Last fall I ended up teaching a statistics course for engineers. I
work at a small university in Norway, and the available textbooks in
Norwegian were appallingly bad. So I ended up writing a few notes,
and ... now I have an almost complete book that my students and
colleagues urge me to publish. Well, good.

I do of course take a bayesian perspective, but do by necessity
present the other view as well. I think the Bayesian approach is
didactically superior to the frequentist one, and would have chosen a
Bayesian starting point even if I had been a frequentist.

My own background is from mathematics, not statistics, so my
notational standards may be different. My formulas, too. So I
wondered if anyone here would consider giving me feedback on
notational and other issues with the book. Whatever you have time
for. For instance this m / mu thing. In mathematical probability we
frankly don't care about the name, but I have this feeling (bayesian)
statisticians reserve them for each their use.

The book is in Norwegian, so I don't expect anyone to read the text.
Only formulas, diagrams and the like. If you are interested in having
a look and maybe also giving me some feedback, please email me, and
I'll send you a download link.
--

Svein Olav Nyberg
http://www.nonserviam.com/solan/

    "Did you ever contribute anything to the
     happiness of Mankind?"

    "Yes, I myself have been happy!"

                  - John Henry Mackay

The Name Index file for Jaynes's Probability Theory has been updated.

Hello everyone.

Perhaps someone here can confirm some of my suspicions, or at least correct some
of my misinterpretations.  It seems to me that the area where Bayesian inference
should clearly win out over classical methods is in the analysis and forecasting
of financial time series.

What mystifies me is that most books devoted to speculation and/or investment,
or financial economics, emphasize the use of classical inference procedures,
when we should know a priori, that it is unlikely these methods will find
"significant" (both practical and statistical) results due to the competitive,
adaptive nature of the markets.

Lets take, for example tests of market efficiency. According to these
"experts"--the markets are "efficient" in the weak sense that past price history
allegedly does not help predict future history, in the sense of obtaining a
"statistically significant" result.

They make the claim, for example, that markets don't have trends (ie.
persistently under and overreact to information), and I believe even 1 book on
financial time series analysis could not find a "significant" trend in the S&P
price data from the entire bull market run from 1992 through 2004!  I have to
ask--just what would it take to get their tests to recognize a trend if there
really was one?

Yet, in other circumstances, there are all sorts of recommendations to remove
"trends" from data for further analysis.  But I thought there weren't supposed
to be trends in the first place?  Of course--they are "stochastic" trends.

Does the idea of a "long run frequency" even make sense in the context of a
historical, competitive process like financial markets?

The classical logic -- if we can't rule out the null (ie. p(data|null) > 0.5),
the alternative is probably false, seems especially falacious. We are dealing
with a process where:

1. our "sample" is a segment of historical data, where the exact underlying
economic factors that lead to it, are not likely to be repeated,

2. the process is not likely to remain stable, as traders who lose are weeded
out, and dominant strategies lose their edge as others learn them.

3. changes in the rules of the game itself--ie regulatory, economic, cultural,
etc.

It seems guaranteed that this type of process is almost guaranteed to generate
data where the noise dominates the signal.  That doesn't mean there isn't any
signal there, at least with informative prior information.

Can anyone explain to me why economists continue to go through the ritual of
"significance" tests, when it seems clear that Bayesian methods, and the idea of
informative, yet subjective priors, seems to be a more useful way forward?  Can
anyone give other instances where hypothesis tests or "confidence intervals"
lead to absurd conclusions?

Hi RR,

Intuitively I'd agree with you, but then I know nothing about economics.
As to why frequentist approaches persist, tradition (especially in
education) is obviously a strong factor, but I wouldn't look to this list
for detailed analysis of the frequentist mindset.

Just a few comments:

"The classical logic -- if we can't rule out the null, the alternative is
probably false". I don't think anyone would advance this argument. The
classical logic is the weaker idea that if we can't rule out the null, we
can't confidently say that the alternative is true - which is a tautology
we can't argue against. Most frequentists would admit that the alternative
is probably true in many cases where we can't rule out the null; this is
tolerated because false negatives are assumed to be less costly than false
positives.

