[R] What are the pros and cons of the log.p parameter in (p|q)norm and similar?

[Bill Dunlap]

In maximum likelihood problems, even when the individual density values are
fairly far from zero, their product may underflow to zero.  Optimizers have
problems when there is a large flat area.
   > q <- runif(n=1000, -0.1, +0.1)
   > prod(dnorm(q))
   [1] 0
   > sum(dnorm(q, log=TRUE))
   [1] -920.6556

A more minor advantage for some probability-related functions is speed.
E.g., dnorm(log=TRUE,...) does not need to evaluate exp().
   > q <- runif(1e6, -10, 10)
   > system.time(for(i in 1:100)dnorm(q, log=FALSE))
      user  system elapsed
      9.13    0.11    9.23
   > system.time(for(i in 1:100)dnorm(q, log=TRUE))
      user  system elapsed
      4.60    0.19    4.78

 -Bill

On Tue, Aug 3, 2021 at 11:53 AM Duncan Murdoch <murdoch.duncan using gmail.com>
wrote:

> On 03/08/2021 12:20 p.m., Michael Dewey wrote:
> > Short version
> >
> > Apart from the ability to work with values of p too small to be of much
> > practical use what are the advantages and disadvantages of setting this
> > to TRUE?
> >
> > Longer version
> >
> > I am contemplating upgrading various functions in one of my packages to
> > use this and as far as I can see it would only have the advantage of
> > allowing people to use very small p-values but before I go ahead have I
> > missed anything? I am most concerned with negatives but if there is any
> > other advantage I would mention that in the vignette. I am not concerned
> > about speed or the extra effort in coding and expanding the
> documentation.
> >
>
> These are often needed in likelihood problems.  In just about any
> problem where the normal density shows up in the likelihood, you're
> better off working with the log likelihood and setting log = TRUE in
> dnorm, because sometimes you want to evaluate the likelihood very far
> from its mode.
>
> The same sort of thing happens with pnorm for similar reasons.  Some
> likelihoods involve normal integrals and will need it.
>
> I can't think of an example for qnorm off the top of my head, but I
> imagine there are some:  maybe involving simulation way out in the tails.
>
> The main negative about using logs is that they aren't always needed.
>
> Duncan Murdoch
>
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