the appropriate tensor product of n univariate approximations. If each

univariate approximation is based on a two-point central difference (which

involves 2 function evaluations), then the total number of function

evaluations in the tensor product is 2^n. So, if you have a bivariate

distribution, then its density is simply the second-order cross partial

derivative, which can be evaluated accurately with 4 function evaluations.

You can see that this problem quickly becomes non-trivial due to curse of

dimensionality.

Hope this helps.

Ravi.

--------------------------------------------------------------------------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

--------------------------------------------------------------------------

-----Original Message-----

From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-

bounces at stat.math.ethz.ch] On Behalf Of Cuvelier Etienne

Sent: Friday, May 06, 2005 3:03 AM

To: r-help at stat.math.ethz.ch

Subject: Re: [R] Numerical Derivative / Numerical Differentiation of

unknownfunct ion

Is there is a similar function to calculate the numerical value of the

density of a given

multivariable distribution?

I have a function of a distribution H(x1, ...,xn) (not one of the known

distributions),

i.e. I can calculate a value of H for any (x1..., xn) .

And I want to calculate h(x1...,xn) for any (x1...,xn) BUT I don't know

the

analytical

expression of the density H.

--

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PLEASE do read the posting guide! http://www.R-project.org/posting-

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From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-

bounces at stat.math.ethz.ch] On Behalf Of Cuvelier Etienne

Sent: Friday, May 06, 2005 3:03 AM

To: r-help at stat.math.ethz.ch

Subject: Re: [R] Numerical Derivative / Numerical Differentiation of

unknownfunct ion

-----Original Message-----

From: Berton Gunter [mailto:gunter.berton at gene.com]

Sent: 05 May 2005 23:34

To: 'Uzuner, Tolga'; r-help at stat.math.ethz.ch

Subject: RE: [R] Numerical Derivative / Numerical Differentiation of

unknown funct ion

But...

See ?numericDeriv which already does it via a C call and hence is much

faster (and probably more accurate,too).

From: Berton Gunter [mailto:gunter.berton at gene.com]

Sent: 05 May 2005 23:34

To: 'Uzuner, Tolga'; r-help at stat.math.ethz.ch

Subject: RE: [R] Numerical Derivative / Numerical Differentiation of

unknown funct ion

But...

See ?numericDeriv which already does it via a C call and hence is much

faster (and probably more accurate,too).

density of a given

multivariable distribution?

I have a function of a distribution H(x1, ...,xn) (not one of the known

distributions),

i.e. I can calculate a value of H for any (x1..., xn) .

And I want to calculate h(x1...,xn) for any (x1...,xn) BUT I don't know

the

analytical

expression of the density H.

--

No virus found in this outgoing message.

Checked by AVG Anti-Virus.

______________________________________________

R-help at stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help

PLEASE do read the posting guide! http://www.R-project.org/posting-

guide.html