The big question is whether Bayesian methods can succeed where frequentist
methods have failed or whether modelling of economics is just, for now,
too difficult for any computationally feasible approach. I would assume
that several people have tried and failed with Bayesian methods.

Konrad

------------------------------------
Dr Konrad Scheffler
Computer Science Division
Dept of Mathematical Sciences
University of Stellenbosch
http://www.cs.sun.ac.za/~kscheffler/
------------------------------------

--- In etjaynesstudy@yahoogroups.com, Konrad Scheffler <konrad@...> wrote:

> Just a few comments:
>
> "The classical logic -- if we can't rule out the null, the alternative is
> probably false". I don't think anyone would advance this argument. The
> classical logic is the weaker idea that if we can't rule out the null, we
> can't confidently say that the alternative is true - which is a tautology
> we can't argue against. Most frequentists would admit that the alternative
> is probably true in many cases where we can't rule out the null; this is
> tolerated because false negatives are assumed to be less costly than false
> positives.

I've always been puzzled by the classical logic.  Many nulls are point nulls,
that is: H0:  x=0, where x is some population parameter of interest.  However,
what is the chance that the population parameter is EXACTLY zero?  Basically,
nil.  Therefore, if the alternative is H1:  x<>0, then we CAN confidently say
that the alternative is true, regardless of the results of any statistical
testing we conduct.  The interesting question isn't "is x non-zero" (because it
assuredly is) but rather "is x far enough away from zero to matter".  Whether
something "matters" (ie is important) or not is something that no statisical
test can tell you.  It is very harmful to build implicit loss functions into the
logic of statistical inference, which the classical method does.

>
> The big question is whether Bayesian methods can succeed where frequentist
> methods have failed or whether modelling of economics is just, for now,
> too difficult for any computationally feasible approach. I would assume
> that several people have tried and failed with Bayesian methods.
>

I'm not an expert (MA in Economics), but I can tell you that Bayesian methods
are very hard to find in economics..... the classical/frequentist approach rules
the roost.  You can (and in fact, you probably would) obtain a PhD in Economics
without hearing the word "Bayesian" once.

Darren McHugh
Toronto, Canada

> I've always been puzzled by the classical logic.  Many nulls are point
> nulls, that is: H0:  x=0, where x is some population parameter of
> interest.  However, what is the chance that the population parameter is
> EXACTLY zero?  Basically, nil.  Therefore, if the alternative is H1:
> x<>0, then we CAN confidently say that the alternative is true,
> regardless of the results of any statistical testing we conduct.  The
> interesting question isn't "is x non-zero" (because it assuredly is) but
> rather "is x far enough away from zero to matter".  Whether something
> "matters" (ie is important) or not is something that no statisical test
> can tell you.  It is very harmful to build implicit loss functions into
> the logic of statistical inference, which the classical method does.

I agree - many of the nulls that are actually used are ones to which we
should assign a prior probability of zero. But things become trickier when
you consider chi-squared likelihood ratio tests for comparison of nested
models: here the question becomes one of whether the more complicated
model, with its associated parameter point estimates, is better than the
simpler (null) model.

In the case of nested models we know that, given perfect parameter
estimates, the more complex model would be at least as good a description
of underlying reality as the simpler model. But given that parameter
estimates are obtained from the data the simpler model will often be
better. So model comparison using LRT is a type of hypothesis test where
the null has nonzero prior.

Of course the nature of the question is entirely different for Bayesian
approaches, where overparameterisation ceases to be an issue. But
sometimes one is committed to using ML approaches for computational
reasons.

>
> I'm not an expert (MA in Economics), but I can tell you that Bayesian methods
are very hard to find in economics..... the classical/frequentist approach rules
the roost.  You can (and in fact, you probably would) obtain a PhD in Economics
without hearing the word "Bayesian" once.
>
> Darren McHugh
> Toronto, Canada

This is interesting to me, as I own a few Bayesian econometrics
texts--Lancaster's Bayesian Econometrics and Greenburg's Intro to Bayesian
Econometrics.

