R help - Apr 2008 - integration error when I use "optim" and "integrate" simultaneously

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 
-- 
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.

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.
>
> ______________________________________________
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>
Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901