HDTenEightyP/NetNews huggingface dataset:
From: hillyer@rrc.chevron.com (Martin J. Hillyer)
Newsgroups: sci.math.stat
Subject: Re: Non-linear Regression in Chemistry
Date: 4 Sep 92 03:05:52 GMT
Reply-To: hillyer@rrc.chevron.com
Organization: Chevron, Richmond, California

In article 42744@kuhub.cc.ukans.edu, jeff@kuhub.cc.ukans.edu (Jeff Bangert) writes:
>A chemist has asked me to solve a problem: she has data and a model
>which is to be fit by 'least squares'.  It looks like non-linear
>regression, except that:
>
>    1. the model has two equations
>    2. both are non-linear
>    3. there are parameters common to the two equations.
>
>I would like to know:
>
>    1. is there a 'standard' method for solving this problem?
>    2. is there literature in stat or chemistry which I could read?
>
>Clearly, I can form the sum of squared errors for each equation and
>add them together.  I have lots of methods for minimizing the result.
>However, this seems to ignore the question of the weighting of the two
>equations.
>
>I solved this kind of problem several years ago by writing FORTRAN +
>IMSL.  Now that it has come up again, I wish I had some backup
>literature that at least suggests the 'standard' solution method.  I
>don't like reinventing the wheel.
>
>Since the current data matrix is small, 4 by 2, I'm going to use
>non-linear optimization in Quattro Pro this time.  It produces nice
>graphs.  But, if I stick with QP, I'll also have to calculate the
>standard errors of the parameter estimates.  Right now, I'm not
>looking forward to this.
>
>Thanks for the help,
>-- 
>Jeff Bangert			jeff@kuhub.cc.ukans.edu
>Computer Center			jeff@ukanvax.bitnet
>University of Kansas
>Lawrence, KS 66045
>(913)864-0466


It's a little hard to know the exact formulation of the problem from your post, but if you are referring to 2 equations which arise from chemical kinetics of coupled reactions, you won't get the proper answer by adding the sum of squared errors from the two equations.  This is because the errors for the two equations are most likely different, which would require some weights to be applied, - but the proper weighting is unknown.  Further, the errors for the two responses  are likely to be correlated to an 

unknown extent.  Box and Draper (1965) showed that what should be minimized is the determinant of z'z, where z is the residual matrix for the set of experiments.   They derived this result by Bayesian arguments using a non-informative prior on the coefficents distribution.  Kang (1988) showed that this determinant criterion is also the maximum likelihood solution.  

There also is other literature on this multiresponse problem, so you should be able to find other articles.  Try Technometrics. 

Box and Draper (1965)  "The Bayesian Estimation of Common Parameters from Several Responses" Biometrika, 52, 355.

Kang (1988) "Topics in Multiresponse Regression Analysis", Ph.D. Thesis, U. Wisconsin, Madison.

Martin

Organization: Statistics, Carnegie Mellon, Pittsburgh, PA
Newsgroups: sci.math.stat
Date: Thu,  3 Sep 1992 21:55:05 -0400 
From: Brian Junker <bj20+@andrew.cmu.edu>
Subject: Re: Simple Proof that c=median minimizes E[ |X-c| ] needed.

Here are some ideas off the top of my head, that should get you going in
the right direction.  You will need some decent calculus skills, but
that's about it. 

Case 1.  X is a real-valued continuous random variable with density f(x)
such that xf(x) -> 0 as x -> +infinity and as x -> -infinity.  Write
E[|X-c|] as the sum of two integrals, one going from -infinity to c and
the other going from c to +infinity, where neither integral involves
abs. val's anymore.  Differentiate this sum with respect to c and
explore...

Case 2.  x_1, x_2, ... x_n are fixed real numbers (i.e. you have a
sample of size n).  Then c=the sample median minimizes the sum of
absolute deviations |x_1-c| + |x_2-c| + ... + |x_n-c|.  You can do the
cases n=2, 3, and 4 "by hand" by graphing the sum of abs. deviations as
a function of c---it is piecewise linear with bends at the data points
x_1, x_2, ...  What do you have to do to give a rigorous proof for n
data points now? 

