The recent surge of machine learning has motivated computer architects to focus intently on accelerating related workloads, especially in deep learning. Deep learning has been the pillar algorithm that has led the advancement of learning patterns from a vast amount of labeled data, or supervised learning. However, for unsupervised learning, Bayesian methods often work better than deep learning. Bayesian modeling and inference works well with unlabeled or limited data, can leverage informative priors, and has interpretable models. Despite being an important branch of machine learning, Bayesian inference generally has been overlooked by the architecture and systems communities. In this paper, we facilitate the study of Bayesian inference with the development of BayesSuite, a collection of seminal Bayesian inference workloads. We characterize the power and performance profiles of BayesSuite across a variety of current-generation processors and find significant diversity. Manually tuning and deploying Bayesian inference workloads requires deep understanding of the workload characteristics and hardware specifications. To address these challenges and provide high-performance, energy-efficient support for Bayesian inference, we introduce a scheduling and optimization mechanism that can be plugged into a system scheduler. We also propose a computation elision technique that further improves the performance and energy efficiency of the workloads by skipping computations that do not improve the quality of the inference. Our proposed techniques are able to increase Bayesian inference performance by 5.8 × on average over the naive assignment and execution of the workloads.