http://groups.google.com/group/sci.stat.math?hl=en
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Today's topics:
* how to obtain prior - 3 messages, 3 authors
http://groups.google.com/group/sci.stat.math/browse_thread/thread/d20d54c8c6cf8e40?hl=en
* Shorthand for labeling statistical differences? - 5 messages, 5 authors
http://groups.google.com/group/sci.stat.math/browse_thread/thread/76f1102494dad9e6?hl=en
* Joint pdf and Conditional Expectation - 2 messages, 2 authors
http://groups.google.com/group/sci.stat.math/browse_thread/thread/c7f56e2f50678acc?hl=en
* What will be the combination of regions? - 3 messages, 2 authors
http://groups.google.com/group/sci.stat.math/browse_thread/thread/ba6072881be7a1b3?hl=en
* Linear (?) Model Question - 3 messages, 3 authors
http://groups.google.com/group/sci.stat.math/browse_thread/thread/b48e06b259c147dd?hl=en
* Log-Normal: Means and Variances - 2 messages, 2 authors
http://groups.google.com/group/sci.stat.math/browse_thread/thread/281495749e54b5f8?hl=en
* Sample Size - 1 messages, 1 author
http://groups.google.com/group/sci.stat.math/browse_thread/thread/ff810bbd9cf63993?hl=en
==============================================================================
TOPIC: how to obtain prior
http://groups.google.com/group/sci.stat.math/browse_thread/thread/d20d54c8c6cf8e40?hl=en
==============================================================================
== 1 of 3 ==
Date: Mon, Nov 12 2007 2:06 am
From: Lou Thraki
hrubin@odds.stat.purdue.edu (Herman Rubin) wrote:
> In article <1194462402.820693.13550@v3g2000hsg.googlegroups.com>,
> bahoo <b83503104@yahoo.com> wrote:
>> Hi,
>
>> To use an informative prior for a multinomial distribution, does the
>> following make sense?
>> 1. Start with a uniform prior.
>> 2. Compute the posterior.
>> 3. The posterior is filtered by a signal processing method. The
>> outcome of the method is used to build a new prior, which is NOT
>> uniform.
>> 4. Go to step 2.
>
>> Thanks!
>> bahoo
>
> There prior should come from the user's ASSUMPTIONS,
> and not from the distribution of the data. However,
> there is the idea of robustness if one is unsure of
> the prior, and this is a tricky subject. It is not
> the case that robustness is merely a function of how
> close the assumed prior is to the true prior as a
> distribution, and is highly asymmetric.
Could you explain what is the definition a true prior?
== 2 of 3 ==
Date: Mon, Nov 12 2007 10:49 am
From: duncan smith
bahoo wrote:
> On Nov 8, 12:45 pm, hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
>> In article <1194462402.820693.13...@v3g2000hsg.googlegroups.com>,
>>
>> bahoo <b83503...@yahoo.com> wrote:
>>> Hi,
>>> To use an informative prior for a multinomial distribution, does the
>>> following make sense?
>>> 1. Start with a uniform prior.
>>> 2. Compute the posterior.
>>> 3. The posterior is filtered by a signal processing method. The
>>> outcome of the method is used to build a new prior, which is NOT
>>> uniform.
>>> 4. Go to step 2.
>>> Thanks!
>>> bahoo
>> There prior should come from the user's ASSUMPTIONS,
>> and not from the distribution of the data. However,
>> there is the idea of robustness if one is unsure of
>> the prior, and this is a tricky subject. It is not
>> the case that robustness is merely a function of how
>> close the assumed prior is to the true prior as a
>> distribution, and is highly asymmetric.
>> --
>
> However, if the prior comes from another model, is it OK then?
> That is, one model uses the data to compute a posterior, then supplies
> it as a prior to another model. This seems to avoid the situation
> where a model uses the data twice.
>
>
It's still using the data twice (if you're using the same data to inform
the second model).
