In this paper, we consider the problem of building descriptive three-dimensional (3-D) maps from sparse and noisy range sensor data. We expand our previously proposed method leveraging Bayesian kernel inference for prediction of occupancy in locations not directly observed by a range sensor. In this paper, we show that our kernel inference approach generalizes previous “counting sensor model” approaches from discrete occupancy grids to continuous maps. Our approach enables prediction about occupancy in regions unobserved by the range sensor based on local measurements, and smoothly transitions to a prior in regions lacking sufficient data for reliable inference. Furthermore, we demonstrate quantitatively using simulated data that the mapping performance of our method can be improved by considering rays as continuous observations, rather than sampling discrete free-space point observations along rays. Though the maps produced by our method are in principle continuous, discretizing space affords us several computational advantages, including the ability to apply recursive Bayesian updates, that allow us to perform inference very efficiently, even on large datasets. To demonstrate this advantage, we present experimental results applying this method to large-scale lidar data collected with a ground robot, showing real-time performance. Other field robotics applications, including underwater 3-D mapping with sonar, are explored qualitatively.