I know frequentist theories are dominant, but it appeared to me that there were
some significant Bayesian inroads, particularly at some top programs, and as
well as at the Federal Reserve.

The Name Index file for Jaynes's Probability Theory has been updated to show
names that are referred to in a footnote, e.g. 234n for a name in a footnote on
page 234.

Arnold Baise

30th International Workshop on

Bayesian Inference and Maximun Entropy

Methods in Science and Engineering

Chamonix, France, July 4-9, 2010

http://maxent2010.inrialpes.fr/

For 30 years the MaxEnt workshops have explored the use of Bayesian and Maximum
Entropy methods in scientific and engineering applications. All aspects of
probabilistic inference, such as techniques, applications and foundations, are
of interest. The workshop includes a one-day tutorial session, state-of-the-art
lectures, invited papers, contributed papers and poster presentations. Selected
papers by the program committee will be edited and published in a book.

Especially encouraged are papers whose content is novel, either as to approach
or area of application.

Abstracts (one page of about 400 words) of the proposed papers should be
submitted via this Web site by April 11, 2010 (midnight, GMT).

List of provisional topics and organizers:
--------------------------------------------------------------
History and axiomatic foundation of probability and Information theory
(K.H. Knuth, A. Caticha, J. Skilling, ...)
Bayesian inference in astronomy and astrophsics
(T. Loredo, S. Gull, ...)
Information geometry and information theory
(F. Barbaresco, H. Snoussi, P. Gibilisco, C. Rodriguez, )
Algorithms for Bayesian computation.
(A. Quinn, R. Fischer, ...)
Bayesian Computed Tomography: medical imaging
(Ch. Bouman, K. Sauer, E. Miller, J.M. Lina, ...)
Non parametric Bayesian methods and experimental design
(F. Bac, M. Jordan, Z. Ghahramani, E. Barat, ...)
Bayesian classification, clustering, pattern recognition, image segmentation
(J. Center, M. Jordan, ...)
Time series, spectral estimation. deconvolution and source separation.
(P.O. Amblard, Ch. Jutten, ...)
Information theory and quantum tomography.
(Ch. Benjaballah, C. Caves, A. Vourdas, ...)
Bayesian and maximum entropy inference in action: Industrial applications
(E. Mazer, P. Cheesman, J. Skilling, M. Modares, ...)
Non-Extensive Statistics
(C. Tsallis, J.S. Dehesa, ...)
Bayesian Cognitive and Neuroscience
(P.O. Amblard, Pierre Bessière ...)
Bayesian Robotics
(K.H. Knuth, P. Bessière, ...)

http://maxent2010.inrialpes.fr/

_______________________________
Dr Pierre Bessière - CNRS
*****************************
LIG Lab
INRIA
655 avenue de l'Europe
38334 Montbonnot
FRANCE

Mail: Pierre.Bessiere@...
Http://www.Bayesian-Programming.org
Tel:   +33 4 76 61 55 09
Skype: Pierre.Bessiere
_______________________________




http://Bayesian-Programming.org/spip.php?rubrique8





[Non-text portions of this message have been removed]

While working through Jaynes's book I compiled a list of what I believe
are (mostly minor) errors and misprints.  These are in addition to Kevin
Van Horn's list at http://ksvanhorn.com/bayes/jaynes/index.html
<http://ksvanhorn.com/bayes/jaynes/index.html>
For the References and Bibliography sections, however, I combined his
list of errors with mine for the convenience of having a single list for
these two sections.  The list has been uploaded as Errata.doc, and at
the same time I've updated the NameIndex.xls file.
Comments, corrections and suggestions for further entries are welcome.

