RE: AI-GEOSTATS: Re: Lagrange Multiplier

2006-10-11 Thread Ted Harding
On 11-Oct-06 Njeri Wabiri wrote:
 Dear list
 Just a newbabie question
 What is the statistical interpretation of the Lagrange
 multiplier in kriging.
 At least I know if its positive we have a high kriging
 variance and vice versa.
 
 Grateful for a response and a reference
 
 Njeri 

The general interpretation of a Langrange multiplier is
as follows.

In the context of an extremal problem (find the max/min)
of a function

  f(x1,x2,...,xk)

subject to a constraint

  g(x1,x2,...,xk) = c

when you express it as solving the extremal problem for

  f(x1,x2,...,xk) - L*g(x1,x2,...,xk)

(and then using the constraint equation to eliminate L),
the value of L is equal to the rate of change of the
extremal value of f (as so found) with respect to variation
in the value of c.

Otherwise put: for a particular value of c, the extremal
value of f is (say) fmax(c). Then L = dfmax(c)/dc. The
same is true with several constraints (and a corresponding
number of lagrange multipliers), in that the i-th L is
equal to the partial derivative of fmax(c1,c2,...,cr)
with respect to ci.

[This assumes that the function f has a max/min which
can be found analytically by solving the equation[s]
obtained by setting derivative[s] equal to 0. The above
is not quite so directly true when the maximum is attained
on the boundary of the region defined by the constraints,
as in a Linear Programming problem, for instance; though
something similar is also true there.]

I can supply a demonstration of the above, if requested.

So, if (in a statistical context) a sum of squares if
minimised, or a likelihood is maximised, subject to constraints,
then the above applies to the sum of squares, or likelihood,
or whatever.

Hoping this helps,
Ted.


E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 094 0861
Date: 11-Oct-06   Time: 21:27:33
-- XFMail --
+
+ To post a message to the list, send it to ai-geostats@jrc.it
+ To unsubscribe, send email to majordomo@ jrc.it with no subject and 
unsubscribe ai-geostats in the message body. DO NOT SEND 
Subscribe/Unsubscribe requests to the list
+ As a general service to list users, please remember to post a summary of any 
useful responses to your questions.
+ Support to the forum can be found at http://www.ai-geostats.org/


RE: AI-GEOSTATS: Skewed Distributions

2006-05-19 Thread Ted Harding
AI-GEOSTATS
On 19-May-06 Digby Millikan wrote:
 Is it correct that the probability of being above or below
 the mean of a skewed distribution is not necessarily 0.5?

Very much true that it may not be 0.5!

As a general (though not absolutely true) rule, if a distribution
is positively skewed then the mediam (0.5-point) is less than
the mean, and for a negatively skewed distribution the median
is greater than the mean. This often applies to the staddard
distributions which turn up in practice.

However, there is no general absolutely sure relationship
between median and mean for non-symmetric distributions.

Intuitively, the position of the median is independent of how
you re-distribute the probability for values less than the
median, and independent of how you re-distribute it for values
greater than the median, so long as you keep 50% on either side.

However, the mean is very much influenced by precisely where
each bit of probability is located, so you can swing the mean
around as much as you like without affecting the mediam.

Best wishes,
Ted.


E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 094 0861
Date: 19-May-06   Time: 15:43:57
-- XFMail --
+ To post a message to the list, send it to ai-geostats@jrc.it
+ To unsubscribe, send email to majordomo@ jrc.it with no subject and 
unsubscribe ai-geostats in the message body. DO NOT SEND 
Subscribe/Unsubscribe requests to the list
+ As a general service to list users, please remember to post a summary of any 
useful responses to your questions.
+ Support to the forum can be found at http://www.ai-geostats.org/


RE: [ai-geostats] Lagrange Multiplier

2005-09-19 Thread Ted Harding
On 19-Sep-05 Colin Badenhorst wrote:
 Hi List,
 
 I've noticed that the latest version of my estimation software
 now stores the Lagrange multiplier (parameter) for each estimated
 block in my model. I was wondering if anyone had any thoughts on
 how I could use this variable in some practical sense to further
 interpret or validate my estimates. Unfortunately, my understanding
 of the Lagrange multiplier has always been poor, so I'm not sure
 exactly what it means.