Duncan
== 3 of 3 ==
Date: Mon, Nov 12 2007 10:52 am
From: hrubin@odds.stat.purdue.edu (Herman Rubin)
In article <fh98jl$ckh$1@aioe.org>,
Lou Thraki <louthraki@usenet.invalid> wrote:
>hrubin@odds.stat.purdue.edu (Herman Rubin) wrote:
>> In article <1194462402.820693.13550@v3g2000hsg.googlegroups.com>,
>> bahoo <b83503104@yahoo.com> wrote:
>>> Hi,
>>> To use an informative prior for a multinomial distribution, does the
>>> following make sense?
>>> 1. Start with a uniform prior.
>>> 2. Compute the posterior.
>>> 3. The posterior is filtered by a signal processing method. The
>>> outcome of the method is used to build a new prior, which is NOT
>>> uniform.
>>> 4. Go to step 2.
>>> Thanks!
>>> bahoo
>> There prior should come from the user's ASSUMPTIONS,
>> and not from the distribution of the data. However,
>> there is the idea of robustness if one is unsure of
>> the prior, and this is a tricky subject. It is not
>> the case that robustness is merely a function of how
>> close the assumed prior is to the true prior as a
>> distribution, and is highly asymmetric.
>Could you explain what is the definition a true prior?
The true prior is the one you should be using according to
your assumptions. Unfortunately, the computing power of
the human mind, or in fact of the largest computers, is
usually quite incapable of calculating this. So one has to
use an assumed prior; the same holds for the loss function
in general. In addition, the cost of computing can be
quite high for a "complicated" loss-prior combination.
One cannot get around this merely by adding the cost of
computing to the loss, as the cost of computing the
cost of computing is usually FAR greater than the cost of
computing. But one might be able to find a convenient
prior for which the prior risk can be analyzed, and shown
to be close to what could be obtained. That is a good
approximation can be shown in many cases.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
==============================================================================
TOPIC: Shorthand for labeling statistical differences?
http://groups.google.com/group/sci.stat.math/browse_thread/thread/76f1102494dad9e6?hl=en
==============================================================================
== 1 of 5 ==
Date: Mon, Nov 12 2007 6:30 am
From: Cueball
I have a stats question. Or more like a stats representation question.
In brief: if one has a bar graph showing some sample means and wants to indicate in a figure which means are statistically different without
too many asterisks and lines, how does one do that?
In detail: I have a bar graph of 6 sample means. The 1st and 2nd bars are statistically different from the 3rd, 4th 5th and 6th, but not
from each other. The 3rd is also different from the 5th and 6th.
Ordinarily in papers, I see statistically signifcant differences shown with a line over the two relevant bars and an asterisk indicating
that they are different. However, in this case, there would be far too many lines/asterisks for all the combinations of differences. I'd
like to know if there's a better way of conveying this fact that is also understood by the general scientific audience.
So is there a shorthand for this sort thing? Any thoughts would be appreicated!
TIA,
-Mark
== 2 of 5 ==
Date: Mon, Nov 12 2007 7:53 am
From: "David Jones"
Cueball wrote:
> I have a stats question. Or more like a stats representation question.
>
> In brief: if one has a bar graph showing some sample means and wants
> to indicate in a figure which means are statistically different
> without too many asterisks and lines, how does one do that?
>
> In detail: I have a bar graph of 6 sample means. The 1st and 2nd bars
> are statistically different from the 3rd, 4th 5th and 6th, but not
> from each other. The 3rd is also different from the 5th and 6th.
>
> Ordinarily in papers, I see statistically signifcant differences
> shown with a line over the two relevant bars and an asterisk
> indicating that they are different. However, in this case, there
> would be far too many lines/asterisks for all the combinations of
> differences. I'd like to know if there's a better way of conveying
> this fact that is also understood by the general scientific audience.
>
> So is there a shorthand for this sort thing? Any thoughts would be
> appreicated!
>
How about setting out a 6 by 6 table so that the columns or rows are alligned with your bars, depending on whether they are vertical or horizontal (preferably vertical for the sake of the arrangement?) . Then put no, one, two or three stars, depending on "significance" of the difference, in each cell. Possibly put dots on the diagonal. Add an additional set of labels for those things not already labelled for the bar plot.
David Jones
== 3 of 5 ==
Date: Mon, Nov 12 2007 9:10 am
From: Gus Gassmann
On Nov 12, 2:30 pm, Cueball <b...@blah.org> wrote:
> I have a stats question. Or more like a stats representation question.
