Newsgroup sci.stat.math 11831

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In article <3297B7A3.2DE7@postoffice.worldnet.att.net>,
kenneth paul collins   wrote:
>Ilias Kastanas wrote:
>> 
>> In article <329393FD.10CE@orci.com>, Bob Massey   wrote:
>> >kenneth paul collins wrote:
>> >>
>> >> .....       . All such attempts can be disproven by presenting the
>> >> system with something that "breaks" the syntax. (This is also my main
>> >> objection to Goedel's "Incompleteness".)
>> 
>>         Side note: I didn't follow this exchange, but "breaking the syntax"
>>    is irrelevant to Goedel Incompleteness.
>
>By "syntax" I was referring to the "rules" of the "proof". I stand on what I 
>posted. ken collins
	The "rules" of "proof" have been shown to be _the_ rules of proof;
   that is the Completeness theorem.  If you see something wrong there, maybe
   you could state what.  As it is, breaking the rules is pointless and
   self-defeating... and irrelevant to the Incompleteness theorem.
							Ilias

In article <578q7t$6sc@darkstar.ucsc.edu>,
Jonathan Gibbs  wrote:
>kenneth paul collins (KPCollins@postoffice.worldnet.att.net) wrote:
>: A machine that is designed so that it can "divide & conquer" 
>: can render such infinities irrelevant. Basically, such a 
>: machine transforms all problems into Geometry, and, instead 
>: of "algorithms", use cross-correlation among continuua to 
>: arrive at solutions.
>
>[tons snipped]
>Sounds very facinating ken, can you point me to a good reference on
>this stuff? Perhaps a journal paper...
	Journal article or not, this is about analogue computation...
   Which can take many forms; e.g. build a model of a graph, edges being
   pieces of string of appropriate lengths, and hold it up under the
   effect of gravity;  use pegs and rubber bands around them; and so on.
   One can obtain approximate solutions to a number of problems.  On the
   other hand, it is certainly a different subject.
							Ilias

In article ,
Paul Velleman  wrote:
>In article , Bill
>Simpson  wrote:
>> Several people are mentioning the use of robust statistical methods.  This
>> is essentially what I said.
>> For example, using "robust regression" amounts to an assumption that the
>> errors have a double exponential (Laplace) distribution.  (Since robust
>> regression minimizes the absolute errors, which is the way to get the MLE
>> for a model with Laplace distributed errors)
>There are, in fact, many better robust regression methods than least
>absolute residuals. Some are maximum liklihood for some error model, but
>many are not.
And all of these have their restrictions, unless symmetry of the errors
is assumed.  The one which has the minimal assumptions is least squares,
which only assumes properties of the mean; this one allows for linear
combinations of dependent variables, as means are additive, while 
essentially nothing else is.
The question is, roubst against what?  Symmetry is a very strong
assumption, compared to a few moments.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu	 Phone: (317)494-6054	FAX: (317)494-0558

In article <19961124005200.TAA06276@ladder01.news.aol.com>,
  wrote:
>Marks Nester  in
>
>writes:
>> Why not bypass the null hypothesis, proceed directly
>> to point/interval estimates
>There are many statisticians who agree with you. In particular, many
>Bayesians lean toward this point of view. However I think the solid
>majority of statisticians find classical hypothesis testing, which usually
>includes implausible null hypotheses, to be useful.
>It's really more a question of the reporting of results than of
>statistical technique. I can say that "a 95% confidence interval for x is
>1 to 2" or "I reject the null hypothesis that x=0 at the 5% significance
>level." The first statement gives more information, the second is often
>more useful for communicating results.
>But if you don't like hypothesis testing, don't do it.
I do not see that either is likely to give the information needed
for further action.  Therefore, they are not useful for communicating
results.
Given more information about the experimental situation, a 
confidence interval may allow the computation of at least an
approximation to the likelihood function, and it can be combined
with other data.  Rejection of the null hypothesis gives much
less information.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu	 Phone: (317)494-6054	FAX: (317)494-0558

I am wondering if anyone out there knows where and/or if I can get my
hands on software which would allow me to carry out the Bootstrap
algorithm?  I have about 7,000 reiteration to perform and I don't look
forward to programming my own macro in Fortran.  If anyone has any
usefull info on this, please let me know, it would be greatly
appreciated, thanks!
Cheers, Eric S

In article <576gt4$jho@nuscc.nus.sg>, engp6074@leonis.nus.sg says...
>anyone has any idea how to compute the centroid of 5 points in a 
>4 dimensional space ?
>
>For 2 points, it would be given by the mid-point of the 2 points.
>For 3 points, it would be given by the centroid of the triangle with 
>the 3 points as vertex. How about 5 points ?
>
It seems to me that if your treat each point as a column or row vector 
in multidimensional space, then you can add all the vectors together to 
get a sixth vector.  Then, multiply the scalar of (1/ # of vectors or 
points added together).  This resulting vector or point would then be 
equidistant from all the others.
Anyone else,
Bill Stroup
Department of Sociology and Anthropology
Purdue University

