  The method of tempered transitions was proposed by Neal (1996) for tackling
the difficulties arising when using Markov chain Monte Carlo to sample from
multimodal distributions. In common with methods such as simulated tempering
and Metropolis-coupled MCMC, the key idea is to utilise a series of
successively easier to sample distributions to improve movement around the
state space. Tempered transitions does this by incorporating moves through
these less modal distributions into the MCMC proposals. Unfortunately the
improved movement between modes comes at a high computational cost with a low
acceptance rate of expensive proposals. We consider how the algorithm may be
tuned to increase the acceptance rates for a given number of temperatures. We
find that the commonly assumed geometric spacing of temperatures is reasonable
in many but not all applications.
