Parallel tempering in lattice QCD with $O\left(a\right)\mathrm{}$-improved Wilson fermions

We present details of our investigations of the parallel tempering algorithm. We consider the application of action matching technology to the selection of parameters. We then present a simple model of the autocorrelations for a particular parallel tempered system. Finally we present results from applying the algorithm to lattice QCD with $O\left(a\right)\mathrm{}$-improved dynamical Wilson fermions for twin sub-ensemble systems.