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I was reading a paper on Bayesian curve fitting (Dimatteo et. al. Bayesian curve-fitting with free-knot splines, 2001) and came across the symbol $\bumpeq$. It is used a few times throughout the paper but never explicitly defined. After a few google and stackexchange searches, it appears as though the symbol is neither widely used nor conventionally defined.

Below I give an example with context from the cited paper. I apologize in advance for not defining any of the other symbols, but doing so would amount to copying over large portions of text from the paper I have linked to and would be of little use to the question.

From p1059 (equation 8):

Incidentally, we can also see this in the likelihood ratio approximation for the normal model in equation (6) by

$$\frac{p(y|k^c,\xi^c)}{p(y|k,\xi)}\bumpeq\frac{1}{\sqrt{n}}\left(\frac{(y-B_{k,\xi}\hat{\beta})^T(y-B_{k,\xi}\hat{\beta})}{(y-B_{k,\xi^c}\hat{\beta^c})^T(y-B_{k,\xi^c}\hat{\beta^c})}\right)^{n/2}=exp(-\text{BIC}/2)$$

From context it seems that $\bumpeq$ represents an approximation. If this is case, then is it synonymous with more conventional symbols for an approximation like $\approx$ or $\sim$? or is it being used to represent a particular kind of approximation for which $\approx$ or $\sim$ would be insufficient or misleading?

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    $\begingroup$ I'd see it as an old-fashioned version of $\approx$, which seems more common as indicating approximation. Nothing intrinsically statistical about it; it is, or used to be, quite common across mathematics. I was taught it in high school some decades ago. The tilde $\sim$ on the other hand often does mean "distributed as", which clearly does have strong statistical flavour. $\endgroup$ – Nick Cox Aug 13 '13 at 23:12
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    $\begingroup$ If it were me, I'd take advantage of the emails at the top of the paper and ask one of them what the reason for it was. It might simply be an issue of journal style, but in this case I don't think that's it. $\endgroup$ – Glen_b -Reinstate Monica Aug 13 '13 at 23:21
  • $\begingroup$ According to en.wikipedia.org/wiki/Equipollence_(geometry) > "Two directed line segments are equipollent when they have the > same length and direction." with the equation: AB≏CD Meaning: Directed Line Segment AB is Equipollent with Directed Line Segment CD. $\endgroup$ – Akiva May 1 '16 at 15:10
  • $\begingroup$ This was crosslinked in a similar question I asked on the math stack exchange. Because no satisfactory answer has been found here, or rather, it has not been conventionally defined, I thought I would share the conventional definition that I found, although broader to geometry. Perhaps it could offer a clue to its intended use. math.stackexchange.com/questions/1766828/… $\endgroup$ – Akiva May 1 '16 at 15:25
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As far as I can tell, there's no special intent beyond "approximately equal to", i.e. its meaning is not distinct from $\approx$ and has no special statistical connotation I'm aware of. (Though as I said in comments, you could always double check with the authors)

The symbol was once fairly commonly used for that purpose, though I haven't seen it much in more recent publications.

Edit: corey979 points out a recent example via a comment: Jones M.C. & Pewsey, A. (2009) Sinh-arcsinh distributions Biometrika, 96: 4, p761–780 - middle equation in sect. 4.3

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    $\begingroup$ If recent is 2009, then an example might be Jones & Pewsey Sinh-arcsinh distributions - middle equation in sect. 4.3. $\endgroup$ – corey979 Jun 27 '18 at 22:03
  • $\begingroup$ Thanks, yes, that's pretty recent on the scale of recency I had in mind. I have made a small edit to include your valuable information. $\endgroup$ – Glen_b -Reinstate Monica Jun 27 '18 at 23:59

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