Case 3.  X is a discrete random variable taking on the values x_1, x_2,
.... with probabilities p_1, p_2, .... The ideas you explored above
should be useful in proving that the median minimizes E[|X-c|] for this
case.

-BJ
From: huff@mcclb0.med.nyu.edu (Edward J. Huff)
Newsgroups: sci.math.stat
Subject: How many samples?
Date: 3 Sep 92 01:11:36 GMT
Followup-To: sci.math.stat
Organization: NYU Chemistry Dept.

I am involved in development of a new measurement technique and am planning
to do some statistical analysis.  Will the statistics experts out there
please tell me if I am making any serious mistakes, suggest ways to extract
more information from the data, or point me toward the proper books or
software to use?  Please send E-mail replies, I will summarize if there is
interest.  Thanks.

We measure a quantity which should be related to the mass of an object.  We
want to calculate statistics which indicate how precise the measurement is.

We have a population of objects which is about 90% pure.  We can repeat the
measurement a limited number of times on the same object.  We want to take
a sample of measurements, throw out the measurements of impurity objects,
and calculate the average and standard deviation for the pure objects. 
What critera should be used to throw out impurities?  How many samples are
needed for routine measurements?  How many samples are needed before this
question can be answered the first time?

The purity might not be known in advance.  How many measurements must be
made to conclude that either the population is not pure at all, so that a
measurement is meaningless, or that it is reasonably pure?

In a related experiment, we have a mixture of two objects of different
masses, say 40% of each, with 10% impurities.  We want to take a sample of
measurements and classify each as object A, B, or impurity, and calculate
an average and standard deviation for A and B.

When the mass of A gets close to that of B, so that the tails overlap
seriously, what is the proper way of calculating averages for the two
distributions?

If these questions are answered in some standard text, please recommend one
which is slanted toward this sort of problem.

--
Edward J. Huff   huff@mcclb0.med.nyu.edu   (212)998-8465
Keck Laboratory for Biomolecular Imaging
NYU Chemistry Deptartment, 31 Washington Place, New York NY 10003
Posted from the new Mac NewsWatcher 1.3d5
From: sunidh@m.njit.edu (Sunil Dhar)
Newsgroups: sci.math.stat
Subject: Chi-Squared parameter
Date: 28 Aug 92 16:56:55 GMT
Reply-To: sunidh@m.njit.edu (Sunil Dhar)
Organization: New Jersey Institute of Technology

A colleage of mine has the following problem for which reference is needed.

Problem: Suppose we have data (in general need not be i.i.d.) from either a 
Chi-squared u1 or Chi-squared u2. One has to decide which portion of the
data has come from which Chi-squared distribution (u1 or u2). 	

Sunil K. Dhar
Department of Mathematics
NJIT, Newark,NJ
Newsgroups: sci.math.stat
From: rcrump@beach.csulb.edu (Randy Crump)
Subject: Differences in diagnostic utility: Tests?
Organization: Cal State Long Beach
Date: Thu, 3 Sep 1992 23:32:46 GMT

I work in a clinical research setting where we frequently examine
parameters obtained during exercise stress testing in an effort
to develop methods that will permit an increased sensitivity and
specificity for the prediction of coronary artery disease.  Our 
usual approach is to apply two different variables or sets of 
variables to the same sample, and then ask which provides the 
better diagnostic utility.

I have been structuring an agreement matrix with the cells
containing those patients correctly and incorrectly classified by
each variable set; I then test for a difference in the discordance 
using McNemar's test.  I am also looking at comparing the areas 
under the two ROC curves.

I would appreciate any suggestions of any other methods I should
be considering.

