Re: Problem behavior with FindMaximum
- To: mathgroup at smc.vnet.net
- Subject: [mg59690] Re: Problem behavior with FindMaximum
- From: Peter Pein <petsie at dordos.net>
- Date: Thu, 18 Aug 2005 00:16:25 -0400 (EDT)
- References: <ddur1e$oc4$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
James H. Steiger schrieb:
> Hello all:
>
> I wonder if you could give me some advice about behavior of FindMaximum[]
> that I cannot seem to decipher.
>
> There is a broad class of problems in statistics that involves finding the
> maximum
> of a function of several parameters, all but one (call it "a") of which are
> *nuisance parameters*.
> The function is evaluated at any value of "a" by maximizing it w.r.t. all
> the nuisance parameters.
>
> A simple example (constructed just for Mathgroup -- the actual
> functions I work with are messier) should make this clear.
>
>
> myFunc1[a_, b_] := 1/((a - 16)^2 + 1) - (a - b)^2
> myFunc2[a_] := FindMaximum[myFunc1[a, b], {b, 0}][[1]]
>
> FindMaximum returns a list, the first element of which is the maximized
> value of the function,
> the second of which is a replacement rule specifying the value of b at which
> the maximum occurs.
>
> As you can quickly verify, myFunc2 is well behaved, and you can plot myFunc2
> without incident.
>
> Plot[myFunc2[a],{a,14,18}] produces a nice plot with no error messages
>
> Here is where the problem arises. Suppose you want to use FindMaximum[] to
> obtain the maximum of myFunc2 which clearly occurs at
> a=16.
>
> If you input the command
>
> FindMaximum[myFunc2[x],{x,14}]
>
> you obtain a pair of error messages (can anyone tell me how to copy these in
> Mathematica as text?)
>
> -----------------
>
> FindMaximum::nnum: The function value 1/((1+<<1>>)^2) - (0.+a)^2 is not a
> number at {b}={0.}
>
> FindMaximum::nnum: The function value 0.2 - (14. -b)^2 is not a number at
> {a}={14.}
>
> -----------------
>
> Is there some problem of "scope" of these variables that I am not aware of?
> Or is there some bug in FindMaximum[]?
> Is there a fix?
>
> Thanks to all,
>
> Jim
>
>
> James H. Steiger, Professor and Director
> Quantitative Methods and Evaluation
> Dept. of Psychology and Human Development
> Vanderbilt University
> Peabody College #512
> Nashville, TN, 37203
>
> Phone: 615-322-7060
> email: james.h.steiger at vanderbilt.edu
>
Hi Jim,
it is always a good idea to leave numeric Functions unevaluated for
nonnumeric arguments:
myFunc1[a_, b_] := 1/((a - 16)^2 + 1) - (a - b)^2
myFunc2[a_?NumericQ] := FindMaximum[myFunc1[a, b], {b, 0}][[1]]
^^^^^^^^^^
now myFunc2 behaves as expected:
FindMaximum[myFunc2[x], {x, 14}]
{0.9999999999999858, {x -> 15.99999988089842}}
(looks exact, when displayed in a notebook).
--
Peter Pein
Berlin
http://people.freenet.de/Peter_Berlin/