In article <3297AF2F.41C67EA6@ifp.uiuc.edu>,
Igor Kozintsev   wrote:
>Hello,
>The following distribution is called Generalized Gaussian
>and is widely used in image processing:
>\begin{equation}
>f_{X}(x)=\left[\frac{\nu \eta (\nu ,\sigma )}{2\Gamma (1 / \nu)}\right]
>\exp (-[\eta (\nu ,\sigma ) |x|]^\nu ),
>\end{equation}
>where
>\begin{equation}
>\eta = \eta(\nu ,\sigma ) = {\sigma}^{-1}
>\left[\frac{\Gamma (3/\nu )}{\Gamma (1/\nu)}\right]^{1/2}.
>\end{equation}
>(sorry for this latex code)
>I need to generate random numbers for this distribution
>and evaluate first three moments of the distribution (conditioned 
>on variable to be in some interval) on the computer.
To begin with, I suggest that we simplify the expressions,
by not evaluating all constants.  As I do not write LaTeX,
I will use the simpler "newsgroup TeX"
	f(x) = A exp(-B |x|^\nu),
where B is chosen to get the right variance, and A to make it
a probability distribution.
As for computing the moments of a truncated distribution, unless
\nu is a rational number with very small numerator, it is going to
involve numerous computations of incomplete gammas.
As for generating random variable from this distribution, acceptance-
rejection methods ignore the A anyhow.  For \nu at least 1, the 
logarithm of the density is concave, and so the methods for that
can be used.  Otherwise, I suggest that |x|^\nu = |y|, with the
appropriate sign attached, and that the appropriate \Gamma distribution
be simulated.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu	 Phone: (317)494-6054	FAX: (317)494-0558

To see the role of parameters in statistical models clearly it is useful to 
consider a special case: a linear model
   y = X\beta + e
where y is the nx1 vector of responses, X is an nxp design matrix of rank 
p, \beta is a px1 vector of parameters and e is an nx1 vector of error 
terms; for simplicity taken to be iid normal with zero mean and known 
scale.
The effect of the equation is to impose the condition that the vector E(y) 
is in the subspace of E^n spanned by the columns of X, which form a basis 
for this space. The parameters \beta, are the coefficients of E(y) 
expressed as a linear combination of the elements of this basis. But we 
could equally well chose any other basis to describe the model. The 
parameters would change by an invertable linear transformation but the 
model would be essentially the same.
The geometry of more general models is more complicated, but a similar 
arbitrariness underlies the choice of parameter vector.
Models are a means of describing the assumptions made about the probability 
distributions of the random variable involved, the particular equation and 
parameterization used to introduce the model sould be seen as 
representative of an equivalence class of such representations.
Murray Jorgensen
In article <571k9f$3fvq@b.stat.purdue.edu>,
   hrubin@b.stat.purdue.edu (Herman Rubin) wrote:
>In article <32935F01.769@biostat.mc.duke.edu>,
>Marek Ancukiewicz   wrote:
>>Herman Rubin wrote:
>
>>> I am replying to the original article, which I missed.
>>> The answer is trivial, if looked at carefully.
> 
>>> The customary use of the term _parameter_ is a large
>>> part of the problem.  A better use would be that a
>>> parameter is anything deducible from the model, or
>>> in particular, from the probability distribution.
>>> Thus, any function of parameters is a parameter.
>
>>This definition of a parameter, as "anything deducible from
>>the model" is an elegant one, but it seems too broad to me. 
>>Certainly, the tradition in many branches of mathematics is that 
>>a parameter is meant to be a number, a vector, or, perhaps, a 
>>matrix. How do we know that  "anything deductible" could be 
>>represented by those entities? It seems quite possible, but is 
>>there some philosophical justification to this? Perhaps statistics
>>only restricts istelf to such class of problems which can be
>>stated in terms of numbers?
>
>On the contrary, the usual restriction of parameter, and random
>variable, to a class of entities as above is artificial and
>not of much value, unless some very strong smoothness assumptions
>are made.  The question is, where to stop?  
>
>It is "well known" that any countable set of real numbers can be 
>described by a single real number; this is both trivial and
>useless.  From a pedagogical standpoint, it is much better to
>think of a stochastic process as a function-valued random variable
>rather than as an indexed set of random variables, and it is 
>better to think of the true cdf as a function-valued parameter
>than as a function from the real numbers to parameters.

