[Rd] dbeta may hang R session for very large values of the shape parameters

[Kosmidis, Ioannis]

Dear all,

we received a bug report for betareg, that in some cases the optim call in betareg.fit would hang the R session and the command cannot be interrupted by Ctrl-C…

We narrowed down the problem to the dbeta function which is used for the log likelihood evaluation in betareg.fit. 

Particularly, the following command hangs the R session to a 100% CPU usage in all systems we tried it (OS X 10.8.4, Debian GNU Linux, Ubuntu 12.04) with either R-3.0.1 and with the R-devel version (in all systems I waited 3 minutes before I kill R):

## Warning: this will hang the R session
dbeta(0.9, 1e+308, 10)

Furthermore, through a trial and error investigation using the following code

## Warning: this will hang the R session
x <- 0.9
for (i in 0:100) {
 a <- 1e+280*2^i
 b <- 10
 cat("shape1 =", a, "\n")
 cat("shape2 =", b, "\n")
 cat("Beta density", dbeta(x, shape1 = a, shape2 = b), "\n")
 cat("===\n")
}

I noticed that:
* this seems to happen when shape1 is about 1e+308, seemingly irrespective of the value of shape2 (run the above with another value of b), and as it appears only when x>=0.9 and x < 1 (run the above lines with x <- 0.89999 for example and everything works as expected). 
* similar problems are encountered for small x values when shape2 is massive.

I am not sure why this happens but it looks deep to me. The temporary fix for the purposes of betareg was a hack (a simple if command that returns NA for the log likelihood if any shape parameter has values greater than 1e+300 say). 

Nevertheless, I thought that this is an issue worth reporting to R-devel (instead of R-help), especially since dbeta may be used within generic optimisers and figuring that dbeta is the problem can be hard --- it took us some time before we started suspecting dbeta.

Interestingly, this appears to happen close to what R considers infinity. Typing
1.799e+308
into R returns Inf.

I hope the above limited in scope analysis is informative.

Best regards,
Ioannis



-- 
Dr Ioannis Kosmidis
Department of Statistical  Science,
University College,
London, WC1E 6BT, UK
Webpage: http://www.ucl.ac.uk/~ucakiko