Arnold Baise





[Non-text portions of this message have been removed]

30th International Workshop on

Bayesian Inference and Maximun Entropy

Methods in Science and Engineering

Chamonix, France, July 4-9, 2010

http://maxent2010.inrialpes.fr/

For 30 years the MaxEnt workshops have explored the use of Bayesian and Maximum
Entropy methods in scientific and engineering applications. All aspects of
probabilistic inference, such as techniques, applications and foundations, are
of interest. The workshop includes a one-day tutorial session, state-of-the-art
lectures, invited papers, contributed papers and poster presentations. Selected
papers by the program committee will be edited and published in a book.

Especially encouraged are papers whose content is novel, either as to approach
or area of application.

Abstracts (one page of about 400 words) of the proposed papers should be
submitted via this Web site by April 11, 2010 (midnight, GMT).

List of provisional topics and organizers:
--------------------------------------------------------------
History and axiomatic foundation of probability and Information theory
(K.H. Knuth, A. Caticha, J. Skilling, ...)
Bayesian inference in astronomy and astrophsics
(T. Loredo, S. Gull, ...)
Information geometry and information theory
(F. Barbaresco, H. Snoussi, P. Gibilisco, C. Rodriguez, )
Algorithms for Bayesian computation.
(A. Quinn, R. Fischer, ...)
Bayesian Computed Tomography: medical imaging
(Ch. Bouman, K. Sauer, E. Miller, J.M. Lina, ...)
Non parametric Bayesian methods and experimental design
(F. Bac, M. Jordan, Z. Ghahramani, E. Barat, ...)
Bayesian classification, clustering, pattern recognition, image segmentation
(J. Center, M. Jordan, ...)
Time series, spectral estimation. deconvolution and source separation.
(P.O. Amblard, Ch. Jutten, ...)
Information theory and quantum tomography.
(Ch. Benjaballah, C. Caves, A. Vourdas, ...)
Bayesian and maximum entropy inference in action: Industrial applications
(E. Mazer, P. Cheesman, J. Skilling, M. Modares, ...)
Non-Extensive Statistics
(C. Tsallis, J.S. Dehesa, ...)
Bayesian Cognitive and Neuroscience
(P.O. Amblard, Pierre Bessière ...)
Bayesian Robotics
(K.H. Knuth, P. Bessière, ...)

http://maxent2010.inrialpes.fr/
_______________________________
Dr Pierre Bessière - CNRS
*****************************
LIG Lab
INRIA
655 avenue de l'Europe
38334 Montbonnot
FRANCE

Mail: Pierre.Bessiere@...
Http://www.Bayesian-Programming.org
Tel:   +33 4 76 61 55 09
Skype: Pierre.Bessiere
_______________________________




http://Bayesian-Programming.org/spip.php?rubrique8





[Non-text portions of this message have been removed]

I'm working through Probability Theory with a colleague at work and we can't
settle on the right answer for Exercise 2.1. For those of you way past this one
it's basically, "Show how the product and sum rules can provide a general form
for P(C|A+B) or explain why it's not possible." I've tried every manipulation of
the rules and can't generalize it. However my colleague points out that a Venn
diagram shows that P(C|A+B) = P(C|A) + P(C|B) - P(C|AB). Can someone point out
what we're missing?

Thank you,
Troy

Hi Troy,

A Venn diagram does not show that - Venn diagrams partition the space of
proposition truth values (or random variables in traditional probability
theory) and these are on the _left_ of the conditional. They do not
partition the space of statements on which we can condition (on the right
of the conditional). Your colleague may be thinking of the traditional
Venn diagram for the sum rule, which is: P(A+B|I) = P(A|I) + P(B|I) - P(AB|I).

To get a general rule, are we allowed to replace A+B with ((A+B),I)?
(Otherwise one would end up conditioning on nothing, which is not allowed
in Jaynes's framework.) We then get:

P(C|(A+B),I) = P(C,(A+B)|I)/P(A+B|I)
              = [P(AC|I) + P(BC|I) - P(ABC|I)]/[P(A|I) + P(B|I) - P(AB|I)]

Is this the sort of answer you were looking for?

