The remark that was made earlier on the list regarding the

exponentiation of lognormal kriging applies to both point

and block estimates. Taking simply the antilog

of your kriged estimates leads to a biased estimate.

As you rigthly guess, computing a semivariogram on

the original values or the logtransforms usually leads

to different results. Logarithmic transformation is typically

performed to reduce the influence of high values on the estimation

of the semivariogram (e.g. positively skewed histograms of

heavy metal concentrations) and so the resulting histogram

is expected to be less

erratic than the original semivariogram.

My advice is that if you have to deal with highly skewed

histograms and want to avoid the problems associated with the

logtransform and backtransform of your estimates, use an

indicator approach to model the local cdf and use the ccdf mean

as an estimate and the ccdf variance as a measure of uncertainty.

Another option is to use a normal score transform (see Deutsch

and Journel, p. 76 or my book) that ensures that the

histogram of transformed data is perfectly symmetric

regardless the shape of the original histogram.

Use simple kriging to derive the mean and variance of the

ccdf that is Gaussian in that case, and backtransform the

results. Note that if you have a lot of data below the detection

limits, you better go with an indicator approach or consider

splitting your data into different subsets (use of different

populations and corresponding RFs).

Pierre

________ ________

| \ / | Pierre Goovaerts

|_ \ / _| Assistant professor

__|________\/________|__ Dept of Civil & Environmental Engineering

| | The University of Michigan

| M I C H I G A N | EWRE Building, Room 117

|________________________| Ann Arbor, Michigan, 48109-2125, U.S.A

_| |_\ /_| |_

| |\ /| | E-mail: goovaert@...

|________| \/ |________| Phone: (734) 936-0141

Fax: (734) 763-2275

http://www-personal.engin.umich.edu/~goovaert/

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

On Thu, 18 Feb 1999, Bill Thayer wrote:

> Hello,

> In the past I have asked the list for their opinion on the use of

> log-transformed data in developing variograms and then using the

> variograms to generate block estimates and estimation variances of the

> log-transformed data. I am now aware of the problems this creates when

> one tries to back transform the results (both the block estimates and

> their estimation variances).

>

> What is the opinion of the list on using log-transformed data to develop

> variograms and using the variograms to generate a grid of point

> estimates. I am not interested in the associated estimation variances.

> I plan on back-transforming the point estimates (simply taking the

> exponents of the point estimates) and then use bootstrapping to estimate

> confidence intervals for the mean concentration (i.e. mean of the

> back-transformed point estimates). My data is lead concentration

> measured from (grab) soil samples. It seems to me that simply taking

> the exponent of the kriged point estimates is OK because the kriged

> estimates do not represent mean concentrations over a block. Is this

> sound reasoning? I would also like feedback on the use of the

> logtransformed data to develop variograms. In other words, it is not

> clear to me that the difference between the squares of log-tranformed

> data is analogous to the the same calculation using untransformed data.

>

> Thanks in advance for any feedback. I will post a summary of the

> responses I receive,

> Bill

>

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