We propose a new application of stochastic point-based rendering, which was recently proposed for implicit surfaces, to large-scale laser-scanned 3D point data. Specifically, we propose a scheme to apply the rendering to transparent and fused visualization of recent large and complex laser-scanned data from cultural assets. Our scheme uses 3D points that are directly acquired using a laser scanner as the rendering primitives. For laser-scanned data that consist of more than 10(7) or 10(8) 3D points, the pre-processing stage takes only a few minutes, and the rendering stage is executable at interactive frame rates. We do not encounter rendering artifacts originating from the indefiniteness of depth-sorted orders of rendering primitives. Fused visualization with various visual assistants is also possible. We demonstrate the effectiveness of our scheme by visualizing a campus building and a culturally important festival float.