In a constrained optimisation problem, e.g. minimising a function
y(x, y, ...) with constraints expressed in the form

  g(x, y, ...) = c

the value of the Lagrange multiplier associated with constraint
g(x, y, ...) = c can be interpreted as the rate of change of the
optimum value of f(x, y, ... ) with respect to change in c.

Otherwise put, if say c1, c2, ... are the values of the constraint
functions, the minimisation of f(x, y, ... ) will lead to a
particular value of f() which will depend on the values of
c1, c2, ... which were used, so it is a function

  fmin(c1, c2, ... )

of these. If U1, U2, ... are the Lagrange multipliers in the
Lagrangean formulation of the problem, then

  U1 = dfmin(c1, c2, ... )/dc1

and similarly for U2 etc.

Does this help?

Best wishes,
Ted.



E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 094 0861
Date: 19-Sep-05   Time: 12:33:34
-- XFMail --

* By using the ai-geostats mailing list you agree to follow its rules 
( see http://www.ai-geostats.org/help_ai-geostats.htm )

* To unsubscribe to ai-geostats, send the following in the subject or in the 
body (plain text format) of an email message to [EMAIL PROTECTED]

Signoff ai-geostats

RE: [ai-geostats] A banal question...

2005-05-02 Thread Ted Harding
 of giving you quite a lot
about the detailed behaviour of the terrain. In particular
it could probably be applied to help determine the overall
hydrography of the region -- e.g. what complexity of
drainage systems would you need.

However, as well as the fact that the informativeness of C(h)
depends on properties like stationarity and isotropy, also
a lot of theory about analysing measurements on spatial
processes depends on assuming these properties in order
to make progress. The fundamental issue that depends on
these assumtions is the question: whether the expectation
of a random variable at an arbitrary point will be the
same as the average over several fixed points. In the
mathematical theory, it would be assumed that these held
to an indefinite distance in all directions. In practice,
it is often adequate that they should hold for a sufficient
distance, which is beyind the range at which C(h) falls
to small values. So if I were only concerned to draw
conclusions about what happens within 5km of where I live,
I would not worry about the fact that it all fell apart
20kn away!

I hope this contributes further to clarifying your query!

best wishes,
Ted.

[**] There is a potential source of anisotopy: The region
is intersected by a number of watercourses -- on the size-scale
of rivers (which some of them are) -- which are contained
within raised banks (2-3m high), each of which tends to
run in a straight line for several km. Therefore at certain
points, given that the height is 2m or more, it will
remain so for a considerable distance in a particular
direction. Therefore the assumption of stationarity and
isotropy do not hold strictly everywhere. However, the
proportion of the area over which they do not hold is
a very small fraction of the whole.




E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 094 0861
Date: 02-May-05   Time: 18:08:16
-- XFMail --

* By using the ai-geostats mailing list you agree to follow its rules 
( see http://www.ai-geostats.org/help_ai-geostats.htm )

* To unsubscribe to ai-geostats, send the following in the subject or in the 
body (plain text format) of an email message to [EMAIL PROTECTED]

Signoff ai-geostats

RE: [ai-geostats] A matter of pronunciation

2005-04-11 Thread Ted Harding
On 11-Apr-05 Glover, Tim wrote:
 Here's a somewhat esoteric question for those of you who've
 had direct contact with the early giants in the field
 (on whose shoulders we now stand):
 
 What is the correct pronunciation of kriging?
 
 I've heard it CREE-ging, CRIG - ing, CREE-jing, etc. 

Without such direct contact, I think one can nevetheless
answer by appeal to first principles.

Kriging was named after Krige, a South African mining engineer.
As such, his name would have been pronounced approximately
Dutch-fashion, where the g is a kind of throat-clearing sound,
perhaps most practically approximated for English speech by simply
using the standard hard g.

The i, however, would have been between the i in pick
and the ee in peek, so if we denote this by î then
perhaps the best way to pronounce the word would be

  Krîging (with a hard g), i.e. between CRIG-ing and CREE-ging

Awaiting the truth from those who really know,
Best wishes,
Ted.