>
> In brief: if one has a bar graph showing some sample means and wants to indicate in a figure which means are statistically different without
> too many asterisks and lines, how does one do that?
>
> In detail: I have a bar graph of 6 sample means. The 1st and 2nd bars are statistically different from the 3rd, 4th 5th and 6th, but not
> from each other. The 3rd is also different from the 5th and 6th.
>
> Ordinarily in papers, I see statistically signifcant differences shown with a line over the two relevant bars and an asterisk indicating
> that they are different. However, in this case, there would be far too many lines/asterisks for all the combinations of differences. I'd
> like to know if there's a better way of conveying this fact that is also understood by the general scientific audience.
>
> So is there a shorthand for this sort thing? Any thoughts would be appreicated!
>
> TIA,
> -Mark
If you want to do it pictorially, you can arrange the means on a
number line. Draw a vertical line between means 2 and 3 to indicate
that 1 and 2 are different from the rest. Draw some kind of bracket,
loop or whatever you can do easily over 1 and 2, 3 and 4, and again
over 4, 5 and 6 to indicate that they are not statistically different.
This should be generalizable for rather a large number of comparisons.
== 4 of 5 ==
Date: Mon, Nov 12 2007 1:54 pm
From: jos jansen
Cueball schreef:
> I have a stats question. Or more like a stats representation question.
>
> In brief: if one has a bar graph showing some sample means and wants to indicate in a figure which means are statistically different without
> too many asterisks and lines, how does one do that?
>
> In detail: I have a bar graph of 6 sample means. The 1st and 2nd bars are statistically different from the 3rd, 4th 5th and 6th, but not
> from each other. The 3rd is also different from the 5th and 6th.
>
> Ordinarily in papers, I see statistically signifcant differences shown with a line over the two relevant bars and an asterisk indicating
> that they are different. However, in this case, there would be far too many lines/asterisks for all the combinations of differences. I'd
> like to know if there's a better way of conveying this fact that is also understood by the general scientific audience.
>
> So is there a shorthand for this sort thing? Any thoughts would be appreicated!
>
> TIA,
> -Mark
Calculate a LSD = least significant difference between two means and
draw a piece of line of LSD-length in your graph; forget about the
hocus-pocus around multiple comparisons.
== 5 of 5 ==
Date: Mon, Nov 12 2007 5:42 pm
From: Richard Ulrich
On Mon, 12 Nov 2007 09:30:48 -0500, Cueball <blah@blah.org> wrote:
> I have a stats question. Or more like a stats representation question.
>
> In brief: if one has a bar graph showing some sample means and wants to indicate in a figure which means are statistically different without
> too many asterisks and lines, how does one do that?
>
> In detail: I have a bar graph of 6 sample means. The 1st and 2nd bars are statistically different from the 3rd, 4th 5th and 6th, but not
> from each other. The 3rd is also different from the 5th and 6th.
[snip]
That sounds pretty concise to me. A footnote.
--
Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
==============================================================================
TOPIC: Joint pdf and Conditional Expectation
http://groups.google.com/group/sci.stat.math/browse_thread/thread/c7f56e2f50678acc?hl=en
==============================================================================
== 1 of 2 ==
Date: Mon, Nov 12 2007 7:58 am
From: dondora
hi there.
I'm solving probability problems.
And I've got some questions to ask to everybody here.
In a joint pdf of two continuous random variables X and Y,
I know how to calculate P[ 0 < X < 1 ] and P[ Y <= 1] and so on like
these things.
But I'm doing nothing to this problem P[X > Y].
Besides I'm not figuring out what it means and what I have to do.
Would you explain how to solve that and what it means?
Another thing, Given pdf of the continuous random variables X and Y,
I know E[ X | y ] = integral( x * fx(x | y) dx from -
infinity to +infinity
but I wonder what this E[X | Y] means. I scrutinized my text book but
it didn't cover it.
Do you know the difference between E[X | y] and E[X | Y] and how to
calculate E[ X | Y ]
Please help me. I'm going to wait for your clear-cut answer.
Thanks.
