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

Spencer Graves spencer.graves at pdf.com
Fri Mar 28 04:01:45 CET 2003

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.,

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
>>>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]'.
>>>= \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.
>>>R-help at stat.math.ethz.ch mailing list
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