why is probability and statistics a hard subject?
Nasser Abbasi
of upper division / first year graduate.
This is the hardest course I have ever taken so far, Yet, I am not sure why
it is hard.
Looking at the math on its own, it is hard, but manageable, upper level
calculus I would say. But for some reason, I find the whole subject hard to
do well at.
May be it requires more experience? more insight? more problem solving
practice? I do not think it is the math skills which is the problem, I think
there is something inherently hard about solving problems in probability and
statistics, which is hard for me to pint point.
I was wondering if others have felt the same way about this subject. And if
you have, did it become easy for you later on? and how did this happen?
Nasser
Paige Miller
Nasser, I don't know you personally, and so I don't know what is in
your brain that makes it hard. But you are not alone. Many people
simply don't get it. I suppose its really no different than people who
don't understand high school geometry, there are many of those people
as well, and it may seem trite to say that some subjects "either you
understand it or you don't", but that is my experience. Some subjects
just don't click with some students ... there are other subjects that
I have trouble understanding and putting into practice.
Another problem I have found, and this may or may not be the case for
you, is that some statistics courses are poorly taught. When I was in
college, the statistics classes were sometimes taught by people who
were not trained in statistics. This results in a situation where
students find it is difficult to learn. A colleague of mine (not a
statistician) once said that statistics was the most poorly taught
class in her entire college experience. Certainly not all classes are
poorly taught, but some undoubtedly are.
The last issue might be your mathematical background. Since you say
the math is manageable, then maybe that's not your problem, but some
people enter statistics courses with a poor handle on the relevant
mathematics, and those people will have a very difficult time
understanding and using statistics.
--
Paige Miller
paige\dot\miller \at\ kodak\dot\com
Gus Gassmann
>
> - Show quoted text -
I think there is more to it, yet. I teach a stats course to business
students. Mathematically inclined students are often intimidated by
the fact that there are no absolute answers. ("What do you mean, you
are 95% confident. Don't you know for sure?") Not so mathematically
inclined students get lost when I have to explain to them that there
are several "means" and that the sample mean can have an expected
value. To try to get them to understand that z = (x - E(x))/s(x) is a
universal formula with multiple applications is a lost cause. They try
to memorize a different standardization formula for seventeen special
cases, which they invariably do not recognize properly. I believe
statistics is inherently difficult. The philosophy behind a hypothesis
test, for instance, is quite sophisticated.
Old Mac User
Regardless of the course title, "statistics" is taught in diverse ways
by diverse people in diverse environments. A non-statistician
teaching "statistics" in an engineering department will almost
certainly teach in a fashion that's very different from another non-
statistician who lives in a social sciences environment or medical
environment. To make matters worse, some teach from the viewpoint
"here's some great software... now I'll show you how to use it. As one
poster has rightly said, hypothesis testing rests upon some deep
concepts. In the hands of a skilled instructor, most people can "get
it". Taught by an amateur it turns into a bunch of equations, rules,
and "be careful of this" footnotes.
As a rough overview (and I know that all will not agree with this" the
"statistics story" usually follows this path. (1) Tell me what
physical system you are working with (cards, dice, colored balls in an
urn, etc.) and I'll tell you the probability of the occurrence of
certain events. Then a sudden switch to (2)... give me some data and
how it came to be and I'll tell you the probability that those data
came from a certain circumstance. That circumstance is usually founded
on "the null hypothesis" (an expression I have not used in the past
50+ years of teaching!! There are better ways to say it.). Oftentimes
the instructor moves from (1) to (2) without a clear warning that a
major change in happening at this point.
Go to "Is Statistics Hard?" http://www.tufts.edu/~gdallal/hard.htm
for a more professional comment on this. OMU
Kenneth M. Lin
"Nasser Abbasi" <n...@12000.org> wrote in message
news:sEyYi.940$ck5...@newsfe09.phx...
non-statisticians that emphasize "plugging in numbers into the formulas"
without any insight into why. Looking back, I was shocked at how much I
struggled with simple probability problems because the teachers failed to
explain even simple concepts such as independent events.
When I was a teaching assistant I was reprimanded for suggesting that the
students read the textbook and the department sided with the lecturer.
Robert Dodier
> The philosophy behind a hypothesis test, for instance,
> is quite sophisticated.
Yet the sophistication is beside the point.
The difficulty of hypothesis testing is entirely an
artifact of its authors (Fisher, Neyman, etc) having
thrown out the machinery that would make it comprehensible.
