### volume weighting

**(inverse volume weighting, 1/V**_{max} method)
(method of accommodating the Malmquist bias)

**Volume weighting** is a technique for accommodating
the Malmquist bias (and I think may be able to
deal with the Eddington bias). The weighting
is actually done using the inverse of the volume,
thus it is sometimes referred to as **inverse volume weighting**.
The goal is dealing with systematic errors
in the sampling of different luminosities
(absolute magnitudes) in surveys.
This method of dealing with it is to calculate
a volume for each luminosity, consisting of the
volume of space in which an object of that
luminosity would be detected by the survey.
**V**_{max}
is the term used for such a volume, i.e., a
V_{max}
exists for each possible luminosity.
When counting objects of a given luminosity,
when using it statistically,
multiply the count times
1/V_{max}
(and the technique is also known as the **1/V**_{max} method).
Examples of applicability would be in deriving (from the survey data)
a mean luminosity of objects within some a volume of space,
or a density function of luminosities over
such a volume.

(*statistics,astronomy,bias,technique*)
**Further reading:**

https://en.wikipedia.org/wiki/Malmquist_bias#Volume_weighting

http://www.astro.ubc.ca/people/jvw/ASTROSTATS/lectures/PL_15_2013_www.pdf

Index