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Statistical Inference for Scientific Instruments: Event Analysis for the Gamma-Ray Large Area Space
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| Scientific instruments are becoming more complex, are making indirect measurements that require complex interpretation, and are returning enormous quantities of data that require powerful methods of analysis. The Large Area Telescope (LAT) instrument on the Gamma-ray Large Area Space Telescope (GLAST) satellite is a prime example of an instrument where powerful statistical methods are needed at all stages of the data analysis -- the instrument makes indirect measurements of the incident gamma-rays, requiring complex event reconstruction to estimate the directions and energies of the photons; classification is needed to determine whether the event was caused by a gamma-ray or a charged particle; the detection and characterization of celestial sources of gamma-rays requires complex statistical hypothesis testing which is dependent strongly on the statistical characterization of the reconstruction and classification stages. In this proposal we focus on the first of these stages, on which all the others are built. The first task is to estimate the directions and energies of the incoming photons. The tracker element of the LAT is a series of 18 tungsten foils, interleaved with silicon microstrip detectors. Incident gamma-rays interact with the tungsten and are converted into electron-positron pairs. These charged particles trigger the microstrip detectors. However, the electron and positron are affected by numerous physics processes as they traverse the detector. The primary process that blurs the response is multiple scattering, which causes the tracks of the electron and positron to deviate from the ideal straight line paths. Other processes result in the ejection of further electrons from the material of the detector, and the production of further gamma-rays by positron annihilation. These gamma-rays can be converted into electron-positron pairs later in the detector. These processes and others produce charged particles that also interact with the silicon microstrips and provoke a response in the detector. The current analysis methodology being developed by the LAT collaboration involves finding the straightest tracks through the microstrip responses, a Kalman filter to estimate the trajectories of the primary electron and positron, and from the trajectories estimating the direction and energy of the photon. We propose an alternative methodology, based on nonparametric estimation using particle filters, that can more effectively use the full physics distributions for multiple scattering and other physics processes, and should give more accurate estimates of the direction and especially the energy of the incident photons and the uncertainties of these estimates - essentially a psf per event, which will enable more powerful and accurate estimation methods to be used in later stages of the data analysis. Improving the estimate of the photon's energy from thetracker response has been identified as an important goal for the event analysis. Preliminary work, funded by the NASA Ames Director's Discretionary Fund has demonstrated the applicability of the methodology to the LAT event analysis problem. This proposal is to further develop the new analysis methodology, and to integrate it into the GLEAM software environment being developed by the GLAST collaboration. A successful outcome would result in a greater science return from the mission deemed of highest priority in its category by the NRC Decadal Review, and also a wider knowledge of a new, powerful statistical methodology amongst the astrophysics and particle physics communities. |
Bibliography
| | Modern Statistical Methods for GLAST Event Analysis
arXiv:astro-ph/0703738
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