One can succeed at it, but it is more than a little like
riding a bicycle backwards, or walking 1000 miles while
balancing an egg on one's head.
Robert Dodier
Herman Rubin
Nasser Abbasi <n...@12000.org> wrote:
>I am taking a course in probability and statistics now. It is at the level
>of upper division / first year graduate.
>This is the hardest course I have ever taken so far, Yet, I am not sure why
>it is hard.
>Looking at the math on its own, it is hard, but manageable, upper level
>calculus I would say. But for some reason, I find the whole subject hard to
>do well at.
>May be it requires more experience? more insight? more problem solving
>practice? I do not think it is the math skills which is the problem, I think
>there is something inherently hard about solving problems in probability and
>statistics, which is hard for me to pint point.
Knowing how to calculate solutions of formulated
problems is the least important part of both the
mathematics and probability aspects. It is
understanding the concepts.
Do you understand what limit is, what derivative
is, what integral is (NOT the inverse of derivative)?
Being able to produce the definition is not enough;
one needs to be able to use the concepts in situations
which have not been taught.
The same holds for probability; it does not start with
relative frequency, or with binomial coefficients, or
with the consideration of equally likely events.
Try to understand the ideas, not memorize formulas and
guess which one to use.
>I was wondering if others have felt the same way about this subject. And if
>you have, did it become easy for you later on? and how did this happen?
>Nasser
--
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
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
Robert Dodier
> give me some data and how it came to be and I'll
> tell you the probability that those data came from
> a certain circumstance.
It is quite revealing that you have stated a general
problem in terms of a quantity ("the probability that
those data came from a certain circumstance") which
does not exist, according to conventional frequentism.
Everybody is really a Bayesian, even you.
> Go to "Is Statistics Hard?"
> http://www.tufts.edu/~gdallal/hard.htm
> for a more professional comment on this.
A classic statement of the needlessly convoluted logic
surrounding hypothesis tests. It's useful to read it,
if only to know what to steer away from.
Robert Dodier
Old Mac User
This...
> give me some data and how it came to be and I'll
> tell you the probability that those data came from
> a certain circumstance.
was really an unfortunate choice of words... my fault.
Better... but still imperfect... "give me some data and how it came to
be
and I'll tell you those data did not come from certain
circumstances... with
probabilities attached thereto.
Richard Ulrich
wrote:
> I am taking a course in probability and statistics now. It is at the level
> of upper division / first year graduate.
>
> This is the hardest course I have ever taken so far, Yet, I am not sure why
> it is hard.
>
> Looking at the math on its own, it is hard, but manageable, upper level
> calculus I would say. But for some reason, I find the whole subject hard to
> do well at.
>
> May be it requires more experience? more insight? more problem solving
> practice? I do not think it is the math skills which is the problem, I think
> there is something inherently hard about solving problems in probability and
> statistics, which is hard for me to pint point.
Like some other repliers, I suspect that your teacher is not
a thoroughly "good statistician", or you would not feel this way.
One of the basics is to learn the vocabulary. Are you paying
close attention to definitions?
For a different sort of introduction to the "problem solving,"
maybe you could take a look at S. Siegel's 1956 book on
Nonparametric Statistics. (After 30 years, a newer edition
came out, with a co-author; but you don't need the newer
version for this exercise). The book does not touch the calculus
part, I think. It is organized as a "cookbook" of problems
with so-many groups; and dichotomous or ranked data,
which may or may not be "matched data."
It will introduce you to much vocabulary, and might provide
a substantial framework.
Another suggestion, for figuring out "what's it all about" - find
SM Stigler's books on the history of statistics, like "History of
Statistics. The measurement of uncertainty before 1900."
>
> I was wondering if others have felt the same way about this subject. And if
> you have, did it become easy for you later on? and how did this happen?
>
I know that I was interested in research results before I ever
learned much statistics. So, what I was learning seemed useful.
I also discovered, along the way, that when I could not follow
a particular textbook, it might help a LOT to find a similar book
(same shelf in the library) and browse it, for an alternate
introduction.
If you don't know how these results are ever used, it might
also be helpful to find a book like "Readings in Statistics in XXX",
for whatever XXX is your field.
--
Rich Ulrich, wpi...@pitt.edu
http://www.pitt.edu/~wpilib/index.html
Nasser Abbasi
"Richard Ulrich" <Rich....@comcast.net> wrote in message
news:kqm7j355u5esbdgn0...@4ax.com...
>
> Like some other repliers, I suspect that your teacher is not
> a thoroughly "good statistician", or you would not feel this way.
