- Hi Brian,

One hundred realizations are typically generated

mainly for CPU reasons.

You are perfectly right that this number is

too small when looking at small probabilities

like 0.05 or 0.01. It's why I wouldn't recommend

using stochastic simulation to derive probability of occurrence

of events at pixel locations. Just use kriging to build

your local probability distributions.

Use simulation if you have a transfer function, such as flow

simulator, that requires a model of spatial uncertainty,

or if you need to derive block probability distributions

(upscaling or aggregation problems).

More generally, there is more research to be done on the

use of stochastic simulation for probabilistic assessment,

including the question of equally-probability of realizatiuons

being generated.

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 Mon, 29 Apr 2002, Brian R Gray wrote:

>

> I am curious about the use of 100 realizations to generate a probability

> map. is this a standard approach? if so, is a "small" p-value (such as

> .05) used? if so, it would seem like 100 iterations might be a smallish

> sample size for distinguishing, say, .05 (ie 5 outcomes out of 100) from,

> say, .01. is 100 used because it seems like it is a reasonable number or

> because of the computer time restrictions?

>

> do geostat folks treat these as realizations or as pseudo-realizations?

>

> brian

>

> ****************************************************************

> Brian Gray

> USGS Upper Midwest Environmental Sciences Center

> 575 Lester Avenue, Onalaska, WI 54650

> ph 608-783-7550 ext 19, FAX 608-783-8058

> brgray@...

> *****************************************************************

>

>

>

> Chaosheng Zhang

> <Chaosheng.Zhang@nui To: ai-geostats@...

> galway.ie> cc: Dave McGrath <dmcgrath@...>

> Sent by: Subject: AI-GEOSTATS: Risk Assessment with Gaussian Simulation?

> ai-geostats-list@uni

> l.ch

>

>

> 04/27/2002 10:25 AM

> Please respond to

> Chaosheng Zhang

>

>

>

>

>

> Dear list,

>

> First, I would like to say thank you to Gregoire for keeping this list

> alive.

>

> I'm trying to do "risk assessment", and I have some questions about risk

> assessment with Gaussian Simulation:

>

> (1) How to produce a probability map?

>

> With Gaussian simulation, we can produce many maps/realisations, e.g., 100.

> Based on the 100 maps, a probability map of higher than a threshold can be

> produced. I wonder how to produce such a probability map? My understanding

> is that for each pixel, we just count how many values out of the 100 are

> >threshold, and the number is regarded as the "probability". Am I right? It

> seems that this is a time consuming procedure with GIS map algebra. Are

> there any suggestions for a quick calculation?

>

> (2) Is a probability map better than a Kriging interpolated map for the

> purpose of risk assessment?

>

> (3) Is "PCLASS" function in IDRISI 32 Release 2 better/easier than the

> probability map from Gaussian simulation?

>

> >From the online help of IDRISI 32 R2, Section "Kriging and Simulation

> Notes", it says "If the final goal of simulated surfaces will be to

> directly reclassify the surfaces by a threshold value, and calculate a

> probability of occurrence for a process based on that threshold,

> conditional simulation may be unnecessary. Instead kriging and variance

> images may be created and then used together with PCLASS." Any comments?

>

> (4) How to carry out "PCLASS"?

>

> Following the above question, I have a problem in doing PCLASS. I cannot

> input the file name of Kriging variance to the field of "Value error" of

> the documentation file. It seems that this field only accepts a "value",

> not an "image file name" or anything in text. Anyone has the experience?

>

> Cheers,

>

> Chaosheng Zhang

> =================================================

> Dr. Chaosheng Zhang

> Lecturer in GIS

> Department of Geography

> National University of Ireland

> Galway

> IRELAND

>

> Tel: +353-91-524411 ext. 2375

> Fax: +353-91-525700

> Email: Chaosheng.Zhang@...

> ChaoshengZhang@...

> Web: http://www.nuigalway.ie/geography/zhang.html

> =================================================

>

>

>

>

> --

> * To post a message to the list, send it to ai-geostats@...