In article , T.Moore@massey.ac.nz
(Terry Moore) wrote:
> 
> In article <32977892.4EE@students.wisc.edu>, Tatsuo Ochiai
>  wrote:
> > 
> > Suppose X ~ N(mu, sigma^2). Then, what is the formula for
> > 
> >      E[X|X=>X^*] : Expected value of X given X is greater than or
> > equal      to some fixed number X^*
> 
> Let Z = (X-mu)/sigma.
> Then E[X|X=>X^*] = mu + sigma*E[Z|X=>X^*]
> = E[Z|Z=>Z^*] where Z^* = (X^*-mu)/sigma.
> 
> The latter can be integrated easily.
> E[Z|Z=>Z^*] = 1/sqrt(2pi) integral(Z^*,oo, z exp(-z^2 /2) dz)
> = 1/sqrt(2pi) [-exp(-z^2 /2)](Z^*,oo)
> = 1/sqrt(2pi) [1 - exp(-Z^*^2 /2)].
Sorry, I forgot to divide by P(Z=>Z^*) which is best
looked up in tables as there is no closed form formula.
Terry Moore, Statistics Department, Massey University, New Zealand.
Imagine a person with a gift of ridicule [He might say] First that a
negative quantity has no logarithm; secondly that a negative quantity has
no square root; thirdly that the first non-existent is to the second as the
circumference of a circle is to the diameter. Augustus de Morgan

----------------------------
Formerly: Attitude responses
----------------------------
On 24 Nov 1996 aacbrown@aol.com wrote:
> Marks Nester  in
> 
> writes:
> 
> > Why not bypass the null hypothesis, proceed directly
> > to point/interval estimates
> 
> There are many statisticians who agree with you. In particular, many
> Bayesians lean toward this point of view. However I think the solid
> majority of statisticians find classical hypothesis testing, which usually
> includes implausible null hypotheses, to be useful.
Bayesians may also test implausible null hypotheses.
I think it is sad if a majority of statisticians consider
it useful to test implausible null hypotheses.
If tradition binds them to this approach then I
believe that it is a silly tradition.
If a null hypothesis can reasonably be assumed to be implausible
(surely this is generally the case)
then why can't a statistician have the gumption to bypass testing 
a silly null hypothesis and proceed directly to 
point/interval estimates etc.?
> I can say that "a 95% confidence interval for x is 1 to 2"
> or "I reject the null hypothesis that x=0 at the 5% significance level."
> ... the second is often more useful for communicating results.
Why/how is it more useful?
The second expression is even longer than the first.
Is it useful to use more words in order to impart less information?
Not all traditions are good traditions.
----------------------------------------------------------------
This is my final transmission on this topic, though I shall
read with interest any further comments Aaron or others may have.
-----------------------------------------------------------------
Marks R. Nester

On 23.11.96 pfv2@cornell.edu (Paul Velleman ) wrote:
> In article , Bill
> Simpson  wrote:
>
> > For example, using "robust regression" amounts to an assumption that the
> > errors have a double exponential (Laplace) distribution.  (Since robust
> > regression minimizes the absolute errors, which is the way to get the MLE
> > for a model with Laplace distributed errors)
> >
> There are, in fact, many better robust regression methods than least
> absolute residuals. Some are maximum liklihood for some error model, but
> many are not.
Which ones are you referring to ? I'm well aware that there are robust  
regression estimators which for some error model provide optimal  
efficiency (for almost every error distribution other than normal you  
should be able to find a robust regression estimator better than the OLS),  
but I don't recall any of them being derived as ML estimators.
Michael

In article <57agih$jo6@netserv.waikato.ac.nz>,
Murray Jorgensen  wrote:
>To see the role of parameters in statistical models clearly it is useful to 
>consider a special case: a linear model
>   y = X\beta + e
>where y is the nx1 vector of responses, X is an nxp design matrix of rank 
>p, \beta is a px1 vector of parameters and e is an nx1 vector of error 
>terms; for simplicity taken to be iid normal with zero mean and known 
>scale.
>The effect of the equation is to impose the condition that the vector E(y) 
>is in the subspace of E^n spanned by the columns of X, which form a basis 
>for this space. The parameters \beta, are the coefficients of E(y) 
>expressed as a linear combination of the elements of this basis. But we 
>could equally well chose any other basis to describe the model. The 
>parameters would change by an invertable linear transformation but the 
>model would be essentially the same.
These are parameters, but there are many others.  The length of \beta
in some coordinate system is a parameter.  If \beta has two elements,
the representation in polar coordinates is a different set of parameters.
>The geometry of more general models is more complicated, but a similar 
>arbitrariness underlies the choice of parameter vector.
>Models are a means of describing the assumptions made about the probability 
>distributions of the random variable involved, the particular equation and 
>parameterization used to introduce the model sould be seen as 
>representative of an equivalence class of such representations.
Parameters are used in two different ways.  As I have stated before,
anything computable from the model alone is a parameter.  A parametrization
consists of a set of parameters adequate to specify the model.  There is
no requirement of irredundancy in a parametrization.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu	 Phone: (317)494-6054	FAX: (317)494-0558

I have been reading about premarketing clinical trials
of a medication. The manufacturer says that there
were 3 adverse reactions out ot 2796 patients. This, he
says, yields a crude incidence of adverse reactions
of 1.1 per thousand with a "very wide" 95% confidence
interval of 2.2 cases per 10,000 to 3.1 cases
per 1000.
How does one make a confidence interval estimate in
this case? The number of reactions is so small that
I don't think I can approximate the s.d. by
sqrt(((p(1-p))/n); and when I do, I don't get the result
given.
Thanks.
---
 * 1st 2.00 #8935 * A gem is not polished without rubbing
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