Thank you,

Randy Crump
Newsgroups: sci.math.stat
From: mpp@cs.brown.edu (Michael P. Perrone)
Subject: Re: Question on ratio estimate
Organization: Center for Neural Science, Brown University
Date: Fri, 4 Sep 1992 20:37:40 GMT

T. Scott Thompson writes:
>To apply this to your problem let K = 2, J = 1 and set 
>Z_i = (X_i,Y_i).  Set
>
>	g(z) = z(1) / z(2)  so that G = [ 1 / m(y),  -m(x)/m(y)^2 ].

but i thought that z(1) and z(2) may be correlated
thus the i.i.d. assumption may be bad in general.

if the z(1) and z(2) are i.i.d. then
g(z) approaches a lorentzian distribution as n --> infinity
since the z(1) and z(2) both approach gaussian distributions.


- Michael
From: chaas@coe.drexel.edu (Chuck Haas)
Newsgroups: sci.math.stat
Subject: Re: info on "trends"
Date: 26 Aug 92 20:58:37 GMT
Organization: Drexel University
X-Useragent: Nuntius v1.1b2

There are both parametric and non-parametric tests for trend. 
Regression involves highly parametric assumptions which might not be
applicable to a given problem. Be more specific and we can expand this
discussion.
Newsgroups: sci.math.stat
Subject: Estimating the parameters for truncated GLM
From: chris@tahi.isor.vuw.ac.nz (Chris Johnston)
Date: Wed, 2 Sep 1992 03:08:12 GMT
Organization: Institute of Statistics and Operations Research, VUW, Wellington, NZ
Keywords: Truncated distribution, Gamma, General linear models


I need to find a function to estimate the parameters in a GLM of the truncated
gamma. Lokked in statlib but can't find anything. This does not mean nothing is
there as I haven't used it before now.

Really would be helpful if it was a fn that could run in Splus.

I'm wishing really hard so if anyone can help I would be grateful!!!

Chris
Organization: Doctoral student, Statistics, Carnegie Mellon, Pittsburgh, PA
Newsgroups: sci.math.stat
Date: Mon, 31 Aug 1992 11:29:53 -0400 
From: Kok Hooi Tan <kt14+@andrew.cmu.edu>
Subject: ftp site for ULTRA rng

Sometime ago the code for the  "ULTRA" random number generator by Zaman
and Marsaglia
was placed on a certain ftp site, but I have lost the information. Can
someone who knows send me 
the site name please? 

Thanks,
|---------------------------|
|Kok Hooi Tan               |     
|Dept of Statistics         |     
|Carnegie Mellon University |     
|Pittsburgh, PA 15213       |     
|---------------------------|
From: jeff@kuhub.cc.ukans.edu (Jeff Bangert)
Newsgroups: sci.math.stat
Subject: Non-linear Regression in Chemistry
Date: 3 Sep 92 06:42:30 CDT
Organization: University of Kansas Academic Computing Services

A chemist has asked me to solve a problem: she has data and a model
which is to be fit by 'least squares'.  It looks like non-linear
regression, except that:

    1. the model has two equations
    2. both are non-linear
    3. there are parameters common to the two equations.

I would like to know:

    1. is there a 'standard' method for solving this problem?
    2. is there literature in stat or chemistry which I could read?

Clearly, I can form the sum of squared errors for each equation and
add them together.  I have lots of methods for minimizing the result.
However, this seems to ignore the question of the weighting of the two
equations.

I solved this kind of problem several years ago by writing FORTRAN +
IMSL.  Now that it has come up again, I wish I had some backup
literature that at least suggests the 'standard' solution method.  I
don't like reinventing the wheel.

Since the current data matrix is small, 4 by 2, I'm going to use
non-linear optimization in Quattro Pro this time.  It produces nice
graphs.  But, if I stick with QP, I'll also have to calculate the
standard errors of the parameter estimates.  Right now, I'm not
looking forward to this.

