Engineering topics

Connors, Alanna

Publications and source records attributed to Connors, Alanna.

4 records

DOE OSTI2014

A fully Bayesian method for jointly fitting instrumental calibration and X-ray spectral models

Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is 'pragmatic' in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use a principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2010

ON COMPUTING UPPER LIMITS TO SOURCE INTENSITIES

A common problem in astrophysics is determining how bright a source could be and still not be detected in an observation. Despite the simplicity with which the problem can be stated, the solution involves complicated statistical issues that require careful analysis. In contrast to the more familiar confidence bound, this concept has never been formally analyzed, leading to a great variety of often ad hoc solutions. Here we formulate and describe the problem in a self-consistent manner. Detection significance is usually defined by the acceptable proportion of false positives (background fluctuations that are claimed as detections, or Type I error), and we invoke the complementary concept of false negatives (real sources that go undetected, or Type II error), based on the statistical power of a test, to compute an upper limit to the detectable source intensity. To determine the minimum intensity that a source must have for it to be detected, we first define a detection threshold and then compute the probabilities of detecting sources of various intensities at the given threshold. The intensity that corresponds to the specified Type II error probability defines that minimum intensity and is identified as the upper limit. Thus, an upper limit is a characteristic of the detection procedure rather than the strength of any particular source. It should not be confused with confidence intervals or other estimates of source intensity. This is particularly important given the large number of catalogs that are being generated from increasingly sensitive surveys. We discuss, with examples, the differences between these upper limits and confidence bounds. Both measures are useful quantities that should be reported in order to extract the most science from catalogs, though they answer different statistical questions: an upper bound describes an inference range on the source intensity, while an upper limit calibrates the detection process. We provide a recipe for computing upper limits that applies to all detection algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1998

The Locations of Gamma-Ray Bursts Measured by Comptel

The COMPTEL instrument on the Compton Gamma Ray Observatory is used to measure the locations of gamma-ray bursts through direct imaging of MeV photons. In a comprehensive search, we have detected and localized 29 bursts observed between 1991 April 19 and 1995 May 31. The average location accuracy of these events is 1.25 deg (1 sigma), including a systematic error of approx. 0.5 deg, which is verified through comparison with Interplanetary Network (IPN) timing annuli. The combination of COMPTEL and IPN measurements results in locations for 26 of the bursts with an average "error box" area of only approx. 0.3 deg (1 sigma). We find that the angular distribution of COMPTEL burst locations is consistent with large-scale isotropy and that there is no statistically significant evidence of small-angle autocorrelations. We conclude that there is no compelling evidence for burst repetition since no more than two of the events (or approx. 7% of the 29 bursts) could possibly have come from the same source. We also find that there is no significant correlation between the burst locations and either Abell clusters of galaxies or radio-quiet quasars. Agreement between individual COMPTEL locations and IPN annuli places a lower limit of approx. 100 AU (95% confidence) on the distance to the stronger bursts.

Kippen, R. Marc↗

NASA NTRS1988

An all sky study of fast X-ray transients

In the HEAO 1 A-2 survey of fast X-ray transients, a search of 2 to 20 keV scanning data was made for brief increases in flux, greater than 4 millicrabs, on timescales approximately 1 to 10 to the 4th s above a 12-hour average. The search was divided into two regions, and all-sky survey of the Galaxy, and a survey of the Magellanic Clouds. In the latter, 37 events were found and identified with 4 of the 5 brighest sources in the LMC, plus 2 as flares from a foreground star. Np X-ray bursts, no gamma-ray bursts, and no events from the SMC were found. In the all-sky survey, after excluding well-known variable sources, out of the equivalent of approximately 104 days of data, 15 events were found which falling into 2 broad categories: flares from coronal sources, roughly isotropically distributed, with optically thin thermal spectra; and harder fast transients apparently distributed near the Galactic plane. The first were identified as flares from ubiquitous active cool dwarf stars. It was hypothesized that the second may have been from distant Be-neutron star binaries. However, at least two of the harder, more luminous events remained unidentified. Future research should examine the nature of these rare events, and how they may fit into a hierarchy of hard fast transients from gamma-ray bursts to outbursts from pulsar systems.

Connors, Alanna↗