Regards,
Konrad

-------------------------------------
Dr Konrad Scheffler
Associate Professor, Computer Science
Dept of Mathematical Sciences
Stellenbosch University
http://www.cs.sun.ac.za/~kscheffler/
-------------------------------------

On Wed, 31 Mar 2010, troy.jackson92 wrote:

> I'm working through Probability Theory with a colleague at work and we
> can't settle on the right answer for Exercise 2.1. For those of you way
> past this one it's basically, "Show how the product and sum rules can
> provide a general form for P(C|A+B) or explain why it's not possible."
> I've tried every manipulation of the rules and can't generalize it.
> However my colleague points out that a Venn diagram shows that P(C|A+B)
> = P(C|A) + P(C|B) - P(C|AB). Can someone point out what we're missing?
>
> Thank you,
> Troy
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

As several conferences had very close dead-lines we received numerous demands
for a short dead-line extension:

The new dead-line is April 19th

30th International Workshop on

Bayesian Inference and Maximun Entropy

Methods in Science and Engineering

Chamonix, France, July 4-9, 2010

http://maxent2010.inrialpes.fr/

For 30 years the MaxEnt workshops have explored the use of Bayesian and Maximum
Entropy methods in scientific and engineering applications. All aspects of
probabilistic inference, such as techniques, applications and foundations, are
of interest. The workshop includes a one-day tutorial session, state-of-the-art
lectures, invited papers, contributed papers and poster presentations. Selected
papers by the program committee will be edited and published in a book.

Especially encouraged are papers whose content is novel, either as to approach
or area of application.

Abstracts (one page of about 400 words) of the proposed papers should be
submitted via this Web site by April 19, 2010 (midnight, GMT).

_______________________________
Dr Pierre Bessière - CNRS
*****************************
LIG Lab
INRIA
655 avenue de l'Europe
38334 Montbonnot
FRANCE

Mail: Pierre.Bessiere@...
Http://www.Bayesian-Programming.org
Tel:   +33 4 76 61 55 09
Skype: Pierre.Bessiere
_______________________________





[Non-text portions of this message have been removed]

I was recently looking over Jaynes resolution of Bertrand's paradox
using transformation groups (what a simple, beautiful idea!), and I
discovered what appears to be an inconsistency.

I'm troubled by equation 5 in "The Well Posed Problem"

http://bayes.wustl.edu/etj/articles/well.pdf

I don't have PTLOS in front of me, but this same equation appears
there in the same way.

This equation expresses the relationship between the probability
density for chord midpoints over a circle of radius R, f(r), and the
probability density for chord midpoints over a smaller circle of
radius aR, h(r). The equation is

a^2 h(ar) = f(r).

Jaynes goes on to plug this equation into a different relation, and
derives that f(r) must be a power law with the exponent not specified
by scale invariance. But equation 5 is already enough by itself to
determine not only that f(r) is a power law, but to establish what the
exponent is. You can verify that h(r) = c/r^2 obeys this functional
relationship. This can be derived as the only differentiable solution
by differentiating 5 with respect to a, setting a to 1, and solving
the resulting differential equation.

2a h(ar) + a^2 r h'(ar) = 0
h'(r) = -(2/r) h(r)
h(r) = c/r^2

There is only one linearly independent solution to a first order
linear differential equation, so this determines h(r) up to the
proportionality constant c (which we could get by normalization).

Now the troubling part is that this exponent (-2) disagrees with the
exponent we get from translation invariance (-1).

Can anyone shed some light on what is going on here? Am I missing
something about how to manipulate functional equations? Is equation 5
wrong, and if so, where was the mistake in the derivation? Or do scale
and translation invariance actually disagree, meaning that Bertrand's
problem does not have a unique solution after all?

What do you think?

Regards,
Jason W Merrill

I've compiled a Subject Index for Jaynes's book, and uploaded it as
SubjectIndex.xls.  I'd appreciate any suggestions for expanding or improving it.

