Do I See What I Think I See? Goodness-of-Fit, Residuals, and New Feature Detection in the Low-Counts Limit

Details Do I See What I Think I See? Goodness-of-Fit, Residuals, and New Feature Detection in the Low-Counts Limit Do I See What I Think I See? Goodness-of-Fit, Residuals, and New Feature Detection in the Low-Counts Limit

Sep 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006head....9.1359c&link_type=abstract

American Astronomical Society, HEAD meeting #9, #13.59; Bulletin of the American Astronomical Society, Vol. 38, p.376

Statistics

Scientific paper

In the Spring semester of 2006, SAMSI in NC hosted a special workshop on Astrostatistics. Here we report on one particular challenge: "goodness-of-fit" and feature detection and characterization for high resolution/low count data (such as for Chandra X-rays or CGRO and GLAST gamma-rays). In other words, for low-count data, how does one: a/ define a "good-enough-fit" to a particular "known physics" model in an image or spectrum; and b/ detect and characterize the mismatch, if the fit is not "good enough" (and there is no simple parametric model for the residuals).
For our "challenge" data, we used CGRO/EGRET all-sky >1GeV observations (actual and simulated). For the "known physics" we used models of diffuse emission from GALPROP (of Strong, Moskalenko and Reimer) plus the 3rd EGRET catalog (Hartman et al).
We found that we could use a flexible, multiscale-inspired model folded through the instrument response, to represent the residual. Once embedded in a likelihood framework (either Bayesian, or with simple complexity penalties) one can exploit likelihood-based measures for detection significance. At the same time, if this unknown component is significant, the flexible model now characterizes its shape. These flexible models ranged from EMC2 of Esch et al. (also Nowak and Kolaczyk; and Willett and Nowak) to Markov Random Fields. We used fast implementations of MCMC, tailored for this purpose, which not only "fit" the data, but gives us samples from which to calculate the appropriate significances and uncertainties.
We demonstrate our method with diffuse emission in both CGRO/EGRET and Chandra images.
This work was sponsored by NASA/AISR program, the Chandra X-ray Center, and NSF.

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