>
Actually my professor is distinguished in the field of probability and
statistics. He is a known expert in this field with many scientific
publications. I myself just find the subject more slippery than other
subjects. I think probability and statistics simply requires more time to
sink in than any other subject. This subject simply requires more experience
and practice to become good at it, or it may be simply that I was not born
to be a statistician. I think people who are really good at this must have
their brains wired differently than the rest of us :)
> One of the basics is to learn the vocabulary. Are you paying
> close attention to definitions?
>
I try to, but more diagrams and pictures would help. Our textbook does not
have too many of these.
> For a different sort of introduction to the "problem solving,"
> maybe you could take a look at S. Siegel's 1956 book on
> Nonparametric Statistics. (After 30 years, a newer edition
> came out, with a co-author; but you don't need the newer
> version for this exercise). The book does not touch the calculus
> part, I think. It is organized as a "cookbook" of problems
> with so-many groups; and dichotomous or ranked data,
> which may or may not be "matched data."
>
> It will introduce you to much vocabulary, and might provide
> a substantial framework.
>
Ok, I'll look it up. I just ordered a book called "Applied Statistics
Algorithms by P. Griffiths " here is the amazon link
http://www.amazon.com/gp/product/0130379875/002-5270856-0528819
I like to see algorithms of things. It helps me to understand something when
I see the steps needed to solve it. My brain is more mechanical in a way.
> Another suggestion, for figuring out "what's it all about" - find
> SM Stigler's books on the history of statistics, like "History of
> Statistics. The measurement of uncertainty before 1900."
>
ok, thanks, I'll try to look it up also.
Nasser
who has too many books and too little time to read them all.
st...@mimosa.csv.warwick.ac.uk
In article <aMRYi.5101$4k....@newsfe11.phx> you write:
>...
>Actually my professor is distinguished in the field of probability and
>statistics. He is a known expert in this field with many scientific
>publications. I myself just find the subject more slippery than other
>subjects. I think probability and statistics simply requires more time to
>sink in than any other subject. This subject simply requires more experience
>and practice to become good at it, or it may be simply that I was not born
>to be a statistician. I think people who are really good at this must have
>their brains wired differently than the rest of us :)
The logic & concepts underlying "statistics" ARE slippery,
and may take a while to sink in. As an undergraduate,
I understood statistics much better six months after the lectures,
even without studying the notes in the interim. You'll need to:
1) Understand the concepts of independence & conditional independence.
2) Distinguish carefully between what is known & what isn't
(it may help to write unknown quantities in capitals & the
corresponding known/observed/assumed values in lower case).
3) Understand "likelihood" as a measure of compatibility between
observed data & possible parameter values.
I'll try to help...
In mathematics, you start with some axioms (e.g. for Euclidean geometry),
create an ideal universe based on the axioms, and explore this universe
using deduction to prove things like Pythagoras' theorem. Results
from this ideal universe can often be usefully applied to the real world
- for example, to ensure that the corners of the Great Pyramid are
(to all intents & purposes) right angles.
With probability theory, real-world applications are less clear cut
- e.g. what exactly does it mean to say that a coin is "fair"?
Real-world probability is IMHO (and in e.g. Renyi's opinion)
a way to quantify my lack of knowledge about a situation,
rather than being an inherent property of nature.
Any fool can see whether the corners of a pyramid are right angles,
but different fools can quite reasonably have very different
probabilities for the same event :-) - e.g. the result of a tennis match
(witness recent press reports of "strange betting patterns").
With statistical inference, it's still less clear cut
- you observe data and use induction (not deduction)
to infer how the data might have arisen.
Even words like "independence" are misleading. All probabilities are
in practice conditional (on your assumptions, background knowledge etc.),
so everything related to probability is also conditional. The results
of two successive coin tosses are NOT independent: they are only
CONDITIONALLY independent - conditional on your knowing the "true"
probability p of a head (whatever "true" probability means!)
But then you wouldn't be trying to estimate p experimentally anyway.
In practice, if your first toss results in a head, this makes it more
reasonable that the coin is biased towards heads than tails,
so your probability p for heads increases.
Google for "Sally Clark" to see the practical importance of all this.
If you want some mathematical background, Google for "exchangeability".
A natural way to bring mathematical rigour into statistics is
"likelihood" (it may help to draw pictures). Start with the
"sample space" of possible data (e.g. X=no of heads out of 10 tosses).
Think of possible probability models that could give rise to the data.
You might then make reasonable simplifying assumptions such as
"identically distributed", "(conditional) independence" etc.