Arnold Baise

The files I uploaded for this group (NameIndex, SubjectIndex and Errata)
are now available at my website  http://mysite.verizon.net/abaise/
<http://mysite.verizon.net/abaise/>  .

Arnold Baise



[Non-text portions of this message have been removed]

It's something like - "Philosophers can say anything they want, because they
don't have to get anything right."

Anyone know where Jaynes said that? I'm pretty sure it was Jaynes.

It's on page 144 of Jaynes's book:  "Philosophers are free to do whatever they
please, because they don't have to do anything right".

Arnold   




[Non-text portions of this message have been removed]

Jaynes was quoting a colleague:

*"Philosophers are free to do whatever they please, because they don't have
to do anything right."*

Probability Theory <http://books.google.com/books?id=tTN4HuUNXjgC&pg=PA144>,
E. T. Jaynes (quoting a colleague)

*
*

Malcolm Dean
Research Affiliate, Human Complex Systems, UCLA
http://intersci.ss.uci.edu/wiki/index.php/Malcolm_Dean
Member, Higher Cognitive Affinity Group, BRI
http://www.bri.ucla.edu/bri_research/Higher_cog.asp


On Wed, Jun 30, 2010 at 11:04, Arnold Baise <aibaise@...> wrote:

>
>
> It's on page 144 of Jaynes's book:  "Philosophers are free to do whatever
> they please, because they don't have to do anything right".
>
> Arnold
>
> [Non-text portions of this message have been removed]
>
>
>


[Non-text portions of this message have been removed]

Hi all,

I'm self-studying the book and trying to solve exercise 3.2, but no luck so far.

I tried to expand P(A1A2...Ak) by product rule(A1 means color 1 is drawn at
least once), but i dont know how to get P(Aj|A1A2...Aj-1), can anyone tell me
the answer or point to me a correct direction.

original problem:

Suppose an urn contains N = SIGMA(Ni) balls, N1 of color 1, N2 of
color
2, . . . , Nk of color k. We draw m balls without replacement; what is
the probability
that we have at least one of each color? Supposing k = 5, all Ni = 10,
how many do
we need to draw in order to have at least a 90% probability for
getting a full set?

A simple example can help in seeing a solution to this problem.  Suppose we have
just two colors, red and white, and proposition R states at least one red ball
is drawn, and W states at least one white ball is drawn.  Let R´ be the negation
of R, i.e. no red ball is drawn.  Now P(RW) + P(RW)´ = 1, and we also have
      P(RW)´ = P(R´ + W´)                   by de Morgan's law
             = P(R´) + P(W´) – P(R´W´)      by the addition law
Since for two colors P(R´W´) is zero, it follows that
       P(RW) = 1 – P(R´) – P(W´)
Using given parameters N, m etc., it's possible to calculate P(R´) and P(W´),
and hence P(RW).

For three colors, say red, white and blue, the general addition law gives
     P(RWB)´ =  P(R´) + P(W´) + P(B´) – P(R´W´) – P(R´B´)
	        – P(W´B´) + P(R´W´B´)
with P(R´W´B´) again zero.  This indicates the extension needed to handle k
colors.

For the problem given with k = 5, it's possible to set up the equation for five
colors and then estimate the correct value of m.  Rather than do that, I wrote a
program (using the R language) that simulates a random selection without
replacement.  By varying m I found that m = 14 gave an 88% chance of a full set,
and m = 15 gave 91%.  So m = 15 looks like the correct answer.



