[R] A dead problem on deriving the derivative equation.

[Spencer Graves]

If the limits of integration do not include theta, then you can 
interchange the order of integration and differentiation.  To go beyond 
this, I think I would need more specifics.

Spencer Graves
p.s.  You've got the negative of the standard KL divergence;  see, e.g.,
"http://www.cis.hut.fi/aapo/papers/NCS99web/node26.html".

Feng Zhang wrote:
> Not for calculation on numbers, 
> just to derive the symbolic formulation with
> theta, x..
> 
> 
> ----- Original Message ----- 
> From: "Spencer Graves" <spencer.graves at PDF.COM>
> To: "Feng Zhang" <f0z6305 at labs.tamu.edu>
> Cc: <r-help at stat.math.ethz.ch>
> Sent: Thursday, March 27, 2003 6:08 PM
> Subject: Re: [R] A dead problem on deriving the derivative equation.
> 
> 
> 
>>Do you want numbers?  If yes, did you try programming KL(theta) as a 
>>function, then computing
>>
>>D.KL <- (KL(theta+delta)-KL(delta))/delta
>>
>>for some suitably small delta?
>>
>>Spencer Graves
>>
>>Feng Zhang wrote:
>>
>>>Hey, R-listers
>>>
>>>I was totally confused by a seemling simple first derivative
>>>function.
>>>Given the Kullback-Leibler divergence function between
>>>a true pdf function P(x,theta) and an approximation pdf
>>>function Q(theta)=q1(theta1)*q2(theta2)*...*qn(thetan),
>>>where theta=[theta1,theta2, ..., thetan]'.
>>>KL(Q||P) 
>>>= \integration Q(theta)*log(P(x,theta)/Q(theta)) dtheta
>>>
>>>So how to derive the first derivative of KL with respect 
>>>to theta1?
>>>
>>>Thanks for your helpful advices.
>>>
>>>Fred
>>>
>>>______________________________________________
>>>R-help at stat.math.ethz.ch mailing list
>>>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>>
>>
> 
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