19

Is there a word that means the 'inverse of variance'? That is, if $X$ has high variance, then $X$ has low $\dots$? Not interested in a near antonym (like 'agreement' or 'similarity') but specifically meaning $1/\sigma^2$?

Tim
  • 108,699
  • 20
  • 212
  • 390
Hugh
  • 589
  • 3
  • 15
  • 2
    Agreement and similarity are in any case pretty much preempted, at least in formal definitions, for pairwise and other comparisons. However, that doesn't rule out informal talk, e.g. _you can see from the low variance that different measurements tend to agree_ – Nick Cox Nov 25 '15 at 11:41
  • 1
    I added `[bayesian]` tag since, as you can see from my answer and comments, the answer is closely related to Bayesian statistics and it will be easier to find tagged like this. – Tim Dec 02 '15 at 08:33

1 Answers1

33

$1/\sigma^2$ is called precision. You can find it often mentioned in Bayesian software manuals for BUGS and JAGS, where it is used as a parameter for normal distribution instead of variance. It became popular because gamma can be used as a conjugate prior for precision in normal distribution as noticed by Kruschke (2014) and @Scortchi.

Kruschke, J. (2014). Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan. Academic Press, p. 454.

Community
  • 1
Tim
  • 108,699
  • 20
  • 212
  • 390
  • 5
    (+1) I don't recall seeing it outside of this context, where it's convenient to be able to say things like "add the precisions of the prior & the data to get the precision of the posterior", & to use the familiar gamma distribution as a conjugate prior for precision. – Scortchi - Reinstate Monica Nov 25 '15 at 11:45
  • 5
    Also common in multivariate settings, where the precision becomes the inverse of the covariance matrix. (And again, is useful as a parameter for a normal distribution when you need a conjugate prior). – Peter Nov 25 '15 at 21:02
  • 4
    Yes, precision matrix is very helpful when dealing with multivariate Gaussians (as @Peter said), e.g. the formulas for conditional distributions are simpler in terms of precision matrices. Bishop spends many pages describing how this works in the Chapter 3 of his *Pattern Recognition and Machine Learning*, and this then reappears many times throughout the book. – amoeba Nov 25 '15 at 21:17