E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 094 0861
Date: 11-Apr-05   Time: 15:43:05
-- XFMail --

* By using the ai-geostats mailing list you agree to follow its rules 
( see http://www.ai-geostats.org/help_ai-geostats.htm )

* To unsubscribe to ai-geostats, send the following in the subject or in the 
body (plain text format) of an email message to [EMAIL PROTECTED]

Signoff ai-geostats

RE: [ai-geostats] Probability distribution of a moving object be

2005-02-21 Thread Ted Harding
On 21-Feb-05 Sunny Elspeth Townsend wrote:
 Dear list members,
 
 I would like to know how to find the probability distribution for the
 position of an object moving between two known points. I am trying to
 reconstruct the tracks of fishing vessel using satellite data which
 gives the ship's position every 2 hours. The ships do not move often
 move in straight lines, and I want to be able to incorporate the
 uncertainty of where the ship coulf be between the known points. I have
 already found the outer limit of movement which takes the form of an
 ellipse with the start and end points as the foci (for this I assumed
 constant speed).
 
 My question is:
 What is the probability distribution of the object within the ellipse.
 
 I would like to find the statistical distribution but would be happy if
 anyone knows if any GIS software has a function for this.
 
 Please reply to [EMAIL PROTECTED]
 Thank you for any help.
 -- 
   Sunny Elspeth Townsend
   [EMAIL PROTECTED]

You are asking an undefined question here! Your ellipses are
calculated on the basis of constant speed in a straight line
from one determined point, out to some unknown point, and then
at constant speed from there to the next determined point.
Therefore the sum of the two distances travelled is constant,
and the result, as you say, is an ellipse with the two determined
points as foci.

There is an implicit assumption of what this constant speed is,
since you need this to work out what total distance is travelled,
and you do not state what this assumption is based on.

But in any case there will in real life be, between the two
determined points, variations in speed (relative to the water)
and of direction, and further variations in absolute speed and
direction due to currents. Some of these will be random -- due
to external influences such as wind -- and some will be the result
of deliberate choices (which are also likely to be influenced
by external factors, such as locating a shoal of fish which
could cause the vessel to linger in that area, which themselves
have a random character).

The vessel may be following various policies, e.g.

a) basically trying to sail in a straight line at constant
 speed in order to get from A to B
b) zig-zagging haphazardly over an area in order to try to
 locate fish
c) pursuing a systematic sweep over an area on the lines of

 5km E, 200m N, 5km W, 200m N, 5km E, ...

The real probability distribution will depend on how all these
factors combine probabilistically.

You cannot expect any software to have a function for this
unless you are able to supply information about such factors.
You cannot expect the software to guess it for you.

One view of how to approach this kind of question would assume
a kind of random walk or diffusion with drift: There is
an overall tendency to move in a cerain direction, but at
frequent moments of time there are random changes of direction
and possibly also speed. Starting from A, there will (subject
to explicit assumptions about these random changes) be a
probability distribution of position after a given time.
The fact that B is a determined point at a determined time
will impose a condition on this distribution, from which the
conditional probability distribution of position at any
intermediate time can be determined (though not necessarily
easily). In the case of diffusion according to Brownian
motion this is known to probabilists as the Brownian
Bridge.

Such approaches have been applied to probabilistic study of (e.g.)
bird migration, on which there is quite a large literature.

However, no such considerations allow you to escape from the
necessity of thinking realistically about what variations from
uniform motion in a straight line are likely to occur, and
about what random laws they may follow.

Best wishes,
Ted.



E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 094 0861
Date: 21-Feb-05   Time: 10:29:34
-- XFMail --

* By using the ai-geostats mailing list you agree to follow its rules 
( see http://www.ai-geostats.org/help_ai-geostats.htm )

* To unsubscribe to ai-geostats, send the following in the subject or in the 
body (plain text format) of an email message to [EMAIL PROTECTED]

Signoff ai-geostats

RE: [ai-geostats] F and T-test for samples drawn from the same p

2004-12-03 Thread Ted Harding
On 03-Dec-04 Colin Badenhorst wrote:
 Hello everyone,
  
 I have two groups of several thousand samples analysed
 for various elements, and wish to determine if these
 samples are drawn from the same statistical population
 for later variography studies. I propose to test the two
 groups by using a F-test to test the sample variances,
 and a T-test to test the group means, at a given confidence limit.
  
