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https://adsabs.harvard.edu/abs/1999AAS...194.2604V

Bayesian Analysis of High-Resolution Energy Spectra

In this paper, we demonstrate how we have employed state-of-the-art Bayesian computational techniques (e.g., Gibbs sampler and Metropolis-Hastings) to analyze low-count, high-resolution astrophysical spectral data. These algorithms are very flexible and can be used to fit models that account for the complex structure in the collection of high-quality spectra and thus can be expected to be applicable to data obtained with future missions. We explicitly model photon arrivals as a Poisson process and, thus, have no difficulty with high resolution low count X-ray and gamma-ray data. These methods will be useful not only for the soon-to-be-launched CXO and XMM, but also for new generation telescopes such as Constellation-X and GLAST. We explicitly incorporate the instrument response (e.g. via a response matrix and effective area vector), and background contamination of the data into the analysis. In particular, we model the background as the realization of a second Poisson process, thereby eliminating the need to directly subtract off the background counts and the rather embarrassing problem of negative photon counts. The source energy spectrum is modeled as a mixture of a Generalized Linear Model which accounts for the continuum plus absorption and several (Gaussian) line profiles. Generalized Linear Models are the standard method for incorporating covariate information (as in regression) into non-Gaussian models and are thus an obvious but innovative choice in this setting. Using several examples, we illustrate how Bayesian posterior sampling can be used to compute point (i.e., ``best'') estimates of the various model parameters as well as compute error bars on these estimates.



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Bayesian Analysis of High-Resolution Energy Spectra

https://adsabs.harvard.edu/abs/1999AAS...194.2604V

In this paper, we demonstrate how we have employed state-of-the-art Bayesian computational techniques (e.g., Gibbs sampler and Metropolis-Hastings) to analyze low-count, high-resolution astrophysical spectral data. These algorithms are very flexible and can be used to fit models that account for the complex structure in the collection of high-quality spectra and thus can be expected to be applicable to data obtained with future missions. We explicitly model photon arrivals as a Poisson process and, thus, have no difficulty with high resolution low count X-ray and gamma-ray data. These methods will be useful not only for the soon-to-be-launched CXO and XMM, but also for new generation telescopes such as Constellation-X and GLAST. We explicitly incorporate the instrument response (e.g. via a response matrix and effective area vector), and background contamination of the data into the analysis. In particular, we model the background as the realization of a second Poisson process, thereby eliminating the need to directly subtract off the background counts and the rather embarrassing problem of negative photon counts. The source energy spectrum is modeled as a mixture of a Generalized Linear Model which accounts for the continuum plus absorption and several (Gaussian) line profiles. Generalized Linear Models are the standard method for incorporating covariate information (as in regression) into non-Gaussian models and are thus an obvious but innovative choice in this setting. Using several examples, we illustrate how Bayesian posterior sampling can be used to compute point (i.e., ``best'') estimates of the various model parameters as well as compute error bars on these estimates.



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https://adsabs.harvard.edu/abs/1999AAS...194.2604V

Bayesian Analysis of High-Resolution Energy Spectra

In this paper, we demonstrate how we have employed state-of-the-art Bayesian computational techniques (e.g., Gibbs sampler and Metropolis-Hastings) to analyze low-count, high-resolution astrophysical spectral data. These algorithms are very flexible and can be used to fit models that account for the complex structure in the collection of high-quality spectra and thus can be expected to be applicable to data obtained with future missions. We explicitly model photon arrivals as a Poisson process and, thus, have no difficulty with high resolution low count X-ray and gamma-ray data. These methods will be useful not only for the soon-to-be-launched CXO and XMM, but also for new generation telescopes such as Constellation-X and GLAST. We explicitly incorporate the instrument response (e.g. via a response matrix and effective area vector), and background contamination of the data into the analysis. In particular, we model the background as the realization of a second Poisson process, thereby eliminating the need to directly subtract off the background counts and the rather embarrassing problem of negative photon counts. The source energy spectrum is modeled as a mixture of a Generalized Linear Model which accounts for the continuum plus absorption and several (Gaussian) line profiles. Generalized Linear Models are the standard method for incorporating covariate information (as in regression) into non-Gaussian models and are thus an obvious but innovative choice in this setting. Using several examples, we illustrate how Bayesian posterior sampling can be used to compute point (i.e., ``best'') estimates of the various model parameters as well as compute error bars on these estimates.

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      In this paper, we demonstrate how we have employed state-of-the-art Bayesian computational techniques (e.g., Gibbs sampler and Metropolis-Hastings) to analyze low-count, high-resolution astrophysical spectral data. These algorithms are very flexible and can be used to fit models that account for the complex structure in the collection of high-quality spectra and thus can be expected to be applicable to data obtained with future missions. We explicitly model photon arrivals as a Poisson process and, thus, have no difficulty with high resolution low count X-ray and gamma-ray data. These methods will be useful not only for the soon-to-be-launched CXO and XMM, but also for new generation telescopes such as Constellation-X and GLAST. We explicitly incorporate the instrument response (e.g. via a response matrix and effective area vector), and background contamination of the data into the analysis. In particular, we model the background as the realization of a second Poisson process, thereby eliminating the need to directly subtract off the background counts and the rather embarrassing problem of negative photon counts. The source energy spectrum is modeled as a mixture of a Generalized Linear Model which accounts for the continuum plus absorption and several (Gaussian) line profiles. Generalized Linear Models are the standard method for incorporating covariate information (as in regression) into non-Gaussian models and are thus an obvious but innovative choice in this setting. Using several examples, we illustrate how Bayesian posterior sampling can be used to compute point (i.e., ``best'') estimates of the various model parameters as well as compute error bars on these estimates.
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      In this paper, we demonstrate how we have employed state-of-the-art Bayesian computational techniques (e.g., Gibbs sampler and Metropolis-Hastings) to analyze low-count, high-resolution astrophysical spectral data. These algorithms are very flexible and can be used to fit models that account for the complex structure in the collection of high-quality spectra and thus can be expected to be applicable to data obtained with future missions. We explicitly model photon arrivals as a Poisson process and, thus, have no difficulty with high resolution low count X-ray and gamma-ray data. These methods will be useful not only for the soon-to-be-launched CXO and XMM, but also for new generation telescopes such as Constellation-X and GLAST. We explicitly incorporate the instrument response (e.g. via a response matrix and effective area vector), and background contamination of the data into the analysis. In particular, we model the background as the realization of a second Poisson process, thereby eliminating the need to directly subtract off the background counts and the rather embarrassing problem of negative photon counts. The source energy spectrum is modeled as a mixture of a Generalized Linear Model which accounts for the continuum plus absorption and several (Gaussian) line profiles. Generalized Linear Models are the standard method for incorporating covariate information (as in regression) into non-Gaussian models and are thus an obvious but innovative choice in this setting. Using several examples, we illustrate how Bayesian posterior sampling can be used to compute point (i.e., ``best'') estimates of the various model parameters as well as compute error bars on these estimates.
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