--- In etjaynesstudy@yahoogroups.com, "andy.wu_901" <andy.wu_901@...> wrote:
>
> Hi all,
>
> I'm self-studying the book and trying to solve exercise 3.2, but no luck so
far.
>
> I tried to expand P(A1A2...Ak) by product rule(A1 means color 1 is drawn at
least once), but i dont know how to get P(Aj|A1A2...Aj-1), can anyone tell me
the answer or point to me a correct direction.
>
> original problem:
>
> Suppose an urn contains N = SIGMA(Ni) balls, N1 of color 1, N2 of
> color
> 2, . . . , Nk of color k. We draw m balls without replacement; what is
> the probability
> that we have at least one of each color? Supposing k = 5, all Ni = 10,
> how many do
> we need to draw in order to have at least a 90% probability for
> getting a full set?
>

Hi Jason,

This is probably a longer delayed response than you were hoping for, but
better late than never I guess. A caveat: please don't assume that I know
what I'm talking about here, I'm only working through the derivations for
the first time myself.

The issue is not just that you get a specific exponent while Jaynes gets a
more general form. Your solution corresponds to q=0 in Jaynes's notation,
which is explicitly disallowed (and would anyway give a coefficient of 0).
The two answers are incompatible.

The problem is that, if f(r) is a function only of r (as defined),
h(r) is a function of both r and a (as can be seen from eq 4). So it would
be more correct to write h(r,a) instead of h(r).

Alternatively (perhaps a clearer explanation from the point of view of
your derivation), one could have started by defining h(r) as a function
only of r, and then eq 4 would show that f(r) is a function of both r and
a - so that when you take the derivative df/da the answer is not zero. You
cannot get this derivative without using eq 4.

Hope this helps, and thanks for an interesting question.
Konrad

-------------------------------------
Dr Konrad Scheffler
Associate Professor, Computer Science
Dept of Mathematical Sciences
Stellenbosch University
http://www.cs.sun.ac.za/~kscheffler/
-------------------------------------

On Tue, 20 Apr 2010, Jason Merrill wrote:

> I was recently looking over Jaynes resolution of Bertrand's paradox
> using transformation groups (what a simple, beautiful idea!), and I
> discovered what appears to be an inconsistency.
>
> I'm troubled by equation 5 in "The Well Posed Problem"
>
> http://bayes.wustl.edu/etj/articles/well.pdf
>
> I don't have PTLOS in front of me, but this same equation appears
> there in the same way.
>
> This equation expresses the relationship between the probability
> density for chord midpoints over a circle of radius R, f(r), and the
> probability density for chord midpoints over a smaller circle of
> radius aR, h(r). The equation is
>
> a^2 h(ar) = f(r).
>
> Jaynes goes on to plug this equation into a different relation, and
> derives that f(r) must be a power law with the exponent not specified
> by scale invariance. But equation 5 is already enough by itself to
> determine not only that f(r) is a power law, but to establish what the
> exponent is. You can verify that h(r) = c/r^2 obeys this functional
> relationship. This can be derived as the only differentiable solution
> by differentiating 5 with respect to a, setting a to 1, and solving
> the resulting differential equation.
>
> 2a h(ar) + a^2 r h'(ar) = 0
> h'(r) = -(2/r) h(r)
> h(r) = c/r^2
>
> There is only one linearly independent solution to a first order
> linear differential equation, so this determines h(r) up to the
> proportionality constant c (which we could get by normalization).
>
> Now the troubling part is that this exponent (-2) disagrees with the
> exponent we get from translation invariance (-1).
>
> Can anyone shed some light on what is going on here? Am I missing
> something about how to manipulate functional equations? Is equation 5
> wrong, and if so, where was the mistake in the derivation? Or do scale
> and translation invariance actually disagree, meaning that Bertrand's
> problem does not have a unique solution after all?
>
> What do you think?
>
> Regards,
> Jason W Merrill

I've uploaded a file (Reviews.doc) that lists reviews of  two of
Jaynes's books:  Probability Theory: The Logic of Science, and Papers on
Probability, Statistics and Statistical Physics.

I've provided links to those reviews that are available without
subscription on the internet.

Arnold Baise



[Non-text portions of this message have been removed]

Re Eq 9.48 and 9.49, I see why

log(W)/(nH) --> 1, but it doesn't follow that we can exponentiate

numerator and denominator to get

W/exp(nH) --> 1.

