributions allow for a bespoke adaptation procedure that lends
itself to a Markov chain with efficient problem dependent state space
exploration and improved burn-in properties. Simulation studies show that our
novel MCMC algorithm outperforms competitors when sampling from distributions
with a complex shape, highly correlated components or multiple modes.
