Analyzing scientific datasets created from simulations on modern supercomputers is a daunting challenge due to the fast pace at which these datasets continue to grow. Low cost post analysis machines used by scientists to view and analyze these massive datasets are severely limited by their deficiencies in storage bandwidth, capacity, and computational power. Trying to simply move these datasets to these platforms is infeasible. Any approach to view and analyze these datasets on post analysis machines will have to effectively address the inevitable problem of data loss. Image based approaches are well suited for handling very large datasets on low cost platforms. Three challenges with these approaches are how to effectively represent the original data with minimal data loss, analyze the data in regards to transfer function exploration, which is a key analysis tool, and quantify the error from data loss during analysis. We present a novel image based approach using distributions to preserve data integrity. At each view sample, view dependent data is summarized at each pixel with distributions to define a compact proxy for the original dataset. We present this representation along with how to manipulate and render large scale datasets on post analysis machines. We show that our approach is a good trade off between rendering quality and interactive speed and provides uncertainty quantification for the information that is lost.