== 2 of 2 ==
Date: Mon, Nov 12 2007 12:37 pm
From: "Nasser Abbasi"
"dondora" <koninja@hanmail.net> wrote in message
news:1194883109.773461.192920@y27g2000pre.googlegroups.com...
> hi there.
>
> I'm solving probability problems.
> And I've got some questions to ask to everybody here.
> In a joint pdf of two continuous random variables X and Y,
> I know how to calculate P[ 0 < X < 1 ] and P[ Y <= 1] and so on like
> these things.
> But I'm doing nothing to this problem P[X > Y].
> Besides I'm not figuring out what it means and what I have to do.
> Would you explain how to solve that and what it means?
>
P(X>Y) is the same as P(X-Y>0)
Hence, draw the line Y=X, and integrate the region below this line.
Hence P(X>Y)= double integral as follows (I think :)
x +inf
/ /
| | f(x,y) dx dy
/ /
-inf -inf
> Another thing, Given pdf of the continuous random variables X and Y,
> I know E[ X | y ] = integral( x * fx(x | y) dx from -
> infinity to +infinity
> but I wonder what this E[X | Y] means. I scrutinized my text book but
> it didn't cover it.
For a given value of r.v. Y, X has an expectation. So X is a function of y.
So we are talking about the expected value of a function of random variable.
> Do you know the difference between E[X | y] and E[X | Y] and how to
> calculate E[ X | Y ]
>
You just showed how to calculate E(X|Y)? it is the integral you wrote above.
As for the difference, the lower case letter is a specific value of the
random variable. the random variable is an UPPER CASE letter, and its value,
or realization, is lower case. the lower case y is NOT random, only upper
case letters are random.
One should really write E(X|Y=y) to be clear.
> Please help me. I'm going to wait for your clear-cut answer.
> Thanks.
>
Nasser
==============================================================================
TOPIC: What will be the combination of regions?
http://groups.google.com/group/sci.stat.math/browse_thread/thread/ba6072881be7a1b3?hl=en
==============================================================================
== 1 of 3 ==
Date: Mon, Nov 12 2007 9:23 am
From: zl2k
hi, there
Suppose I have a world map covered by N countries (no public area).
The average neighboring countries for a given country is M. Then what
will be the complexity of the regions that contains country A? By
saying "region", it means people in one country can travel to any
other country of the region only via the countries within the region.
For example, Canada and USA can form a region, so does (Canada, USA
and MEXICO). However, Canada and Mexico can not form a region without
the joint of US. Is this combination exponential? Thanks for your
help.
zl2k
== 2 of 3 ==
Date: Mon, Nov 12 2007 10:56 am
From: "Kenneth M. Lin"
What do you mean by "combination"?
"zl2k" <kdsfinger@gmail.com> wrote in message
news:1194888212.406837.146250@k79g2000hse.googlegroups.com...
> hi, there
> Suppose I have a world map covered by N countries (no public area).
> The average neighboring countries for a given country is M. Then what
> will be the complexity of the regions that contains country A? By
> saying "region", it means people in one country can travel to any
> other country of the region only via the countries within the region.
> For example, Canada and USA can form a region, so does (Canada, USA
> and MEXICO). However, Canada and Mexico can not form a region without
> the joint of US. Is this combination exponential? Thanks for your
> help.
> zl2k
>
== 3 of 3 ==
Date: Mon, Nov 12 2007 11:26 am
From: zl2k
On Nov 12, 1:56 pm, "Kenneth M. Lin" <kenneth_m_...@sbcglobal.net>
wrote:
> What do you mean by "combination"?
>
> "zl2k" <kdsfin...@gmail.com> wrote in message
>
> news:1194888212.406837.146250@k79g2000hse.googlegroups.com...
>
> > hi, there
> > Suppose I have a world map covered by N countries (no public area).
> > The average neighboring countries for a given country is M. Then what
> > will be the complexity of the regions that contains country A? By
> > saying "region", it means people in one country can travel to any
> > other country of the region only via the countries within the region.
> > For example, Canada and USA can form a region, so does (Canada, USA
> > and MEXICO). However, Canada and Mexico can not form a region without
> > the joint of US. Is this combination exponential? Thanks for your
> > help.
