### completeness

(measure of how many of a survey's objects of a certain magnitude have been detected)

The term **completeness** is used for a quantification of the
effectiveness of an observation or survey,
regarding its successful detections.
For a given apparent magnitude,
a survey's completeness is the fraction of objects of that magnitude
that are actually detected, the others presumably lost by noise, such
as that inherent in the instrument. For example, one might say for
a particular survey that for magnitude 20, its completeness is 95%.
Generally, the larger the magnitude (i.e., the fainter the object
appears in the sky), the smaller the completeness fraction.
There is a natural desire to get and use absolutely every bit valid
information possible up to the limits of the instrument,
and *completeness* quantifies the aim or result the effort.

A **completeness limit** for a survey or a dataset derived from it,
and for a given limiting fraction, is the magnitude at which
completeness has fallen to that fraction. One could describe
a dataset as having a 95% completeness limit of magnitude 20,
meaning that at least 95% of any object with magnitude smaller
than 20 is included.

Knowing a survey's completeness depends upon knowing what the survey
hasn't seen, so that must be estimated. If data from a survey with more
sensitivity is available, that can be used. Another
approach is to create mock data based upon the distribution
seen at closer distances, assuming some uniformity across time and space,
and to calculate what is likely to be out there.

Another issue for surveys, termed **contamination** is the appearance
of objects where there are none due to noise, such as instrument noise.
The ratio of real objects to the sum of such real objects
plus the noise-generated apparent objects is termed its **purity**
(at a given magnitude) and analogous **purity limits** can be estimated
for a specific survey.

(*measure,surveys*)
**Further reading:**

http://en.wikipedia.org/wiki/Malmquist_bias

https://ui.adsabs.harvard.edu/abs/2007MNRAS.376.1757J/abstract

https://ui.adsabs.harvard.edu/abs/2005AJ....129.2047V/abstract

https://www.aanda.org/articles/aa/full_html/2016/08/aa28142-16/T3.html

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