Proposed scheme to tag variable sources in the WISE source catalog. 

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From:   fmasci@ipac.caltech.edu
Subject: variability flagging
Date: March 25, 2009 1:00:53 PM PDT
To:   roc@ipac.caltech.edu
Cc:   kam@ipac.caltech.edu, fmasci@ipac.caltech.edu

Hi Roc -

Thought I would write this down before it vaporizes. This can be made more complicated than needed and there's no end to it. The philosophy is simplicity and robustness. So, the plan is to test the hypothesis that a source has significantly varied (with any frequency) during its observation span, i.e., either in a regular periodic way, as a single event, or some growth and/or decay.

  (1)  I believe the best place to do this is on _single frameset_ WPRO measurements that Ken plans to implement in multi-frame WPRO in the near future. Single-frame WPRO measurements will be stored/manipulated in memory for each source apparition.

  (2) For the variability tagging to be robust, we'll probably need to enforce a minimum of N frame apparitions per source (e.g., N = 8, or maybe 12), all with S/N > some threshold. Other criteria could be included to weed out bad cases.

  (3) Given the N 'good' WPRO measurements for a source, one can then use their favorite metric for detecting variability. For example, (i) thresholding on a pseudo (robust) chi-square for the sample series: sum_i[(f_i - med{f_i}) / sigma_i]^2 where f_i are the WPRO flux measurements and sigma_i their prior uncertainties; (ii) Perform a test to detect turning points and/or growth/decay in the flux time-series, or testing that it fluctuates in a manner inconsistent with that expected for a random sequence of the same length. More than one test will be needed to detect the different flavors of variability. Perhaps testing for a significant deviation from pure randomness is sufficient(?). There are a plethora of tests for randomness out there. Most are sample-size dependent (N >= 8 or 12 should work). A probability can also be assigned on getting the observed variation by chance under a null-hypothesis that it's purely random.

  (4) Even though I mentioned it above, I propose we don't separate the various flavors of variability. A source has either varied, or it has not, or there were an insufficient number of good measurements to enable a test on it's flux vs time sequence.

  (5) Furthermore, we should make use of cross-band information in the variability test(s). E.g., a source has varied to a high degree of confidence if the detected variability, whether a single glitch, growth/decay, or flux-sequence that significantly deviates from randomness, is observed in at least *two* different bands.

Frank Masci, 3/25/2009