This typically leads you to consider a family of probability models
corresponding to different possible values of a "parameter"
lying in a "parameter space", e.g. Binomial(n,P) where n=10,
P is the parameter, and P lies in the parameter space [0,1].
If you fix the parameter value P=p this means you fix the probability
distribution for X. For example, if P=p=0.9 then Pr(X=x|P=p)
is Binomial(10,0.9), so that observing X=x=9 is perfectly reasonable,
X=x=4 is surprising, and X=x=0 is astounding (but still possible).
So the points (p=0.9) and (x=9) are highly compatible,
(p=0.9) and (x=4) less so, and (p=0.9) & (x=0) are fairly incompatible.
Similarly any given point p in the parameter space
will typically be compatible with some points x in the sample space
but much less compatible with others.
The measure of compatibility is Pr(X=x|P=p).
However, for statistical inference, probability models are
"the wrong way round". It's not the case that you know P=p
and are directly interested in possible values X=x; instead
you know the data X=x, and want to compare possible values p for P.
If we now think of Pr(X=x|P=p) as just a formula involving x & p,
and fix x, then it becomes a function just of p, called the likelihood
Lik(p;x), and still represents a measure of compatibility between
possible p and the (now fixed) x. If Lik(p;x) is low, this means that
if that were the "true" p, then the data x would have been surprising
- so that particular p has low compatibility with the observed x.
Note that likelihood is very different from probability - for example,
Lik(p;x) does not integrate/sum to 1 over the parameter space.
There are various approaches to statistical inference,
but if you can get an understanding of "likelihood"
then you have a good starting point. Formulae are secondary.
>
>> One of the basics is to learn the vocabulary. Are you paying
>> close attention to definitions?
>>
>
>I try to, but more diagrams and pictures would help. Our textbook does not
>have too many of these.
What textbook is it?
There are several good articles on Wikipedia - start browsing from
http://en.wikipedia.org/wiki/Statistics
>...
>Ok, I'll look it up. I just ordered a book called "Applied Statistics
>Algorithms by P. Griffiths " here is the amazon link
>http://www.amazon.com/gp/product/0130379875/002-5270856-0528819
That's a good book, but in statistics the algorithms will generally
not help anyone understand the concepts - e.g. the usual methods of
approximating the inverse Normal CDF (piecewise rational polynomials)
have nothing to do with the nature or use of the inverse Normal CDF!
>
>I like to see algorithms of things. It helps me to understand something when
>I see the steps needed to solve it. My brain is more mechanical in a way.
>
>> Another suggestion, for figuring out "what's it all about" - find
>> SM Stigler's books on the history of statistics, like "History of
>> Statistics. The measurement of uncertainty before 1900."
>>
>
>ok, thanks, I'll try to look it up also.
>
>Nasser
>who has too many books and too little time to read them all.
>
Good luck! -- Ewart Shaw
--
J.E.H.Shaw [Ewart Shaw] st...@uk.ac.warwick TEL: +44 2476 523069
Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
http://www.warwick.ac.uk/statsdept http://www.ewartshaw.co.uk
3 ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@|:"2^:2))&.>@]^:(i.@[) <#:3 6 2
bm...@scn.org
This is excellent advice for any course in science or engineering.
Different texts use different words and sometimes simply reading
something presented two different ways allows it to sink in. Plus
part of learning is repetition. Read something in three books and you
have to read it and think about it three times. When I was a student
I noticed the more sources I read on a topic the more I learned about
and understood the topic. I have also noticed, with age, that when I
used multiple sources the stuff stuck with me whereas when I used only
one source because the concepts were so simple they did not stick
nearly as well. After all, if muliple sources were not important why
would we even need teachers? Just reading the book would be
adequate. It is clear teachers do more then simply set the pace. I
have also noticed you can skip the teacher nicely providing you use
multiple books. Some books and some teachers simply do not click with
some students. The only solution is to find other books. I will also
grant that some people have a wiring problem in their brain that makes
some subjects very, very hard. The solution to that problem is to
find a different major that does not need the impossible subject and
is compatible with the wiring.
