integration error when I use "optim" and "integrate" simultaneously

[kathie]

Dear R users,

When I use two functions, 'optim' and 'integrate', simultaneously, I always get an error like this

--------------------------------------------------------------------------
numint = function(z) {
        dlnorm(z,mu[1],sqrt(exp(g[1]))) * dnorm((z-mu[2])/sqrt(exp(g[2])))/sqrt(exp(g[2]))
}

integrate(numint,lower=0,upper=Inf)$value


Error in integrate(numint, lower = 0, upper = Inf) : non-finite function value
-----------------------------------------------------------------------------

Dr. Ripley said for this problem long time ago

"You are trying to use a derivative-based optimization method without supplying derivatives.  This will use numerical approximations to the derivatives, and your objective function will not be suitable as it is
internally using adaptive numerical quadrature and hence is probably not close enough to a differentiable function (it may well have steps)."


So, I am trying to avoid this 'integrate' in R, but I have no idea.  

Any suggestion will be greatly appreciated.

Kathryn Lord

[Charles C. Berry]

On Sat, 26 Apr 2008, kathie wrote:

>
> Dear R users,
>
> When I use two functions, 'optim' and 'integrate', simultaneously, I always
> get an error like this
>
> --------------------------------------------------------------------------
> numint = function(z) {
> dlnorm(z,mu[1],sqrt(exp(g[1]))) *
> dnorm((z-mu[2])/sqrt(exp(g[2])))/sqrt(exp(g[2]))
> }
>
> integrate(numint,lower=0,upper=Inf)$value
>
>
> Error in integrate(numint, lower = 0, upper = Inf) : non-finite function
> value
> -----------------------------------------------------------------------------
>
> Dr. Ripley said for this problem long time ago
>
> "You are trying to use a derivative-based optimization method without
> supplying derivatives.  This will use numerical approximations to the
> derivatives, and your objective function will not be suitable as it is
> internally using adaptive numerical quadrature and hence is probably not
> close enough to a differentiable function (it may well have steps)."
>
>
> So, I am trying to avoid this 'integrate' in R, but I have no idea.
>
> Any suggestion will be greatly appreciated.

The implied advice in the quotation above is to use the derivatives.

The function you have is the product of a lognormal and a normal density.
You need the derivatives of those w.r.t their means and variances. You can
probably look these up someplace if the challenge of hacking them out is
too daunting. (Hint: how do you find the MLEs for these densities?)

You can appreciate why integrate() sometimes complains if you spend some
time looking at

  curve( numint, 0, uplim )

for suitably chosen values of mu and g and uplim. Say

  mu <- c(1,1)
  g <- c(10,1)
  uplim <- 0.000001.

But replacing integrate with a better quadrature rule for this particular
problem probably will not smooth it out enough to substitute for
derivatives.

HTH,

Chuck

>
> Kathryn Lord
> --
> View this message in context: http://www.nabble.com/integration-error-when-I-use-%22optim%22-and-%22integrate%22-simultaneously-tp16918109p16918109.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Charles C. Berry                            [phone]
                                             Dept of Family/Preventive Medicine
E mailto:[hidden email]            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.