Scientific ray tracing now can include realistic shading and material properties, but tracing rays through partitioned data to calculate global illumination is inefficient because of the I/O overhead incurred by rays migrating from one partition to another. For such data, ray scheduling methods have demonstrated improved rendering performance by amortizing costs across a large group of rays. However, ray schedulers are prone to long-tail effects where much time is spent computing the solution for the final few rays, particularly for irregular ray tracing workloads. Solving this long-tail problem is increasingly important to maintain performance as complex ray tracing becomes more common for scientific analysis and for direct simulation of ray-like phenomena. In response, this dissertation introduces the concept of controlled redundancy to the domain of ray scheduling by means of speculation. We demonstrate that for both out-of-core and in situ rendering scenarios, speculatively scheduling rays to different regions of space both increases utilization of underlying resources and reduces total rendering time. In addition, we establish a communication abstraction to form a scheduling framework for novel asynchronous speculation. Furthermore, we incorporate simple heuristic prediction models, making the framework highly adaptable to a spectrum of scene characteristics. The framework is flexible enough to support a wide range of rendering techniques, including many variants of volume rendering and geometry rendering. Facilitated by high utilization, our scheduling method achieves many-times higher throughput on a multi-node, distributed system than prior methods, making our method fit for both interactive and offline applications.