S. F. Thomas
(( cuts ))
> Different texts use different words and sometimes simply reading
> something presented two different ways allows it to sink in. Plus
> part of learning is repetition. Read something in three books and you
> have to read it and think about it three times. When I was a student
> I noticed the more sources I read on a topic the more I learned about
> and understood the topic. I have also noticed, with age, that when I
> used multiple sources the stuff stuck with me whereas when I used only
> one source because the concepts were so simple they did not stick
> nearly as well. After all, if muliple sources were not important why
> would we even need teachers? Just reading the book would be
> adequate. It is clear teachers do more then simply set the pace. I
> have also noticed you can skip the teacher nicely providing you use
> multiple books. Some books and some teachers simply do not click with
> some students. The only solution is to find other books. I will also
> grant that some people have a wiring problem in their brain that makes
> some subjects very, very hard. The solution to that problem is to
> find a different major that does not need the impossible subject and
> is compatible with the wiring.
>
These are very useful observations, with which I concur. I would add
that it is very useful to go back to the original sources. I agree with
the poster that says statistics IS hard. That is why the statisticians
disagree amongst themselves. Nobody disagrees at the level of the
technical mathematics, mind you; rather it's at the level of core,
foundational concepts that the disagreements set in.
In my case, I learned so-called classical statistics (Neyman-Pearson) as
an undergraduate engineer. Then as a graduate student, I got introduced
to Bayesian statistics. I was totally impressed, because it promised to
make statistical life a lot simpler. It rather boldly postulated that
the unknown parameters could be treated exactly as random variables, and
the frequency model could be understood now as a conditional pdf, given
the parameter-considered-as-random-variable. But then I at some point
read Rev. Thomas Bayes' original 18th (?) century article, only to find
that he expressed grave misgivings back then.
Then I came across the book "Foundations of Statistical Inference: A
Symposium" by Godambe and Sprott (eds.) (1971). It was then I realized
that statistics as a discipline rested on rather shaky foundations, for
the classicists and Bayesians could not agree with each other. If the
respective exponents could not agree amongst themselves, it should be no
wonder that students find the subject hard. By all means we can all
follow cookbook recipes, but at a level of deep and true understanding,
it is perhaps another matter.
Somewhere along the line I read R. A. Fisher (1951), "Statistical
Methods and Scientific Inference", and A. W. F. Edwards, "Likelihood"
(1972). It is from these that I fully came to appreciate that the
_entire_ inferential import of any experiment, given any proposed model,
is wholly contained within the likelihood function. That is the core
kernel about which all agree. The only problem was that there was no
likelihood calculus to evaluate composite hypotheses, and thus to
perform marginalization, except by a simple rule of maximization. Fisher
famously said, the likelihood of w1 or w2 is like the income of Peter or
Paul, we don't know what it is until we know which is meant. He was then
led to maximization rules, which threw up a stream of paradoxes,
especially in the case of multi-parammeter problems. It is that central
difficulty that in my opinion lies at the root of the bifurcation of the
discipline into the classical and Bayesian schools.
The Bayesians cut through the Gordian knot by, in effect, elevating the
likelihood function to the status of a probability density function.
From this position it becomes a simple matter to evaluate composite
hypotheses and perform marginalization to eliminate nuisance parameters
in multi-parameter problems -- the simple expedient is a rule of
integration for the evaluation of composite hypotheses and of
marginalization. The paradoxes engendered by likelihood marginalization
go away.
The classicists remained cautious, rejecting the Bayesian expedient of
considering the unknown parameters of frequentist models to be random
variables, certainly not of the frequentist sort, and even not of a
subjective belief sort. Hence their indirect and long-winded "solutions"
to the problem of inference, which in a familiar example may be stated
thusly: IF one were to perform an experiment an infinite number of
times, then a confidence interval based on the experimental data and
constructed in a certain well-defined way, would contain the value of
the true parameter, whatever it is, 95% of the time. Thus inferential
statements require appeal to a long series of experiments that have not
been, and will never be performed.
Edwards would simply say: look at the likelihood! All would agree that
this is good advice for a one- or two-parameter problem, but totally
useless otherwise.
Anyway, then I encountered Zadeh's fuzzy set theory, which made a lot of
sense up to a point. I realized that probabilities could be fuzzy: I
considered the thought-experiment: If a friend fabricated an entirely
new thumb-tack, never before seen or used anywhere, with an entirely new
geometry. Contemplating this thumb-tack, one asks, what is the
probability that it would land top down if tossed. One looks at its
geometry, its weight distribution etc. and one is prepared to assert,
before-hand, that it would do so with a "high" probability. Now you toss
it and observe a result. What should be your new estimate of the
probability of it landing top down, on another throw?
Or consider this example due to Zadeh. Given the statement, "most Swedes
are tall", and an assumed Gaussian model with mean mu and standard
deviation sigma, what is the fuzzy range of values allowed for mu and
sigma consistent with the statement. How would a classical exponent
solve such a problem? How would a Bayesian exponent? How would a fuzzy
exponent, who at the time were insisting rather dogmatically that
fuzziness had nothing at all to do with probability.