 Before I do this, I wonder how I would interpret the results
 of the test if, for example:
  
 1. The F-test suggests no significant statistical difference
 between the variances at a 90% confidence limit, BUT
 2. The T-test suggests a significant statistical difference
 between the means at the same, or lower confidence limit.
  
 Has anyone come across this scenario before and how are they
 interpreted?

On the face of it, the scenario you describe corresponds to
a standard t-test (which involves an assumption that the
variances of the two populations do not differ), though I'm
not sure what you mean in (2) by significant at the same,
or lower confidence limit. (Do I take it that in (1) you
mean that the P-value for the F test is 0.1 or less?)

However, if you get significant difference between the variances
in (1), then it may not be very good to use the standard
t test (depending on how different they are). A modified
version, such as the Welch test, should be used instead.

There is an issue with interpreting the results where the
samples have initially been screened by one test, before
another one is applied, since the sampling distribution
of the second test, conditional on the outcome of the
first, may not be the same as the sampling distribution of
the second test on its own. However, I feel inclined to
guess that this may not make any important difference
in your case.

Hoping this helps,
Ted.



E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 094 0861  [NB: New number!]
Date: 03-Dec-04   Time: 14:15:09
-- XFMail --

* By using the ai-geostats mailing list you agree to follow its rules 
( see http://www.ai-geostats.org/help_ai-geostats.htm )

* To unsubscribe to ai-geostats, send the following in the subject or in the 
body (plain text format) of an email message to [EMAIL PROTECTED]

Signoff ai-geostats

RE: [ai-geostats] FW: spatial relationships

2004-09-02 Thread Ted Harding
On 02-Sep-04 Glover, Tim wrote:
 Thisa reminds me of a site where the failure of variogram modeling
 actually told me quite a bit about the problem at hand.  It was a large
 field where dumptruck loads of soil with a contaminant had been dumped
 randomly and spread.  This was unknown until after a gridded set of
 samples had been taken and a bizarre spotted pattern emerged.  The
 directional variogram showed an unusual hump - increasing variance with
 distance, then decreasing variance with even more distance.  This was
 the clue that some sort of spot activity had occurred. We finally
 tracked down a retired ex-employee who remembered the dumping activity.
 
 Sometimes a failed model tells more than one that fits!

Indeed! It's the difference between discovery and measurement.

Best wishes,
Ted.



E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 167 1972
Date: 02-Sep-04   Time: 14:19:37
-- XFMail --

* By using the ai-geostats mailing list you agree to follow its rules 
( see http://www.ai-geostats.org/help_ai-geostats.htm )

* To unsubscribe to ai-geostats, send the following in the subject or in the body 
(plain text format) of an email message to [EMAIL PROTECTED]

Signoff ai-geostats

RE: AI-GEOSTATS: Naive question on lat-long conventions

2004-04-15 Thread Ted Harding
On 15-Apr-04 Mark Coleman wrote:
 ... In particular, I have been using a small test data set 
 provided by Anselin on crime data in Columbus OH. Each sample point 
 includes a lat-long coordinate. The data set can be found at 
 http://www.spatial-econometrics.com/data/
 
 As an example, the first point in this data set shows latitude=35.62, 
 longitude=42.38. Yet when I check the coordinates of  a random point in
 Columbus OH (not in the dataset), I find coordinates in the range of 
 Lat=40.x, Long= -82.y.

Well, clearly either there's something seriously wrong with the data
(35.62 deg N 42.38 deg W is in the middle of the Atlantic,
 35.62 deg N 42.38 deg E is on the Iraq-Syria border)
or things are different from what one might first think they are.

