On Computing Upper Limits to Source Intensities

Details On Computing Upper Limits to Source Intensities On Computing Upper Limits to Source Intensities

2010-06-22

arxiv.org/abs/1006.4334v1

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

30 pages, 12 figures, accepted in ApJ

Scientific paper

A common problem in astrophysics is determining how bright a source could be and still not be detected. Despite the simplicity with which the problem can be stated, the solution involves complex statistical issues that require careful analysis. In contrast to the 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 (the TypeI error), and we invoke the complementary concept of false negatives (the TypeII 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 TypeII 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 and 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 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.

Affiliated with

Also associated with

No associations

Rating

On Computing Upper Limits to Source Intensities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Computing Upper Limits to Source Intensities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Computing Upper Limits to Source Intensities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-108569