Thanks for the help,
-- 
Jeff Bangert			jeff@kuhub.cc.ukans.edu
Computer Center			jeff@ukanvax.bitnet
University of Kansas
Lawrence, KS 66045
(913)864-0466
Newsgroups: sci.math.stat
Subject: Re: Simple Proof that c=median minimizes E[ |X-c| ] needed.
From: news@massey.ac.nz (USENET News System)
Date: Thu, 3 Sep 92 22:10:35 GMT
Organization: Massey University

In article <3SEP199213440863@utkvx2.utk.edu>, menees@utkvx2.utk.edu (Menees, Bill) writes:
> 
> 	I'm a senior math major taking my first p&s course, and this problem
> has come up and it intrigues me.  My prof. has a proof for it, but he said it
> was way over my head.  Does anyone know of a proof suitable for a senior 
> undergrad?  Thanks in advance.
> 
If you are a senior math major then you should have no difficulty
in following the proof. I suspect the real problem is that it's way
over your prof.'s head. :-)

Well, I must admit that I'm going to cheat. :-) Let's prove the result
for a discrete distribution only.

When c != any possible x
d/dc (sum|x-c|) = number of x's greater than c - number of x's less than c
otherwise this does not exist.
This derivative is decreasing if c < median and increasing if c > median
and as sum|x-c| is continuous and piecewise linear, the minimum either
occurs where there is a discontinuity in the derivative, or where it is
zero over an interval. The latter case corresponds to a median. In the
former case we choose the discontinuity such that on either side
|number of x's greater than c - number of x's less than c| is smallest.

In the continuous case the derivative exists nowhere but a limiting
argument could be used. (This might be over my head :-).


Newsgroups: sci.math.stat
From: mzf@castle.ed.ac.uk (M Firat)
Newsgroups: sci.math.stat
Subject: STATISTICAL AND COMPUTING CONSULTATION
Date: 3 Sep 92 10:52:07 GMT
Organization: Edinburgh University

Hi there,

I am involved in teaching and providing a statistical consultancy service
at the Biometry Section of the Department of Animal Science, Faculty of
Agriculture, University of Cukurova in Turkey. Our University has one of
Turkey's largest Faculties of Agriculture. However, there are only four
statisticians specializing in Biometry, consisting of a Professor, an
Associated Professor, a Doctor and myself.

Our main objectives are to provide a statistical/computing consultancy 
and teaching service, but these have been a great problem as our 
Biometry Section has such a limited number of statisticians. Our clients
are faculty graduate students working on research dissertations and 
other technical staff. Our teaching programme covers all students 
attending courses at the various departments of the Faculty of 
Agriculture. However, as there are no specialized staff in computing, 
these statisticians are required to provide a computing advisory service
as well as a teaching and statistical consultancy. 

When offering a statistical/computing consultancy and teaching service
to a large faculty, it is of course necessary to have experienced
statisticians. This could be possible if our existing statisticians were
to be trained with the help and collaboration of the universities which
have been carrying out teaching and consultancy in statistics and
computing. In future, as the University expands several graduate may be
required to attend MSc or PhD courses in Biometry at overseas
universities that we are in collaboration with.

We would be grateful if you could provide us with any information
relating to conducting a consultancy service (statistical/computing) and
also to organizing a teaching course for Agriculture students and MSc
and PhD students in Biometry. We would also be grateful for any
documentation including articles and video tapes (preferably Beta
system) etc. and the names and addresses of universities which provide a
consultancy and teaching service in statistics and computing. 

We look forward to hearing from you in due course.

For and on behalf of
Cukurova University

Mehmet Firat

University of Edinburgh
Dept. of Math. & Stats.
JCMB, 4617
King's Buildings
Edinburgh EH9 3JZ
UK

email: mzf@uk.ac.ed.castle
tel: (031) 650 8575
From: jira@latcs1.lat.oz.au (Ajin Jirachiefpattana)
Newsgroups: sci.math.stat
Subject: Performance Modeling Tools.
Date: 1 Sep 92 00:50:55 GMT
Organization: Comp Sci, La Trobe Uni, Australia
Originator: jira@elc2.lat.oz.au


Hi,

I just wonder if there are any performance modeling tools apart from 
GSPN and queueing networks. I am currently doing research on
Performance Evaluation of Communication Protocols, and I would like
to know what performance modeling tool is suitable for this application,
and if I would like to use more than one tool, how I can integrate all
of these tools to model and evaluate the performance, and if I need to 
decompose it in the case that this system is too complicated, what 
decomposition techniques I should learn.

