Newsgroup sci.stat.math 11755

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In article <56ah1u$adv@gaia.ns.utk.edu>, %%spam repellent: remove this
prefix%%kennel@msr.epm.ornl.gov wrote:
....
> 
> Depends if you allow "stochastic" evolution rules or not.  If you require
> 'deterministic' evolution for your stochastic system, then no embedding can
> turn water in to wine. 
> 
> More interesting would be the reconstruction whose "stochastic equations
> of motion" are equivalent to the original.
> 
> Take for instance a 2-d stochastic map, e.g. the probability density of
> the future state \rho(x(n)) = F(x(n),x(n-1)) depends on function of the past
> observed value.  If you didn't consider past values, you might be tempted
> to model the system as a 'zero-embedding dimension' IID process, i.e.
> 
> \rho(x(n)) = G(\x(n))
> 
> just a histogram.   But this is in some sense "wrong", because there is
> more information that you haven't correctly discerned, and the observed data
> stream is not IID.
> 
> I believe something relating to this concept is called "model order" by
> the statisticians. 
> 
> But I don't know anything analogous to the arbitrary diffeomorphisms which
> preserve 'equivalence' of deterministic dynamical systems. 
> 
Well - we have a "Stochastic Takens Theorem" which sort of does this -
basically it embeds the deterministic part of the dynamics, leave the
stochastic part as is. There is a review paper containing statements of
the theorems at
http://www.ucl.ac.uk/CNDA/papers/Athens.ps
Note its quite large: 776Kb of postscript. There is also a paper there
concenring embedding determinsitically forced systems ( .../Takens.ps).
Cheers
Jaroslav
-- 
Dr. Jaroslav Stark,
Centre for Nonlinear Dynamics and its Applications
University College London,
Gower Street, WC1E 6BT, UK
Tel: +44-171-391-1368
Fax: +44-171-380-0986
E-Mail j.stark@ucl.ac.uk

S.C., DeJaegher wrote:
First of all, My name is Yoo, Chang-wan, living Seoul, South Korea
Your reseach way is correct.
What is a dependence var. and indepence var. ?
It is very importance to select a variable.
so, if you chose those variables correctly, there are many ways to
reseach your goal.
One-way Anova is very simply way to reseach. 
If there are two dependence variables or more, you had better use Multi
Anova, MANOVA, or use Discrimination Analysis method. Using a MDS,
LISREL, SPSS, SAS, STAT.

In article <328FF1A1.5B22@pop.nlci.com>,
William Stroup   wrote:
>Does anyone know what the assumptions of Structural Equation Modelling are?  Can they be 
>viewed as extensions of path analysis, which itself is an extension of OLS regression 
>and its assumptions?
>I know that there are many books on the subject, most notably the series published by 
>SAGE.  But, these are either checked out of my university library or are missing or 
>mis-shelved.
Path analysis is NOT an extension of least square regression, but a different
way of approaching some structural models not fitting the assumptions needed
for least squares to be reasonable.
Structural equations modeling goes back to the 18th century.  OLS and
path analysis are ways of estimation valid in some examples, as are
other methods.  I produced some of the methods myself a long time ago.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu	 Phone: (317)494-6054	FAX: (317)494-0558

Can anyone help....PLEASE
I have a series of data sets which contain outliers, I have shown this
using Dixons Q statistic.
However to continue analysis of the data I ideally would have a
balanced experimental design with no missing data.
 HOW DO I REPLACE THE POINTS THAT HAVE BEEN SHOWN TO BE OUTLIERS ????
I have heard various suggestions such as "use the mean of the
remaining data", something about the Median,
What is the best method, and is there anything wrong with any of the
others....
Thank in advance 
-------------------------------------------------
Adrian Milton.
Environmental Biologist.
School of Biological Sciences,
University of Liverpool,
PO Box 147,
LIVERPOOL.
L69 3BX.
U.K.
E-mail:	adrian@pop1.liv.ac.uk
Tel:	0151 794 5297
Fax:	0151 794 5289
LIBOV ANDREEVNA: Are you still a student?
TROFIMIV: I expect I shall be a student to the end of my days.
From, The Cherry Orchard II by Anton Chekhov
     //\\
  <*v*>
  - ['-']-
    -"-"-
------------------------------------------------

