Visualizing likelihood density functions via optimal region projection

• We present a novel way to visualize model likelihood density functions.
• Visualize the projection of high-likelihood regions from the high-dimensional space.
• Find the projection most likely to reveal scientific insights.

Effective visualization of high-likelihood regions of parameter space is severely hampered by the large number of parameter dimensions that many models have. We present a novel technique, Optimal Percentile Region Projection, to visualize a high-dimensional likelihood density function that enables the viewer to understand the shape of the high-likelihood region. Optimal Percentile Region Projection has three novel components: first, we select the region of high likelihood in the high-dimensional space before projecting its shadow into a lower-dimensional projected space. Second, we analyze features on the surface of the region in the projected space to select the projection direction that shows the most interesting parameter dependencies. Finally, we use a three-dimensional projection space to show features that are not salient in only two dimensions. The viewer can also choose sets of axes to project along to explore subsets of the parameter space, using either the original parameter axes or principal-component axes. The technique was evaluated by our domain-science collaborators, who found it to be superior to their existing workflow both when there were interesting dependencies between parameters and when there were not.

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