Mylène Bédard: Performance boost for the MALA sampler

Statistical models have been increasing both in terms of complexity and dimensionality. These models cannot be treated analytically; Markov chain Monte Carlo (MCMC) methods have thus become a device of choice to sample from such target distributions. We introduce a generalized version of the Metropolis-adjusted Langevin algorithm (MALA) that features two tuning parameters: the usual step size and an interpolation parameter that accommodates the dimension of the target distribution. We theoretically study the efficiency of this sampler by making use of the local- and global-balance concepts of Zanella (2017) and provide user-friendly tuning guidelines. Although the traditional MALA is theoretically optimal in infinite-dimensional settings, in practice, the annealed MALA remains superior in all contexts. It offers significant efficiency gains both in transience and in stationarity, at no extra computational cost. Simulation studies corroborate our findings. In particular, the efficiency of the annealed MALA compares favourably to that of competing algorithms in various Bayesian logistic regression contexts.