Vitaly Furman wrote:
> 
> Can you tell me which programs do you use to view .PS and .DVI files?
> Also is TeX for Win95 exists?
> And if exists, can I get it somethere for free?
> ---
> Vitaly Furman
> E-mail: vf@etas.kharkov.ua & vf@geocities.com
> http://www.bash.ru/~danko/vitaly.htm
> http://www.geocities.com/SiliconValley/1593
Others have mentioned the relevant software. Some pointers:
The Ghostscript/Ghostview home page can be found at
. Ghostscript is the actual Postscript
interpreter, and Ghostview (GSView for Windows), is the front-end
interface.
Various inplementations of TeX for various computer platforms are
available from the Comprehensive TeX Archive Network (CTAN). You can
find a listing of CTAN sites at
. Choose the one
closest to you and download away! AFAIK it's all freeware, and pretty
much any implementation of TeX will come with a DVI previewer built in.
The only implementation I've used much is GTeX for Windows, which worked
fine for me, and had a reasonably useable DVI previewer. YMMV.
						--Clay
--
Clay Helberg         | Internet: helberg@execpc.com
Publications Dept.   | WWW: http://www.execpc.com/~helberg/
SPSS, Inc.           | Speaking only for myself....

Adrian Milton wrote:
> I have a series of data sets which contain outliers, I have shown this
> using Dixons Q statistic.
> However to continue analysis of the data I ideally would have a
> balanced experimental design with no missing data.
> 
>  HOW DO I REPLACE THE POINTS THAT HAVE BEEN SHOWN TO BE OUTLIERS ????
It's difficult to say without more information about your data and,
in particular, the kind of analysis you are going to do.
As a general rule, if you are able to make a clear cut between
sick and healthy data, you should just throw the sick data away and
pretend they've never existed. On the other hand, if there is a gray
zone of more or less suspicious data, it may be better to choose
robust estimators. Try to make a litterature search on "robust" and
som terms that relate to the parameters you are going to estimate.
Helene Thygesen
Hogelanden WZ 17
3552 AB Utrecht
The Netherlands
+31(0)654 655 631
http://www.post1.com/~helene

In a STAT book from 1960 the author stated the following: "The
statistical fitting of a straight line is generally refered as linear
regression, where the word 'regression' has only historical meaning."
Does anyone know this historic meaning.
Thanks. - RC

Please help me with the following question:
Let b1,...,bk be model parameters, and u be a
function of b1,...,bk: u=f(b1,..., bk). Say, we
have the maximum likelihood estimates B1,..BK
of parameters b1,....,bk. Is then the plug-in
estimate U=f(B1,...,Bk) a maximum likelihood 
estimate of u?
If the answer is YES (my guess) then how to justify 
it?
Thanks,
Marek Ancukiewicz

On Mon, 18 Nov 1996, Adrian Milton wrote:
> Can anyone help....PLEASE
> 
> I have a series of data sets which contain outliers, I have shown this
> using Dixons Q statistic.
> However to continue analysis of the data I ideally would have a
> balanced experimental design with no missing data.
> 
>  HOW DO I REPLACE THE POINTS THAT HAVE BEEN SHOWN TO BE OUTLIERS ????
> 
> I have heard various suggestions such as "use the mean of the
> remaining data", something about the Median,
> 
> What is the best method, and is there anything wrong with any of the
> others....
Barnett and Lewis "Outliers in Statistical Data", Wiley, 1984.
Hawkins, "Identification of Outliers", Chapman and Hall, 1980.
Huber, "Robust Statistical Procedures", SIAM, 1977.
Hope this helps.
Gregory E. Heath     heath@ll.mit.edu      The views expressed here are
M.I.T. Lincoln Lab   (617) 981-2815        not necessarily shared by 
Lexington, MA        (617) 981-0908(FAX)   M.I.T./LL or its sponsors
02173-9185, USA

