We consider a recently proposed class of MCMC methods which uses proximity maps instead of gradients to build proposal mechanisms which can be employed for both differentiable and non-differentiable targets. These methods have been shown to be stable for a wide class of targets, making them a valuable alternative to Metropolis-adjusted Langevin algorithms (MALA); and have found wide application in imaging contexts. The wider stability properties are obtained by building the Moreau-Yoshida envelope for the target of interest, which depends on a parameter $\lambda$. In this work, we investigate the optimal scaling problem for this class of algorithms, which encompasses MALA, and provide practical guidelines for the implementation of these methods.

翻译：我们考虑的是最近提出的一类监测监测中心方法,这种方法使用近距离地图而不是梯度来建立建议机制,既可用于不同的目标,也可用于非差别的目标。这些方法已经证明对于一系列广泛的目标来说是稳定的,使它们成为大都会调整的朗埃文算法(MALA)的宝贵替代方法;在成像环境中得到了广泛应用。通过为感兴趣的目标建造Moreau-Yoshida信封,获得了更广泛的稳定性属性,该信封取决于一个参数$\lambda$。在这项工作中,我们调查了包括MALA在内的这一类算法的最佳规模问题,并为这些方法的实施提供了实用的指导方针。