Re: Problem behavior with FindMaximum
- To: mathgroup at smc.vnet.net
- Subject: [mg59696] Re: [mg59671] Problem behavior with FindMaximum
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 18 Aug 2005 00:16:29 -0400 (EDT)
- References: <200508170800.EAA24807@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
This is a common question. Just change the definition of myFunct2 to
myFunc2[a_?NumericQ] := FindMaximum[myFunc1[a, b], {b, 0}][[1]]
and you will get:
FindMaximum[myFunc2[x], {x, 14}]
{1., {x -> 16.}}
I do not know a good answer to the question how to copy and paste
error messages. I just copy them as Text and then manually remove the
markup characters.
Andrzej Kozlowski
On 17 Aug 2005, at 10:00, James H. Steiger wrote:
> 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
>
>
- References:
- Problem behavior with FindMaximum
- From: "James H. Steiger" <jsteiger@bellsouth.net>
- Problem behavior with FindMaximum