Ron Caldwell wrote:
> 
> In a STAT book from 1960 the author stated the following: "The
> statistical fitting of a straight line is generally refered as linear
> regression, where the word 'regression' has only historical meaning."
> Does anyone know this historic meaning.
> Thanks. - RC
Around the turn of the century, a geneticist named Francis Galton
was studying inherited traits in humans. He discovered that children tend to
grow up to a height that is somewhere between the height of their father and
that of the general population average. He called the effect
"regression toward mediocrity", and invented regression theory to study
such phenomena.
     J.

adrian@liv.ac.uk (Adrian Milton) in  writes:
> I have a series of data sets which contain outliers. . . . However
> to continue analysis of the data I ideally would have a balanced
> experimental design with no missing data. HOW DO I
> REPLACE THE POINTS THAT HAVE BEEN SHOWN TO BE
> OUTLIERS ???? I have heard various suggestions such as "use
> the mean of the remaining data", something about the Median,
> What is the best method, and is there anything wrong with any
> of the others....
An outlier is simply a point that differs from your other data. It is not
always a good idea to replace them. In some cases the outliers tell you
more than the rest of the data. In other cases, your model must
incorporate both.
If your outliers are data errors, the best idea is to correct them. If
that's impossible, and you use a statistical method that does not allow
missing values, then replacing with the average is only a first step.
After doing so, fit your model and get a prediction for each missing
value. Replace the missing values with the predictions. Generate new
predictions and continue until your model stabilizes. This is an ad hoc
approach but it works pretty well in many cases.
If your outliers are correct, but you just don't want them to have too
much influence on the result, you should select a robust method of
analysis. For example, the mean 1995 income of the class that entered
Harvard in 1973 was over $2,000,000. Subtract Bill Gates and Steve Balmer
and the mean drops under $500,000. If you use the median ($85,000) you get
a better picture of how a typical Harvard graduate is doing.
Aaron C. Brown
New York, NY

bryan@feeding.frenzy.com (Bryan Nelson) in <56om0q$m92@news.tamu.edu>
writes:
> I could really use the ansers to the Article published in
> Mathematics Magazine Vol 69, #4 October 1996, It was
> Steve Gadbois Poker with Wild Cards Problem were he
> tries to find the Frequenzy of occurence of certain hands
> when the two jokers are introduced as wild cards to a poker
> hand of 5
I have not seen the problem, but I assume you are talking about five cards
selected at random from the 54-card deck (52 regular cards plus two
jokers). There are 54 choose 5 possible deals, 54x53x52x51x50/(5x4x3x2x1)
= 3,162,510. To figure out the probability of getting a specific hand, you
have to compute how many ways it can happen.
For example there are four royal flushes (one for each suit). You could
get each one naturally, or in five ways with joker 1 replacing one card,
or in five ways with joker 2 replacing one card, or in 10 ways with both
jokers replacing two cards. That's 21 different ways times four suits, or
84 royal flushes.
84/3,162,520 = 0.00002656.
Aaron C. Brown
New York, NY

