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| Quantifying Doubt and Confidence in Image "Deconvolution" |
| Category:
22. Astrostatistics (Siemiginowska and Kashyap) |
Alanna Connors1, D. van Dyk2, J. Chiang3, CHASC
1Eureka Scientific, 2Department of Statisitics, UCI, 3SLAC/Stanford. |
| Presentation Number: 03.01 |
How many times have you viewed a strikingly presented astronomical image --- and, in doubt, asked, "Where are the error bars?" Such doubt can come from several places: 1/ The purely statistical uncertainty of the final measurements (e.g. Poisson statistics); 2/ Possible mismatch between one's astrophysics sky-model and "sky-truth" (source model uncertainty); 3/ Related, additional effect of an uncertain background shape on measurements of the source of interest (background model uncertainty); and 4/ Mis-match between one's current best instrument model and "instrument truth" (instrument or calibration uncertainty). Additionally, there can be doubt in the methods used to process the data -- e.g. "How did they choose their stopping or smoothing parameters?"
A number of different groups very generally attack these kinds of problems by embedding very flexible, non- or semi-parametric models (from wavelets to Bayesian Blocks to Markov Random Fields) in full probabilistic frameworks (i.e. including "foward fitting"). These probability frameworks incorporate sky and instrument models and model-mismatch, as well as "fitting" any smoothing or stopping parameters. The CHASC group has used multiscale and MRF models of diffuse sky emission, plus astrophysics-based sky models, together with a hierarchical Bayesian probability structure. We use MCMC to sample the full highly dimensional posterior probability, which explicitly incorporates all the doubts mentioned above. We then choose two (or more) physically-based summary statistics to quantify (and display) the breadth of the uncertainties. But our "credible regions" have an unusual shape: the "error contours" include two spatial dimensions and one intensity dimension, in one example. We have fun analyzing and comparing differing CCGRO/EGRET viewing periods, including those of the 3C273/3C279 region, using our multi-scale model to capture varying and unexpected emission.
The authors acknowledge NASA AISRP and NSF interdisciplinary funding. |
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