Thanks in advance.

Ajin Jirachiefpattana,
Department of Computer Science & Computer Engineering,
Bundoora, Vic., 3083.
Australia.
jira@latcs1.lat.oz.au
From: dr3u+@andrew.cmu.edu (Daniel Read)
Newsgroups: sci.math.stat
Subject: unweighted mean of means
Date: 2 Sep 92 12:15:55 GMT
Article-I.D.: andrew.8edG3vu00WBN868HYr
Organization: Engineering and Public Policy, Carnegie Mellon, Pittsburgh, PA

I have some questionnaire data from which I wish to derive a "knowledge
index"   by taking the mean response to several of the questions. 
However, these are true-false questions and more of the questions are
true than false.  Moreover, many people are clearly disposed to choose
True as a response rather than False.  Of course, to the degree that
they have this bias their knowledge index is inflated.

I have solved this problem by taking the (unweighted) mean of the mean
answer to false questions plus the mean answer to true questions.

My question:  can you think of anything wrong with doing this?  

BTW, I realize that taking the "mean" of ordinal responses is
problematic, but I'm willing to weather this storm on my own -- which
doesn't mean that I am uninterested in comments on that issue.

Thanks in advance,

daniel 
Newsgroups: sci.math.stat
From: Inge Tastl <tastl@eigvs4.tuwien.ac.at>
Subject: Public Domain multi dim. scaling
X-Xxmessage-Id: <A6C2A1E6FB01A629@eigmmc.tuwien.ac.at>
X-Xxdate: Thu, 27 Aug 92 15: 14:46 GMT
Organization: Institute f. comp. graphics, TU Vienna
X-Useragent: Nuntius v1.1.1d9
Date: Thu, 27 Aug 1992 13:03:23 GMT

Hello!
I need some package for doing multidimensional scaling. Best platform
would be MAC or PC
UNIX workstation also appreciated. 
Does anyone know of such a package; or are there some Mathematica modules;
any help greatly welcome.
Thanks
Inge Tastl

Inst. f. Computergraphics
TU Vienna
Austria
mail: tastl@eigvs4.tuwien.ac.at
Newsgroups: sci.math.stat
From: thompson@atlas.socsci.umn.edu (T. Scott Thompson)
Subject: Re: Simple Proof that c=median minimizes E[ |X-c| ] needed.
Reply-To: thompson@atlas.socsci.umn.edu
Organization: Economics Department, University of Minnesota
Date: Fri, 4 Sep 1992 02:01:11 GMT

news@massey.ac.nz (USENET News System) writes:

>In article <3SEP199213440863@utkvx2.utk.edu>, menees@utkvx2.utk.edu (Menees, Bill) writes:
>> 
>> 	I'm a senior math major taking my first p&s course, and this problem
>> has come up and it intrigues me.  My prof. has a proof for it, but he said it
>> was way over my head.  Does anyone know of a proof suitable for a senior 
>> undergrad?  Thanks in advance.
>> 

[explanation for the discrete case deleted]

>In the continuous case the derivative exists nowhere but a limiting
>argument could be used. (This might be over my head :-).

I think that the continuous version is more straightforward since then
the objective function is _everywhere_ differentiable.  To get a feel
for the continuous case consider that any solution to the problem

             min  E(|x-c|)
              c

must satisfy a first-order condition provided E(|x-c|) is
differentiable in c.  When x is continuous this function is _always_
differentiable since the smooth distribution for x smooths out the
kink point in the absolute value function.  Differentiability only
fails if Pr( x = c ) is strictly positive.