On Thu, 14 Nov 1996, Paul T. Karch wrote:
>  wrote:
-----------------------SNIP----------------------------------------
> If possible, I would like to get references on  Baysian classifiers,
> etc.; by mail or post .  This is for  self-study.  Thanks in advance. 
Devijver, Pierre A. and Kittler, Josef (1982), Pattern  recognition: 
a statistical approach, Englewood Cliffs, N.J.: Prentice/Hall International. 
Duda, Richard O. and Hart, Peter E., (1973), Pattern Classification and scene
analysis, New York: Wiley. 
Fukunaga, Keinosuke (1st ed. 1972, 2nd ed. 1990), Introduction to statistical
pattern recognition, New York(1st ed.), Boston(2nd ed.): Academic Press. 
James, Mike (1985), Classification algorithms, New York: Wiley. 
However, I can't remember seeing any reference that uses the pseudoinverse.
Hope this helps
Gregory E. Heath     heath@ll.mit.edu      The views expressed here are
M.I.T. Lincoln Lab   (617) 981-2815        not necessarily shared by 
Lexington, MA        (617) 981-0908(FAX)   M.I.T./LL or its sponsors
02173-9185, USA

In article <3290D9EF.818@hevanet.com>,
Ron Caldwell   wrote:
>In a STAT book from 1960 the author stated the following: "The
>statistical fitting of a straight line is generally refered as linear
>regression, where the word 'regression' has only historical meaning."
>Does anyone know this historic meaning.
>Thanks. - RC
I think the word comes from the fact that if (X,Y) is bivariate normal
and |corr(X, Y)|<1, then E[Y|x] is closer to E[Y] than x is to E[X] 
(measured in standard units).
John Lawrence

In article <56bbsb$57s@hcunews.hiroshima-cu.ac.jp>,
Hideo Hirose   wrote:
>In Japan, many researchers pronounce LaTeX as "latef." Is it correct? How do you 
>pronounce TeX and LaTeX actually, especially in the united states?
I hear "Lay-Tek" about 9 times out of 10 (spread across speakers from
the UK, the US, and Australia), and between what Leslie Lamport and
Donald Knuth say, I'd call that a reasonable choice. I hear "Lay-Teks"
about 1 time out of 10, and although it doesn't sit well with me, it 
is also perfectly acceptable. I've never actually heard "Lah-Tek" or 
"Lah-Teks", though they'd be OK too.
Note, however, that the Greek "Chi" (X) is a bit more guttural than the
usual English K, so we aren't really saying it "correctly".
I'm not sure where the "f" sound comes from.
Glen

>
>-----------------------SNIP----------------------------------------
>
> If possible, I would like to get references on  Baysian classifiers,
> etc.; by mail or post .  This is for  self-study.  Thanks in advance. 
I would suggest taking a look at
James Press, "Bayesian Statistics".
Regards,
---
Christopher Gordon                    Tel. (012) 326-4205 (w)         
Remote Sensing			      Fax. (012) 323-1157
Inst. for Soil, Climate and Water     email: c_gordon@igkw2.agric.za
Pretoria, South Africa		             chris@bayes.agric.za
Standard disclaimers apply.           Math is like love -- a simple idea but it
				      can get complicated.  -- R. Drabek                                   

In <3290D9EF.818@hevanet.com>, Ron Caldwell  writes:
>In a STAT book from 1960 the author stated the following: "The
>statistical fitting of a straight line is generally refered as linear
>regression, where the word 'regression' has only historical meaning."
>Does anyone know this historic meaning.
>Thanks. - RC
	It comes from a very early data set: a study of the comparative heights of
fathers and sons, in which the heights of the sons REGRESSED towards the mean.
The data was collected and analysed, and the term used, by F. Galton. The data
may be seen graphed - i.e. Galton's original graph - in Tufte's
	Visual Display of Quantitative Information,
with no indication that this is a graph with far reaching consequences, at least
linguistic ones.
--------------------------------------------------------------
"I would predict that there are far greater mistakes waiting
to be made by someone with your obvious talent for it."
Orac to Vila. [City at the Edge of the World.]
-----------------------------------------------
R.W. Hutchinson. | rwhutch@nr.infi.net

