Optimal scaling of MCMC beyond Metropolis

Abstract

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 are few resources 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. In particular, optimal values for Barker’s algorithm are derived and found to be significantly different from that obtained for the MH algorithm. Our theoretical conclusions are supported by numerical simulations indicating that when the optimal proposal variance is unknown, tuning to the optimal acceptance probability remains an effective strategy.

imc-precip-iso: Open monthly stable isotope data of precipitation over the Indonesian Maritime Continent

“…This study uses a symmetrical Gaussian proposal distribution to simplify computing the acceptance ratio (Jones and Qin, 2022;Karras et al, 2022;South et al, 2022;Agrawal et al, 2023). We implemented the entire BLR process using the PyMC3 library within the Python computing environment (Salvatier et al, 2016).…”