We introduce a framework for efficient Markov Chain Monte Carlo (MCMC) algorithms targeting discrete-valued high-dimensional distributions, such as posterior distributions in Bayesian variable selection (BVS) problems. We show that many recently introduced algorithms, such as the locally informed sampler and the Adaptively Scaled Individual adaptation sampler (ASI), can be viewed as particular cases within the framework. We then describe a novel algorithm, the Adaptive Random Neighbourhood Informed sampler (ARNI), by combining ideas from both of these existing approaches. We show using several examples of both real and simulated datasets that a computationally efficient point-wise implementation (PARNI) leads to relatively more reliable inferences on a range of variable selection problems, particularly in the very large $p$ setting.

翻译：我们引入了高效的Markov链条蒙特卡洛(MCMC)算法框架,针对不同价值高维分布,如巴耶西亚变量选择问题的后方分布。我们表明,最近引入的许多算法,如当地知情的采样器和可调整规模的个人适应采样器,可被视为框架中的特殊情况。我们然后通过结合这两种现有方法的构想,描述一种新奇算法,即适应性随机邻居知情采样器。我们用一些真实和模拟数据集的例子显示,计算高效的点对点执行(PARNI)导致对一系列变量选择问题进行相对可靠的推论,特别是在非常大的美元环境下。