Never mind. I have finally figured it out. 
When day ends and you are tired. the simplest
things seem complicated.
Marek Ancukiewicz
> Please help me with the following question:
> 
> Let b1,...,bk be model parameters, and u be a
> function of b1,...,bk: u=f(b1,..., bk). Say, we
> have the maximum likelihood estimates B1,..BK
> of parameters b1,....,bk. Is then the plug-in
> estimate U=f(B1,...,Bk) a maximum likelihood
> estimate of u?
> 
> If the answer is YES (my guess) then how to justify
> it?
> 
> Thanks,
> 
> Marek Ancukiewicz

Robert Dodier wrote:
> If I'm not mistaken, this is true if f is linear, but not generally
> true otherwise. 
Thank you for your help, which I got AFTER writing
my "Never mind" post, and which --I realize --must 
have sounded rudely if mistaken for a response to 
your kind help.
It is not difficult to give a "reductio ad absurdum" 
argument to a general case. 
Say, there exist u1, such that p(data|u1)>p(data|U).
But u is completely determined by b1,...,bk, so the 
inequality would imply that some B1,...,BK are not ML 
estimates.
Marek Ancukiewicz

There was a question, where
: n.w.nelson@education.leeds.ac.uk (nick nelson) wrote:
: >Say I have responses on an attitude scale
: >
: >eg  Do you like this?  lots / some / a little / not at all
: >
: >and two groups eg men and women. What is the best way to
: >establish whethere the two groups differ significantly?
In response,
Warren (wlmay@umsmed.edu) wrote:
: Nick,
: Unless you have reason to believe the categories are equally spaced, I 
: would worry a little about numbering just as you said.  And the general 
: test of association may not tell you what you need to know...how do the 
: proportions relate to each other on an ordinal scale.
 -- I think that Warren gives some things to think about, but numbering 
your categories 1-4, and doing a t-test, is a pretty simple and robust
solution.  Your categories are  *definitely*  ordinal (which is not always
the case), and look like they would often approximate being  'interval'.
In practice, they would have to be quite a bit DIFFERENT from interval
for the t-test to be very misleading  -  that is most likely if your 
ratings do NOT fall across the categories in a ordinary, graduated way.
If that were the case, then it would be MOST likely that you should look
at the 2x4 contingency table, which compares each category.
Rich Ulrich, biostatistician              wpilib+@pitt.edu
Western Psychiatric Inst. and Clinic   Univ. of Pittsburgh

In article <3291EED1.5097@colorado.edu>,
Robert Dodier   wrote:
>Marek Ancukiewicz wrote:
>
>> Let b1,...,bk be model parameters, and u be a
>> function of b1,...,bk: u=f(b1,..., bk). Say, we
>> have the maximum likelihood estimates B1,..BK
>> of parameters b1,....,bk. Is then the plug-in
>> estimate U=f(B1,...,Bk) a maximum likelihood
>> estimate of u?
>> 
>> If the answer is YES (my guess) then how to justify
>> it?
>
>If I'm not mistaken, this is true if f is linear, but not generally
>true otherwise...
>
>If f is invertible, the density of u is related to the density of
>b by
>
>	p_u(u) = p_b( f^{-1}(u) ) |det Df^{-1}(u)|
>
>where (damn this tty notation) f^{-1} is the inverse of f and Df^{-1}
>is the Jacobian of the inverse of f.
Looking at the Jacobian would be relevant if you were interested in
finding the value with maximum posterior probability density, but not
for finding the maximum likelihood value.  Maximum likelihood does
not presuppose any distribution over parameters.
It might be good to know the context of the original question, in
order to tell what is really wanted, but it appears to me that the
answer is simply YES, in that the "plug-in" estimate is what most
people would take to be the DEFINITION of the maximum likelihood
estimate of a function of the parameters.
----------------------------------------------------------------------------
Radford M. Neal                                       radford@cs.utoronto.ca
Dept. of Statistics and Dept. of Computer Science radford@utstat.utoronto.ca
University of Toronto                     http://www.cs.utoronto.ca/~radford
----------------------------------------------------------------------------