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    Maximum Likelihood Estimation of Spectra Information from Multiple Independent Astrophysics Data Sets (2002)
    In:  Other Sources
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    Publication Date: 2019-07-18
    Description: The Maximum Likelihood (ML) statistical theory required to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments is developed in this paper. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral information based on the combination of data sets. The procedure is of significant value to both existing data sets and those to be produced by future astrophysics missions consisting of two or more detectors by allowing instrument developers to optimize each detector's design parameters through simulation studies in order to design and build complementary detectors that will maximize the precision with which the science objectives may be obtained. The benefits of this ML theory and its application is measured in terms of the reduction of the statistical errors (standard deviations) of the spectra information using the multiple data sets in concert as compared to the statistical errors of the spectra information when the data sets are considered separately, as well as any biases resulting from poor statistics in one or more of the individual data sets that might be reduced when the data sets are combined.
    Keywords: Astrophysics
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    NASA TECHNICAL REPORTS
  • 2
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    Maximum Likelihood Estimation of the Broken Power Law Spectral Parameters with Detector Design Applications (2001)
    In:  Other Sources
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    Publication Date: 2019-07-17
    Description: The maximum likelihood procedure is developed for estimating the three spectral parameters of an assumed broken power law energy spectrum from simulated detector responses and their statistical properties investigated. The estimation procedure is then generalized for application to real cosmic-ray data. To illustrate the procedure and its utility, analytical methods were developed in conjunction with a Monte Carlo simulation to explore the combination of the expected cosmic-ray environment with a generic space-based detector and its planned life cycle, allowing us to explore various detector features and their subsequent influence on estimating the spectral parameters. This study permits instrument developers to make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope.
    Keywords: Astrophysics
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    NASA TECHNICAL REPORTS
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