Implicit representations have the potential to represent large volumes succinctly. In this paper we present a multiresolution and progressive implicit representation of scalar volumetric data using anisotropic Gaussian radial basis functions (RBFs) defined over an octree. Our representation lends itself well to progressive level-of-detail representations. Our RBF encoding algorithm based on a Maximum Likelihood Estimation (MLE) calculation is non-iterative, scales in a O(nlogn) manner, and operates in a memory-friendly manner on very large datasets by processing small blocks at a time. We also present a GPU-based ray-casting algorithm for direct rendering from implicit volumes. Our GPU-based implicit volume rendering algorithm is accelerated by early-ray termination and empty-space skipping for implicit volumes and can render volumes encoded with 16 million RBFs at 1 to 3 frames/second. The octree hierarchy enables the GPU-based ray-casting algorithm to efficiently traverse using location codes and is also suitable for view-dependent level-of-detail-based rendering.