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

[Michael Dewey]

Sent off-list

Thanks Bill and Duncan. I only asked for advice but I got an education too.

Michael

On 03/08/2021 21:24, Bill Dunlap wrote:
> 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 
> <mailto: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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-- 
Michael
http://www.dewey.myzen.co.uk/home.html