According to the file
  http://www.spatial-econometrics.com/data/anselin.txt
we are only told that
  % column4 = latitude coordinate
  % column5 = longitude coordinate
but we are not told the units nor the origin. Have a look at the
numbers in
  http://www.spatial-econometrics.com/data/anselin.dat

  min(lat)  = 25.25, max(lat)  = 51.24
  min(long) = 24.95, max(long) = 44.07

Now, 1 degree of latitude is about 60 miles, so if these were
degrees then you're looking at a range of some 1,500 miles N-S;
similarly (though less) for E-W. Even Ohio ain't that big!

So I suspect that we're looking at minutes of arc rather than
degrees, relative to some fixed point. One minute of arc in
longitude is about 1 mile, so you're now looking at about
26 miles N-S.

At the latitude of Columbus (35.62N), 1 minute of arc is about
0.66 miles, so you're looking at about 11 miles E-W.

Also, it seems that the precision is 0.01 minutes of arc,
or about 18 yards (N-S) by 12 yards (E-W).

This all looks plausible ...

Hoping this helps (and wondering if I'm right ... pity people
don't document this sort of thing properly in their data files;
it would only have taken a line to do so.)

Best wishes,
Ted.



E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 167 1972
Date: 15-Apr-04   Time: 17:52:40
-- XFMail --

--
* To post a message to the list, send it to [EMAIL PROTECTED]
* 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 [EMAIL PROTECTED] 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


RE: AI-GEOSTATS: Hypothesis Testing in a Spatial Framework

2003-12-20 Thread Ted Harding
On 19-Dec-03 Warren Schlechte wrote:
 I would like some references for the following type design.
 
 Consider an area, much of which will not be treated. However,
 small sections will be treated, and if the treatment works, the
 density of an organism will be lessened.  The basic question is
 What is the likelihood that the low-density areas would have
 happened by chance, in the absence of the treatment?  If this
 likelihood is very small, then we could suggest the treatment
 is the reason we have lower densities in these areas.  Note,
 there could be a gradient with edge effects.
 
 How would one go about making a decision rule for testing whether
 the treatment was effective?  
 
 My guess is that the non-treated areas will be quite patchy.
 Our hope is that in the treated areas, if the organism isn't
 completely eliminated, the density will be considerably less. 
 [...]
 Warren Schlechte
 HOH Fisheries Science Center

The issues you raise occur also in classical agricultural field
trials, and you might like to consider using classical field
experiment techniques.

For instance, you could select a set of what you call sections
as plots, and randomly allocate half the plots to treatment/control.
Then, if you are mainly interested in a hypothesis-test type of
inference (which your statement suggests is the case), the randomisation
distribution of treatment/control comparison would give you a valid
result. If you can select well-separated plots so that they do not
interfere with each other, this may be all you need.

If gradients are a serious concern, you could make your experiment
more sensitive by identifying strata to use as blocks, within
each of which you expect to find less variation due to this cause.
Then you randomise on plots chosen within each block, and again
make use of the appropriate randomisation distribution.

However, if you need to make a more quantitative inference,
such as producing estimates with confidence intervals (or even
merely doing a t or F test), then you may need to take account
of possible spatio/temporal correlations on order to estimate the
variances of your estimates, and this is not so easy. Again, there
is a good deal of literature about this in the domain of agricultural
experimentation.

Given where you are writing from, it seems you may be looking
at bodies of water. You do not say whether these are rivers/canals
(approximately linear structures), or lakes or seas (2, or even 3,
dimensional). This would affect the type of layout you would
choose.

In canals or lakes, the water may be relatively static, so the
treatment is more likely to remain within the plot, while in
rivers or seas, the presence of currents may disperse it.
The latter complication, as a serious issue, is rare in agricultural
experiments. However, it may perhaps mainly influence your choice of
procedure for measuring the concentration of the organism, though it
could also severely complicate your estimation of variability.

You do not say what the treatment is, by the way.

I hope these thoughts help a bit.
Best wishes,
Ted.



