## GEOSTATS: Random permuation vs Montecarlo

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• I appreciate your patience, geostats. (Also thanks to Don, Tony) I am talking with Phil on significance of Moran s I (spatial autocorrelation). ... Don also
Message 1 of 3 , Nov 28, 1997
(Also thanks to Don, Tony)

I am talking with Phil on significance of Moran's I
(spatial autocorrelation).

paubry@...-lyon1.fr (Philippe Aubry) sama said:
>You will find every thing you want (and even more) in Cliff and Ord ...
Don also recommended it.
I will try to find one here.

>>I wonder how many repetitions of Montecalro are required(sufficient)
>> to prove certain p-val?
>
>OK. First, please, do not use "Monte Carlo" if you are not refering to any
>model which inputs are random. Indeed, "Monte Carlo" is not strictly
>equivalent to "random". When you are drawing at random two entries in a
>vector and permute the values, you are not performing "Monte Carlo" test
>nor simulation, but only "random permutations" (strictly speaking).

Random permutation is quite new to me.

Following understanding of random permuation is correct?

Example:To see whether 5 sampling locations are significantly autocorrelated.

Actually observed data are:
(location_1, value_a )
(location_2, value_b )
(location_3, value_c )
(location_4, value_d )
(location_5, value_e )
Moran'I = Iobs [ namely observed I ]

Then this dataset shall be shuffled by some algorithm into:
repetition_1:
(location_1, value_b )
(location_2, value_d )
(location_3, value_c )
(location_4, value_e )
(location_5, value_a )
Moran'I = I1

repetition_2:
(location_1, value_e )
(location_2, value_d )
(location_3, value_b )
(location_4, value_a )
(location_5, value_c )
Moran'I = I2

......

Here we have obtained
@I = (I1, I2, I3 ......... )

If the above Iobs is within/more_than upper 5% of @I,
then autocorrelation is significant(p<.05), right?

>Next, randomisation tests are exact, but the "definitively true" p-value
>would be obtained only after complete enumeration of all possible
>permutations (in practice, with no more than 9! permutations, i.e. about >
>380000). Complete enumeration leads to the so-called permutation test.

In the above example, permutation test requires 5! = 120 calculation?

> How
>many random permutations are needed for randomization tests ? B.J.F. Manly
>says something like "5000 for everything", but I am much more rigorous
>than him. I suggest you could try 1000, 5000, 10000, 20000 and so on, and
>see if the p-value has changed in a significant way. If you are interested
>in a precise and stable p-value, 10000 up to 100000 random permutations is
>very good (it depends on the set of data). If your computer (and your
>program) is not very efficient, 5000 will be a good number. A good
>algorithm with a rather good PC (e.g. Pentium 200 MhZ) allows everyone to
>do very precise p-value estimations without assuming any asymptotic
>distributional hypotheses ...

This point is very simple and attractive to me, and
to medical doctors who do not like any mathematical equiations.

Can you recommend any book/article on random permuation and montecalro?

I wonder what montecalro means then.

International Centre for Medical Research
Kobe University
Nagao Yoshiro
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• Hello, Without any model (i.e. Gaussian cdf or everything else, e.g. in geostatistics, a Random Function) there is no possible MONTE CARLO TEST . Random
Message 2 of 3 , Dec 4 5:43 AM
Hello,

Without any model (i.e. Gaussian cdf or everything else, e.g. in
geostatistics, a Random Function) there is no possible MONTE CARLO TEST .
Random permutations lead to a RANDOMIZATION TEST ... Using "Monte Carlo
test" or "Monte Carlo method" instead of "randomization test" is rather
common in publications ... but still an eroneous phrase.

About vocabulary, see Kotz and Johnson "Encyclopedia of statistical sciences".

Best regards

Philippe AUBRY

-----------------------------------------
Laboratoire de Biometrie
UMR CNRS 5558
Universite Claude Bernard - Lyon 1
43 bd. du 11 Novembre 1918
69622 VILLEURBANNE Cedex
FRANCE
-----------------------------------------
private fax number : 04.72.74.47.46
-----------------------------------------
e-mail : paubry@...-lyon1.fr
-----------------------------------------

"Quand on est parti de rien, et qu'on n'est pas arrive a grand chose, on
n'a de merci a dire a personne."

Pierre Dac

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• Thanks again, Phil ... It seems to be safer not to use the term Monte carlo pedantically. International Centre for Medical Research Kobe University
Message 3 of 3 , Dec 5 7:08 AM
Thanks again, Phil

Philippe.Aubry@...-lyon1.fr (Philippe Aubry) sama said:
>
>Hello,
>
>
>Without any model (i.e. Gaussian cdf or everything else, e.g. in
>geostatistics, a Random Function) there is no possible MONTE CARLO TEST .
>Random permutations lead to a RANDOMIZATION TEST ... Using "Monte Carlo
>test" or "Monte Carlo method" instead of "randomization test" is rather
>common in publications ... but still an eroneous phrase.

It seems to be safer not to use the term 'Monte carlo' pedantically.

International Centre for Medical Research
Kobe University
nagapee@...

Nagao Yoshiro
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Hello out there,

Besides spatial auto-correlation, cluster analysis, buffer zoning,
multivariate analysis, trend surface analysis, regionalization, point
pattern analysis, interpolation and consequent error surface analysis...

what other powerful techniques, methods, or procedures can you think of for