The trick is to compute the derivative of E(|x-c|).  We can commute
the derivative operator and the expectation integral (showing that
this is OK is the technically difficult part of the proof that your
professor may have had in mind) in order to derive

       d/dc E(|x-c|) = E( d/dc |x-c| )

                     = E [ 1{ x < c } - 1{ x > c } ]

                     = E 1{ x < c } - E 1{ x > c}

                     = Pr( x < c ) - Pr( x > c )

where 1{ ... } is the indicator function taking the value +1 if "..."
is true and zero otherwise.  To see why this is true, simply note that
the derivative of |x-c| with respect to c equals +1 if x < c and -1 if
x > c.  We can ignore the case x = c, since this has zero probability,
and since any reasonable extension of the definition of
differentiability to handle this case would yield a value for the
derivative somewhere between -1 and +1 at the point x = c.
Technically, to verify the first equality you must check that the
conditions of the "Lebesgue dominated convergence theorem" are
satisfied.  You can look this up in any advanced probability theory
text.

Now notice that the derivative is zero if and only if

                Pr( x < c ) = Pr( x > c )

and this equation is solved by choosing c = median(x).  The solution
is unique if the probability density of x is positive on some
neighborhood of the median.

--
T. Scott Thompson              email:  thompson@atlas.socsci.umn.edu
Department of Economics        phone:  (612) 625-0119
University of Minnesota        fax:    (612) 624-0209
Newsgroups: sci.math.stat
From: renato@grover.stat.washington.edu (Renato M. Assuncao)
Subject: listserv for this newsgroup
Originator: renato@ernie.stat.washington.edu
Organization: Univ of Wash , Stat Dept.
Distribution: usa
Date: Thu, 3 Sep 1992 21:44:01 GMT

Dear sci.math.stat:

This is for a friend who has acces to bitnet but not to usenet.
Is there a listserv for this newsgroup or is it "digested" and sent to
some listserv?
I appreciate if you can send messages to my personal e-mail
renato@stat.washington.edu

Thanks.
Newsgroups: sci.math.stat
From: msc_wdqn@jhunix.hcf.jhu.edu (Daniel Q Naiman)
Subject: Time series
Organization: HAC - Johns Hopkins University, Baltimore
Date: Tue, 1 Sep 1992 14:49:44 GMT

I am about to teach a time series course and I'd like to 
know if anyone knows of sources of data available via ftp
or otherwise. Thanks.


Dan Naiman
Department of Mathematical Sciences
Johns Hopkins University

Newsgroups: sci.math.stat
From: winzar@newsman (Hume Winzar)
Subject: Re: unweighted mean of means
Organization: Commerce, Murdoch University
Date: Thu, 3 Sep 92 09:06:05 GMT


>I have some questionnaire data from which I wish to derive a "knowledge
>index"   by taking the mean response to several of the questions. 
>However, these are true-false questions and more of the questions are
>true than false.  Moreover, many people are clearly disposed to choose
>True as a response rather than False.  Of course, to the degree that
>they have this bias their knowledge index is inflated.

>I have solved this problem by taking the (unweighted) mean of the mean
>answer to false questions plus the mean answer to true questions.

An alternative is an approach often used for rescaling multiple choice 
exams:
In this case there is a 50% probability of guessing a correct answer.
So all of the wrong answers must be about half of the guesses - the other 
half of the guesses were correct by pure chance.  After calculating the 
probable number of guesses you can subtract this number from the total 
number of questions.  In this case it reduces to, for each person:
                 SCORE = N(correct) - N(wrong)

Of course this does not get you arround the systematic bias created by the 
propensity to answer TRUE more often.
  - - - - - - - - -
 |      _--_|\     |   Hume Winzar
 |     /      \    |   Commerce School,
 |     *_.--._/    |   Murdoch University,
 |           v     |   Perth, Western Australia
  - - - - - - - - -  
                       E_Mail winzar@csuvax1.csu.murdoch.edu.au
                       Phone: (09) 310 7389
                       Fax:   (09) 310 5004
Newsgroups: sci.math.stat