E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 167 1972
Date: 20-Dec-03   Time: 16:33:43
-- XFMail --

--
* To post a message to the list, send it to [EMAIL PROTECTED]
* 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 [EMAIL PROTECTED] 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


RE: AI-GEOSTATS: analysis of bone surfaces

2003-06-24 Thread Ted Harding
On 24-Jun-03 ANN ZUMWALT wrote:
 I am a graduate student studying the functional morphology of bones.
 Part of my thesis entails characterizing the shape of a relatively
 complex 3D bone surface. I am testing to see whether exercise affects
 the morphology of this surface, so am looking for a way to test for
 differences between shapes/specimens. I am especially interested in
 testing for differences in the rugosity (ie, bumpiness) of the
 surfaces, but am interested in *any* method that would help me analyze
 these surfaces.
 
 I have 3D grid data (x,y,z) that represents the surfaces (I am scanning
 the bones with a 3D laser scanner to obtain this data). Can any of you
 suggest methods to analyze this data that will allow me to
 differentiate surfaces that are morphologically dissimilar?

Hi Ann,
Approaches would somewhat depend on the scale of the rugosity relative
to the global curvature of the bone surface. If you can regard the
surface as effectively flat (i.e. approximately a plane) then one aspect
that could be revealing is the two-dimensional spectrum.

However, if the scale of a bump is appreciable and the bone/specimen
is curved, then you may have to fit a 2-D smooth surface to the overall
shape of the bone, and then evaluate the rugosity say in terms of
perpendicular distance from the fit. You would also then have the problem
of defining position on the fitted surface in order to use say the
spectrum.

What do you mean by morphologically dissimilar?

Ted.



E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 167 1972
Date: 24-Jun-03   Time: 20:30:23
-- XFMail --

--
* To post a message to the list, send it to [EMAIL PROTECTED]
* 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 [EMAIL PROTECTED] 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


RE: AI-GEOSTATS: generating 2-dim point pattern

2003-03-10 Thread Ted Harding
On 10-Mar-03 Peter Bossew wrote:
 I want to generate a set of points in a plane, {(xi,yi)}, such
 that the points are distributed according to a chosen probability
 distribution density f, i.e., the infinitesimal rectangle
 [x,x+dx] X [y,y+dy]  shall contain f(x,y)*dx*dy points.
  How do I do this ??
 
 In other words, I am looking for a generalization of the 1-dim method,
 where this is done with F*(z), where F=cumul(f) and F* = inverse of F,
 and z = random out of [0,1] (or any appropriate interval if f is not
 normalized).
 
 I tried to do it the same way, just using complex numbers, but this
 does not seem to work, and could also not be generalized for n2
 dimensions.

Hi Peter,
The problem with doing it the same way is that the same way only
applies in 1 dimension (as a consequence of the result that F(X) has
a uniform distribution, so that F*(X) has the distribution of X).
In more than 1 dimension, you still only have the result that F(X,Y)
has a uniform distribution, and this is only 1 equation. There is
no _straightforward_ way of basing it on two equations

  (F1(X,Y), F2(X,Y)) = (Z1,Z1) where (Z1,Z2) is uniform on [0,1]x[0,1]

However, there are possible approaches. One is to use conditional
distributions: let F(X) be the marginal distribution for X, and let
G(Y;x) be the conditional distribution of Y given that X=x. Then
both U=F(X) and, for each x, V=G(Y;x) have uniform distributions,
so provided you can invert these as F*(U) and G*(V;x) you can then
sample U=u,V=v and obtain x=F*(u) and then y=G*(v;x).

The practical issues here depend a lot on the form of F(X,Y),
since both obtaining the conditional distribution and inverting
the functions F(X), G(Y;x) may be difficult in practice.

If it is straightforward to obtain the conditional distributions
for Y given X and X given Y, then Gibbs Sampling can enable you to
sample from (X,Y) without inverting the functions.

If you can't obtain the conditional distributions then it may be
impossible to follow such approaches, and then you may need to fall
back on simulating a random process with a known mechanism which has
the property of yielding (X,Y) distributed as f(x,y) -- if you know
of such a process!

If you could describe the density f(x,y) you are trying to sample
from to the list, then perhaps someone can suggest an approach.

 (PS. sorry if it is trivial.)

No, it isn't trivial!

Best wishes,
Ted.



