[Rd] update on dnbinom with large "size"

[Ben Bolker]

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~  thanks!
~  Poisson+warning seems very sensible.
~  Looks like things start to get wonky around size=5e14
(this is for mu=1)
but thinking a little harder about the numerical analysis
will probably give a more precise criterion.

curve(dnbinom(1,mu=1,size=x),from=5e14,to=1e16,log="x",ylim=c(0.32,0.37))

~  Ben Bolker


Prof Brian Ripley wrote:
| On Fri, 4 Jul 2008, Martin Maechler wrote:
|
|>>>>>> "BDR" == Prof Brian Ripley <ripley at stats.ox.ac.uk>
|>>>>>>     on Fri, 4 Jul 2008 09:02:21 +0100 (BST) writes:
|>
|>    BDR> On Thu, 3 Jul 2008, Ben Bolker wrote:
|>    >> -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1
|>    >>
|>    >>
|>    >> ~ turns out I don't need to look at the C code.
|>    >>
|>    >> ~ if one uses the mu/size parameterization of the
|>    >> negative binomial, R computes size/(size+mu) to switch
|>    >> parameterizations.  If size>>mu this gets rounded to 1
|>    >> ... should be easy enough to test and return NA under
|>    >> these circumstances?
|>
|>    BDR> It is all vectorized, so not so easy.  But why is NA
|>    BDR> appropriate, when a Poisson approximation seems more
|>    BDR> appropriate?
|>
|> yes, definitely more appropriate.
|>
|>    BDR> The same issue affects [pqr]nbinom, of course.
|>
|> indeed.
|>
|>    BDR> The short-term advice is of course 'don't do that'
|> :-)
|>
|>    BDR> but use a suitable approximation such as Poisson.  Maybe
|>    BDR> there are reasons to support values of size > 1e10, but
|>    BDR> I suspect only for completeness and maybe it is better
|>    BDR> to at least give a warning.
|>
|> As you know I'm very much in favor of "completeness" here (and
|> have already spent an unreasonable/unpayable amount of hours to
|> achieve that in quite a few cases for R in the past).
|>
|> I'd much prefer a solution without a warning that used the
|> appropriate approximation when needed.
|
| The argument for warning is that one possible reason for doing this is
| to explore the difference between negative binomial and Poisson, and so
| it would be helpful to be warned that a Poisson had been used (as we
| warn in some other cases where accuracy is lost, if not entirely
| consistently).
|
|> I'm now between a workshop and a week of vacation, so I am not
|> promising anything, but I'd plan to get this fixed before the
|> end of the summer.
|>
|>    >> - --------------------------
|>    >> ~ Check it out:
|>    >>
|>    >> curve(dnbinom(1,mu=0.5,size=x),log="x",from=1,to=1e18)
|>    >> abline(h=dpois(1,lambda=0.5),col=2,lty=2)
|>    >> text(1,dpois(1,lambda=0.5)+0.02,"Poisson",col=2,pos=4)
|>
|> a very nice example, thank you, Ben!
|>
|> Regards, Martin
|>
|>    >>
|>    >> ~ I will take a look in the C code when I get a chance to
|>    >> see if I can offer a patch, but in the meantime wanted to
|>    >> alert people to this "feature" ...  (it looks like I will
|>    >> have to go through dnbinom and dbinom_raw to see where
|>    >> the problem is ...)
|>    >>
|>    >> ~ Ben Bolker
|>
|

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