2021/10/22 by Xitong Liang, Samuel Livingstone, Liang, Xitong +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2110.11747
openalex publication_date 2021/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.