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--

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* Support to the list is provided at http://www.ai-geostats.org - Dear all,

Thanks for so many interesting replies and thoughtful discussion. This is

not a summary yet, as I am expecting more to come.

Just to express my feeling about Indicator Kriging. To produce a probability

map, IK might be one of the choices. However, I always feel that too much

information is lost when doing the indicator transformation. When I see so

many "0"s in a dataset, I just feel the data quality is too poor.

Well, the other method of combination of Kriging and Kriging variance for

risk assessment has not been well discussed yet, and I would like to read

more comments.

My last question "(4) how to carry out "PCLASS" " is now answered by the

developer of Idrisi. The fact that the file name of Kriging variance cannot

be entered (with Metadata command) is a bug of the program, which will be

corrected soon. At present time, a text editor may be used to modify the

image documentation file.

Now, let me discuss how I would like to make a probability map based on

Kriging and Kriging variance. For each pixel of the Kriging interpolated

map, there is a value of Kriging variance. The Kriging variance is a measure

of uncertainty (which is related to sampling density and spatial variation,

etc.???). If we assume that the value of the Kriging pixel follow a normal

distribution and the standard deviation is equal to the SQRT of Kriging

variance, the probability of any threshold can be calculated. Furthermore,

to make the risk assessment more realistic, I would like to include other

errors, such as sampling error and laboratory analysis error into risk

assessment. These errors can hardly be quantified, but if we say 10% or 20%

of the pixel value (for soil samples), perhaps there is no objection.

Therefore, the standard deviation of the pixel is increased by adding this

kind of errors.

I am not clear how to calculate the total standard deviation of the two

sources, is it:

Total standard deviation =

SQRT (Kriging Variance + SQUARE (Sampling Errors) ) ?

Any ideas and comments on this method?

Chaosheng Zhang

> On Sat, 27 Apr 2002, Chaosheng Zhang wrote:

alive.

>

> Dear list,

>

> First, I would like to say thank you to Gregoire for keeping this list

>

assessment with Gaussian Simulation:

> I'm trying to do "risk assessment", and I have some questions about risk

>

can

> (1) How to produce a probability map?

>

> With Gaussian simulation, we can produce many maps/realisations, e.g.,

> 100. Based on the 100 maps, a probability map of higher than a threshold

> be produced. I wonder how to produce such a probability map? My

Am

> understanding is that for each pixel, we just count how many values out of

> the 100 are >threshold, and the number is regarded as the "probability".

> I right? It seems that this is a time consuming procedure with GIS map

directly

> algebra. Are there any suggestions for a quick calculation?

>

> (2) Is a probability map better than a Kriging interpolated map for the

> purpose of risk assessment?

>

> (3) Is "PCLASS" function in IDRISI 32 Release 2 better/easier than the

> probability map from Gaussian simulation?

>

>From the online help of IDRISI 32 R2, Section "Kriging and Simulation

> Notes", it says "If the final goal of simulated surfaces will be to

> reclassify the surfaces by a threshold value, and calculate a probability

of

> occurrence for a process based on that threshold, conditional simulation

may

> be unnecessary. Instead kriging and variance images may be created and

then

> used together with PCLASS." Any comments?

the

>

> (4) How to carry out "PCLASS"?

>

> Following the above question, I have a problem in doing PCLASS. I cannot

> input the file name of Kriging variance to the field of "Value error" of

> documentation file. It seems that this field only accepts a "value", not

an

> "image file name" or anything in text. Anyone has the experience?

--

>

> Cheers,

>

> Chaosheng Zhang

> =================================================

> Dr. Chaosheng Zhang

> Lecturer in GIS

> Department of Geography

> National University of Ireland

> Galway

> IRELAND

>

> Tel: +353-91-524411 ext. 2375

> Fax: +353-91-525700

> Email: Chaosheng.Zhang@...

> ChaoshengZhang@...

> Web: http://www.nuigalway.ie/geography/zhang.html

> =================================================

>

* To post a message to the list, send it to ai-geostats@...

* As a general service to the users, please remember to post a summary of any useful responses to your questions.

* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list

* Support to the list is provided at http://www.ai-geostats.org