> > zl2k
To find all of the different ways to arrange r countries out of N
countries. r is from 1 to N in which country A must be included. All
countries in region r must be connected directly or indirectly via
other countries belonging to the same region.
==============================================================================
TOPIC: Linear (?) Model Question
http://groups.google.com/group/sci.stat.math/browse_thread/thread/b48e06b259c147dd?hl=en
==============================================================================
== 1 of 3 ==
Date: Mon, Nov 12 2007 10:07 am
From: elodie.gillain@gmail.com
Consider the model
Yi=1+beta*Xi+beta^2*Xi^2+epsilon_i
withi=1...n
where the epsilon_i are uncorrelated random vars with mean 0 and var
sigma^2.
Xi....Xn are known constants. beta and sigma^2 are unknown parameters.
Question 1:
Is this a linear model?
I would say that it is not. That model is not linear in the
parameters, because of beta^2.
Question 2:
Indicate how to find the least squares estimator (LSE) of beta. Is
this a straightforward estimator? Does one need an algorithm to obtain
the estimator?
I worked out the (X'X)^-1*X'Y estimator. It looks like I am getting
two equations of the form
beta=f1(sumXi, other parameters)
beta^2=f2(sumXi, other parameters)
This will require numerical computation, right?
Does anybody have a pointer to some material on this model.
Thanks for your help.
== 2 of 3 ==
Date: Mon, Nov 12 2007 10:45 am
From: Jack Tomsky
> Consider the model
>
> Yi=1+beta*Xi+beta^2*Xi^2+epsilon_i
> withi=1...n
>
> where the epsilon_i are uncorrelated random vars with
> mean 0 and var
> sigma^2.
>
> Xi....Xn are known constants. beta and sigma^2 are
> unknown parameters.
>
> Question 1:
> Is this a linear model?
> I would say that it is not. That model is not linear
> in the
> parameters, because of beta^2.
>
> Question 2:
> Indicate how to find the least squares estimator
> (LSE) of beta. Is
> this a straightforward estimator? Does one need an
> algorithm to obtain
> the estimator?
>
> I worked out the (X'X)^-1*X'Y estimator. It looks
> like I am getting
> two equations of the form
> beta=f1(sumXi, other parameters)
> beta^2=f2(sumXi, other parameters)
>
> This will require numerical computation, right?
>
> Does anybody have a pointer to some material on this
> model.
>
> Thanks for your help.
>
1. It is not a linear model, as you say, because a linear model means linearity in the parameters.
2. To get the least-squares estimate for beta, first let Zi = Yi - 1. Then the sum of squares is
SS = Sum[Zi - beta*Xi - (beta*Xi)^2]^2
After taking derivatives, d(SS)/d(beta), and setting it equal to zero, you end up with a cubic equation for beta.
There is a closed-form expression for the three roots. Either all three betas are real or one of them is real and the other two are complex conjugates.
In a practical sense, you could probably solve this numerically. One way is to use Excel's Solver to minimize the sum of squares SS.
Jack
== 3 of 3 ==
Date: Mon, Nov 12 2007 11:30 am
From: Ray Koopman
On Nov 12, 10:07 am, elodie.gill...@gmail.com wrote:
> Consider the model
>
> Yi=1+beta*Xi+beta^2*Xi^2+epsilon_i
> withi=1...n
>
> where the epsilon_i are uncorrelated random vars with mean 0 and var
> sigma^2.
>
> Xi....Xn are known constants. beta and sigma^2 are unknown parameters.
>
> Question 1:
> Is this a linear model?
> I would say that it is not. That model is not linear in the
> parameters, because of beta^2.
>
> Question 2:
> Indicate how to find the least squares estimator (LSE) of beta. Is
> this a straightforward estimator? Does one need an algorithm to obtain
> the estimator?
>
> I worked out the (X'X)^-1*X'Y estimator. It looks like I am getting
> two equations of the form
> beta=f1(sumXi, other parameters)
> beta^2=f2(sumXi, other parameters)
>
> This will require numerical computation, right?
>
> Does anybody have a pointer to some material on this model.
>
> Thanks for your help.