E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 167 1972
Date: 10-Mar-03   Time: 08:29:19
-- XFMail --

--
* To post a message to the list, send it to [EMAIL PROTECTED]
* 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 [EMAIL PROTECTED] 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


RE: AI-GEOSTATS: Summary: Extreme Values?

2001-12-29 Thread Ted Harding

On 29-Dec-01 Myers, Jeff wrote:
 Ted's comments on the regulatory perspective bring up some
 interesting issues, assuming this were an hazardous waste site.

Jeff, Thanks for your comments which are very much to the point.

 It's hard to contour yourself out of a situation you sampled
 yourself into.

With your permission (which I assume will not be unreasonably
withheld) I propose to trot out this delightful maxim on
suitable occasions!

Thanks for this too -- just in time to set me smiling for
the New Year.

Best wishes to all,
Ted.


E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 167 1972
Date: 29-Dec-01   Time: 19:22:06
-- XFMail --

--
* To post a message to the list, send it to [EMAIL PROTECTED]
* 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 [EMAIL PROTECTED] 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



Re: AI-GEOSTATS: Comments about software

2001-02-12 Thread Ted Harding

On 12-Feb-01 Isobel Clark wrote:
 I agree that we do not want to turn the AI-Geostats
 list into an advertising free-for-all but it is very
 difficult not to refer to what you consider the
 perfect solution to a particular problem.  

Myself, I think this is fine as far as it goes. If Isobel
knows that the software developed by her house does a
particular job, and this may not be obvious or known to
others, then I cannot see why there should be objection
to her pointing it out in that context (otherwise the
mickey-mouse situation could arise in which non-free
software writers prompt their friends to point it out).

I don't really see an essential difference between saying
that E**SS* can do something specific, and saying that
ARCI*** can do it.

Equally, this should not take the form of an advertising
blurb. Within the list policy of not allowing advertising,
people should be able to mention a product with a decent
restraint, to the extent justified by the context.

I was unhappy about Gregoire's recent assertion that
"it is a demo version of a commercial product and I can not
accept to have it mentioned on the mailing list", since it
carries an implication that no commercial product should
be mentioned even in the context of pointing out that it
may give the solution to a reader's problem. Surely it must
be allowable to say that the solution to a problem can be
found in XXX package, commercial or not?

The delicate question of course is: where is the line that
defines "decent restraint"?

Ted.



Topical Thought:   It is better to arrive, than to travel hopefully.
E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 284 7749
Date: 12-Feb-01   Time: 16:05:48
-- XFMail --

--
* To post a message to the list, send it to [EMAIL PROTECTED]
* 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 [EMAIL PROTECTED] 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



AI-GEOSTATS: Global Warming

2000-12-31 Thread Ted Harding

Greetings!

At the suggestion of Isobel Clark, I have just joined this list.
Below is a message I already posted to the allstat mailing list,
and Isobel has suggested I might get good responses from ai-geostats.

Clearly, I have asked my question somewhat informally, but I think
the intention is clear. I would be most obliged to hear of
work directed towards a relative evaluation of two such hypotheses.

With thank, and best wishes to all for the New Year.
Ted.

===

I would be interested to learn of references to _data_ and to
good discussions of such data which are relevant to a hypothesis
of true global warming.

By "true global warming" I mean in effect a sustained positive
trend in the total heat content of the Earth's air and water
(including major ice and snow masses and no doubt some allowance
for the surface of the Earth itself).

No doubt a good statement of what I mean would have to be more
sophisticated, but you get the idea.

The idea specifically being to consider also an alternative
hypothesis whereby currently reported climatic changes, described
as "global warming", may be manifestations of a redistribution of
heat that is there already.

A nice question in spatial statistics, I feel.

With thanks in advance; interesting contributions will be
summarised to the list.

And, from globally warmed Manchester (-10 deg. C last night,
allegedly), a Happy New Year to all.

Ted.

--End of forwarded message-


--------
E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 284 7749
Date: 31-Dec-00   Time: 12:06:22
-- XFMail --

--
* To post a message to the list, send it to [EMAIL PROTECTED]
* 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 [EMAIL PROTECTED] 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