The problem is an annoying root(2 pi n) that appears in the
Stirling approximation for the factorial...

I've also worked some examples that imply that the convergence
9.49 does not hold.

Does anyone have details on the derivation from 9.48 to 9.49?

Thanks.

If you write log{sqrt(2 pi n)} as (1/2){log(2 pi) + log(n)}, then you
can rearrange to get a term (n + 1/2)log(n).  For large n this
becomes nlog(n), so that log(n factorial) becomes essentially
nlog(n) - n for large n, which allows derivation of 9.49.

Arnold Baise



--- In etjaynesstudy@yahoogroups.com, "jamespale" <jamespale@...> wrote:
>
> Re Eq 9.48 and 9.49, I see why
>
> log(W)/(nH) --> 1, but it doesn't follow that we can exponentiate
>
> numerator and denominator to get
>
> W/exp(nH) --> 1.
>
> The problem is an annoying root(2 pi n) that appears in the
> Stirling approximation for the factorial...
>
> I've also worked some examples that imply that the convergence
> 9.49 does not hold.
>
> Does anyone have details on the derivation from 9.48 to 9.49?
>
> Thanks.
>

Hello ,
  I am reading the book Probability: Logic of Science. I have a doubt on one of
the concept in the book, I want to get some insight which is lacking. If you
can, do reply,

Chap:19 in the COMMENTS section:
Solving for an overdetermined set of equations, Jaynes says that if we have n
variables to be estimated, from N equation,N>n. Each linear equation is a
measurement coming from a different experiment and with a different accuracy.
Now the solution will be linear combination of all the equations.
According to the comment:If we have 3 equations and two unknown and out of the 3
experiments whose output is represented by the 3 equations one experiment is
assumed to be completely accurate. Now if we solve using only two equations out
of the 3 equations.Then the solution is more accurate if we take equation which
have equal accuracy as compared to combination of equations which is completely
accurate with a less accurate equation.

Thanking you,
Regards,
Neeraj

Does anyone have any references for Jayne's opinion on the Many Worlds
Interpretation of quantum theory?

On Sun, Apr 29, 2012 at 7:23 PM, Daniel <buybuydandavis@...> wrote:
> Does anyone have any references for Jayne's opinion on the Many Worlds
Interpretation of quantum theory?

If anyone has access to _The Everett Interpretation of Quantum
Mechanics: Collected Works 1955-1980_, ch18 would be worth checking:
http://lesswrong.com/lw/c3g/seq_rerun_quantum_nonrealism/6h7e

--
gwern
http://www.gwern.net

The correspondence mentioned is available online.
http://ucispace.lib.uci.edu/handle/10575/1158 


They seem to be talking more about Jaynes work in probability theory and
statistical mechanics. Didn't see relevant comments on quantum theory, but
mainly scanned the docs. 

Given Jayne's interest in the foundations of quantum theory, it seems extremely
unlikely to me that he was unaware of MWI. I've read most of his papers since
around 1980, and can't recall a mention anywhere. Surely he was aware, and
surely he had an opinion. 

Buy Buy - Dan Davis



>________________________________
> From: Gwern Branwen <gwern0@...>
>To: etjaynesstudy@yahoogroups.com
>Sent: Sunday, April 29, 2012 4:45 PM
>Subject: Re: [etjaynesstudy] Jaynes on MWI?
>
>On Sun, Apr 29, 2012 at 7:23 PM, Daniel <buybuydandavis@...> wrote:
>> Does anyone have any references for Jayne's opinion on the Many Worlds
Interpretation of quantum theory?
>
>If anyone has access to _The Everett Interpretation of Quantum
>Mechanics: Collected Works 1955-1980_, ch18 would be worth checking:
>http://lesswrong.com/lw/c3g/seq_rerun_quantum_nonrealism/6h7e
>
>--
>gwern
>http://www.gwern.net
>
>
>------------------------------------
>
>Yahoo! Groups Links
>
>
>
>
>
>

[Non-text portions of this message have been removed]