Detecting and Measuring Sources at the Noise Limit

Abstract

In the first part of this paper, a computationally fast source detection method is discussed that is linear in the data and is about as sensitive as nonlinear, iterative methods. This method, described briefly here, is based on applying weights to a running data window (in two dimensions). Practical limitations, such as the window size and resolution, and further considerations regarding this source detection method are examined.

In the second part of this paper, methods are described for improving the handling of data with large uncertainties, even when the signal-to-noise ratio is negative. These methods are suggested as replacements for analyses based on transforming weak measurements into upper limits and then applying techniques using survival statistics. One method can be used for describing a single measurement in terms of a function that gives the confidence that the underlying physical quantity could have been drawn from a specific interval, given the constraints on the allowed values of the quantity. The second method deals with forming distributions from data samples which may consist of many weakly measured values, given the same constraints on the physically allowable values. The last method can be used to fit parametric models to such samples.