  The problem of optimally scaling the proposal distribution in a Markov chain
Monte Carlo algorithm is critical to the quality of the generated samples. Much
work has gone into obtaining such results for various Metropolis-Hastings (MH)
algorithms. Recently, acceptance probabilities other than MH are being employed
in problems with intractable target distributions. There is little resource
available on tuning the Gaussian proposal distributions for this situation. We
obtain optimal scaling results for a general class of acceptance functions,
which includes Barker's and Lazy-MH acceptance functions. In particular,
optimal values for Barker's algorithm are derived and are found to be
significantly different from that obtained for MH algorithms.