If the gradient has three real roots then SS has two local minima,
at the outer roots; the middle root gives a local max.
If you look for *a* solution, you may get the wrong one.
If you turn a minimizer loose, it may return the wrong min.
==============================================================================
TOPIC: Log-Normal: Means and Variances
http://groups.google.com/group/sci.stat.math/browse_thread/thread/281495749e54b5f8?hl=en
==============================================================================
== 1 of 2 ==
Date: Mon, Nov 12 2007 10:15 am
From: elodie.gillain@gmail.com
On Nov 11, 3:02 pm, "Stratocaster" <sto...@verizon.net> wrote:
> "Ray Koopman" <koop...@sfu.ca> wrote in message
>
> news:1194776437.255538.70330@t8g2000prg.googlegroups.com...
>
>
>
> > On Nov 9, 4:12 pm, "Stratocaster" <sto...@verizon.net> wrote:
>
> > > Case I: X+c = Ln(Y)
>
> > > E(Y) = (e^c)*(regular expression for the mean)
> > > V(Y) = (e^c^2)*(regular expression for the variance)
>
> > > Case II: X = Ln(Y+c)
>
> > > E(Y) = (regular expression for the mean) - c
> > > V(Y) = (regular expression for the variance)
>
> > > I would supply my work, but it seems trivial, almost to trivial (which
> is my
> > > concern)... I will post it if you feel it is necessary.
> > > Thanks for taking the time to help me.
>
> > I parse e^c^2 as e^(c^2). For the case I variance,
> > I would write the multiplier as (e^c)^2 = e^(2c).
>
> This is another interesting topic to me. I usually interpret (e^c^2) as
> (e^c)^2, but will agree that (e^c^2) is ambiguous (after all, you interpret
> it differently from me). Regardless, thanks for taking the time to help me.
For case 2,
I would argue that you are defining a location family of Y. In
location families, the expectation if expectation of the Y (the
reference) plus the location parameter (-c). And the variance does not
change. Just my two cents.
== 2 of 2 ==
Date: Mon, Nov 12 2007 2:43 pm
From: "Stratocaster"
<elodie.gillain@gmail.com> wrote in message
> > > > Case I: X+c = Ln(Y)
> >
> > > > E(Y) = (e^c)*(regular expression for the mean)
> > > > V(Y) = (e^c^2)*(regular expression for the variance)
> >
> > > > Case II: X = Ln(Y+c)
> >
> > > > E(Y) = (regular expression for the mean) - c
> > > > V(Y) = (regular expression for the variance)
> For case 2,
> I would argue that you are defining a location family of Y. In
> location families, the expectation if expectation of the Y (the
> reference) plus the location parameter (-c). And the variance does not
> change. Just my two cents.
I had never heard of a location family (or location-scale family) before.
Thanks for pointing this topic out to me. Pretty neat stuff.
==============================================================================
TOPIC: Sample Size
http://groups.google.com/group/sci.stat.math/browse_thread/thread/ff810bbd9cf63993?hl=en
==============================================================================
== 1 of 1 ==
Date: Mon, Nov 12 2007 5:28 pm
From: Richard Ulrich
On Sun, 11 Nov 2007 23:38:10 -0500, Allen McIntosh
<nospam@mouse-potato.com> wrote:
[snip]
>
> To elaborate a little on what Mike says, and to mention a few assumptions:
>
> 1) The formula 1.96*sqrt(...) uses a Normal approximation that doesn't
> work well if n*p is too small
>
> 2) All this assumes that the OP is sampling without replacement
>
> 3) As Mark points out the OP is sampling from a finite population, so
> that 1.96*sqrt(...) should really be multiplied by sqrt(1-n/N) where n
> is the sample size and N is the population size. This term matters when
> the sample is a significant fraction of the population, and matches the
> intuition that when the sample is the entire population, there is no
> uncertainty in the result
There's "no uncertainty in the result" if it is a vote.
There's the same uncertainty as always if the count is
taken as representative of similar groups.
Every mention of the Finite Sampling Fraction should
include the advice that it is almost never appropriate, if you
are not predicting the vote that has yet to be tabulated on
Election Evening.
--
Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
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