## AI-GEOSTATS: Statistics book

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• Hello, I was wondering if some one could reccomend a book on statistics which covers the basic theories of probability (expectations), least squared errors and
Message 1 of 5 , Nov 25, 2002
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Hello,
I was wondering if some one could reccomend a book on statistics which covers the
basic theories of probability (expectations), least squared errors and lagrange multipliers
for understanding the derivation of kriging equations which can be found in many texts.
Regards Digby Millikan.

I have searched the Internet and found the Schaums books which I might have a look at,
Thanks
Regards Digby Millikan

[Non-text portions of this message have been removed]
• Thanks Donald, I ll look into these. Regards Digby Millikan. ... From: Donald E. Myers To: Digby Millikan Sent: Tuesday, November 26, 2002 4:24 AM Subject: Re:
Message 2 of 5 , Nov 26, 2002
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Thanks Donald, I'll look into these.

Regards Digby Millikan.
----- Original Message -----
From: Donald E. Myers
To: Digby Millikan
Sent: Tuesday, November 26, 2002 4:24 AM
Subject: Re: AI-GEOSTATS: Statistics book

The Schaumns Outline book on Probability is not a bad place to start but I
think it does not include much about continuous probability distributions.
There is a book by Miller and Freund on engineering statistics that is not
a bad choice for the rudiments of probability and statistics. Both of these
would provide some background on the expected value of a random variable
(however I think that the Schaums Outline book will only consider discrete
distributions)

As for Lagrange multipliers, that is not really a part of either
probability theory or statistics, it is a part of optimization theory. You
will find some discussion of them in books on matrix theory, particularly
related to eigenvalue problems and maximization/minimization of quadratic
expressions (I think there is a Schaums Outline book on matrix theory)
subject to a constraint. In the case of the kriging equations, the
constraint is unbiasedness of the estimator.

With respect to "least squares", there are two senses to this. One
corresponds to fitting data to a function via least squares, this is
essentially deterministic. The second is more like what happens in the
derivation of the kriging equations, i.e., a certain expected value is
minimized.

Donald E. Myers
http://www.u.arizona.edu/~donaldm

Digby Millikan wrote:

Hello,
I was wondering if some one could reccomend a book on statistics which
covers the
basic theories of probability (expectations), least squared errors and
lagrange multipliers
for understanding the derivation of kriging equations which can be found
in many texts.
Regards Digby Millikan.

I have searched the Internet and found the Schaums books which I might
have a look at,
Thanks
Regards Digby Millikan

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• Thanks Isobel, I have purchased and am reading Practical Geostatistics 2000 at the moment, but as it is a few years since I took maths and statistics courses I
Message 3 of 5 , Nov 26, 2002
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Thanks Isobel,

I have purchased and am reading Practical Geostatistics 2000 at the moment,
but as it is a few years since I took maths and statistics courses I was
going to
review the basic principles to understand the derivation of kriging
equations,

Regards Digby Millikan.

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• Hello, Here is a summary of responses to my posting, thanks to Donald for his most informative summary, and Isobel for her book which I am reading.
Message 4 of 5 , Nov 29, 2002
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Hello,

Here is a summary of responses to my posting, thanks to Donald for his most
informative
summary, and Isobel for her book which I am reading.

//=================================================================
Hello,
I was wondering if some one could recommend a book on statistics which
covers the
basic theories of probability (expectations), least squared errors and
lagrange multipliers
for understanding the derivation of kriging equations which can be found in
many texts.
Regards Digby Millikan.

I have searched the Internet and found the Schaums books which I might have
a look at,
Thanks
Regards Digby Millikan

//=================================================================
The Schaumns Outline book on Probability is not a bad place to start but I
think it does not include much about continuous probability distributions.
There is a book by Miller and Freund on engineering statistics that is not
a bad choice for the rudiments of probability and statistics. Both of these
would provide some background on the expected value of a random variable
(however I think that the Schaums Outline book will only consider discrete
distributions)

As for Lagrange multipliers, that is not really a part of either probability
theory or statistics, it is a part of optimization theory. You will find
some discussion of them in books on matrix theory, particularly related to
eigenvalue problems and maximization/minimization of quadratic expressions
(I think there is a Schaums Outline book on matrix theory) subject to a
constraint. In the case of the kriging equations, the constraint is
unbiasedness of the estimator.

With respect to "least squares", there are two senses to this. One
corresponds to fitting data to a function via least squares, this is
essentially deterministic. The second is more like what happens in the
derivation of the kriging equations, i.e., a certain expected value is
minimized.

Donald E. Myers
http://www.u.arizona.edu/~donaldm
//=================================================================
Digby

What's wrong with Practical Geostatistics 2000?
Isobel
//=================================================================

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• Hi Digby The short answer to your least squares question is because Matheron was a least squares person ;-) There are three basic schools of statistics: (1)
Message 5 of 5 , Nov 29, 2002
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Hi Digby

'because Matheron was a least squares person' ;-)

There are three basic schools of statistics:

(1) least squares (sometimes known as frequentist)
which probably includes the majority of
non-statisticians doing statistics. The least squares
approach might be paraphrased as "closest to the real
answer on average". It is based on the concept of
approximately Normal 'errors'

(2) maximum likelihood. This could be paraphrased as
'that solution from which the samples are most likely
to have come'. This yields much more general but not
always unbiassed answers. For example, the maximum
likelihood estimator of the variance is divided by 'n'
not 'n-1' as in least squares. Maximum likelihood
demands a pretty fair knowledge of the underlying
distribution of the samples, not the errors as such.

(3) bayesian estimation. Based somewhat on a maximum
likelihood method, you can build in your own prior
knowledge about the situation to affect the final
answers. (1) and (2) above rely solely on hard data.

This is, of course, a massive over-simplification but
serves, I think, to emphasise why there are many
different answers to the same problem and why you have
to define what you mean by "best" before you get the
"best answer". I try to cover these concepts in
non-rigorous terms in all my teaching.

It is also true that the mathematics is much simpler
if you use variances than if you use any other
function of differences.

Isobel
http://geoecosse.bizland.com/news.html

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