Anyway, to cut a long story short, I found I could find a way to resolve
all these various views of the matter. The classicists are right that
the unknown model parameters are in no sense a random variable. The
Bayesians are right that we should be able to characterize the
uncertainty directly and marginalize, perform changes of variable
necessary to support decision action, etc. etc. The likelihood people
are right that the likelihood function contains the entire inferential
content of any statistical experiment. And the fuzzicists are right that
our probabilities may be essentially fuzzy, and therefore that our model
parameters may be essentially fuzzy also. In effect, the likelihood
function and the likelihood semantics define a kind of fuzzy set, and
certainly a kind of possibility distribution deriving from a fuzzy set.
The fuzzy-set semantics allows for a way to manipulate likelihood that
Fisher and Edwards could not have imagined, and that addresses the core
Bayesian concern of direct manipulability. There are lots of other
implications besides, new vistas that open up, and old vistas that need
to be looked at again with fresh eyes. Anyway, it's all very exciting
stuff, see my S. F Thomas, "Fuzziness and Probability" (1995).
If it answers anything, it is the OP's question, "is statistics hard?".
The answer is yes, obviously, since the exponents, for good reason, have
not been able to agree amongst themselves. However, that said, I now
believe that if we go back to basics -- what is a phenomenon, what is a
model of a phenomenon, what is probability, what is a probability model,
what is measurement, is it better to have fuzzy measurement as the
general case, from which point measurement is a special approximation,
or to have point measurement as the general case, from which we may
fuzzify or statistify as necessary, what is an instance of a phenomenon,
how is a statistical distribution over the extension set of a phenomenon
defined with reference to a probability model, does limited sample data
lead to fuzzy uncertainty in model parameters, etc. etc. -- we may,
perhaps paradoxically, render statistics less hard, perhaps even easy.
In other words, I am saying that statistics is hard because not enough
attention has been paid to the foundations, and huge superstructures
have been built on what are in my opinion still shaky foundations. So
often, at a deep level, the teachers will not know really what they're
talking about, although at a cookbook level they may be entirely well
enough trained (sic). In such a situation, the student who seeks a deep
understanding, as Nasser obviously does, will find it hard. Possibly
there is a problem with the brain-wiring, but that I rather doubt.
Be all that as it may, the classical paradigm is so entrenched, Bayesian
protestations and assaults notwithstanding, it is likely that Nasser's
grand-children would again be asking the same question that Nasser is
now asking.
Regards,
S. F. Thomas
Nasser Abbasi
<st...@mimosa.csv.warwick.ac.uk> wrote in message
news:fh1q3k$1s0$1...@wisteria.csv.warwick.ac.uk...
> Hi Nasser! [old chess opponent]
>
<cut> very good stuff which I'll make sure I read again.
>
> What textbook is it?
>
our textbook is
Statistical analysis by John Rice. It is a good text, but I think a bit too
dry for me at my level.
> There are several good articles on Wikipedia - start browsing from
> http://en.wikipedia.org/wiki/Statistics
>
I do make use of Wikipedia stuff all the time. very useful.
> Good luck! -- Ewart Shaw
>
> --
> J.E.H.Shaw [Ewart Shaw] st...@uk.ac.warwick TEL: +44 2476 523069
> Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
> http://www.warwick.ac.uk/statsdept http://www.ewartshaw.co.uk
> 3 ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@|:"2^:2))&.>@]^:(i.@[) <#:3 6 2
Thanks again.
ps. here is our famous chess game, I digged it up from my chess book. I see
that you beat me in this game. So you are good in chess and statistics also
:)
London Congress, England. July 30 1976
Round 2, Board 75
W: Nasser Abbasi, Black Shaw,J.E.H
1.e4 c5 2.Nf3 d6 3.g3 Nc6 4.Bg2 g6 5.0-0 Bg7 6.d3 Qc7 7.Nc3 e6 8.Nb5
Qb8 9.Bf4 e5 10.Bg5 a6 11.Nc3 h6 12.Be3 Nge7 13.a4 b6 14.Ne1 0-0 15.f4 Qc7
16.Nd5 Nxd5 17.exd5 Nd4 18.fxe5 Rb8 19.exd6 Qxd6 20.Bf4 Be5 21.c3 Nf5
22.Bxe5 Qxe5 23.Nc2 Bd7 24.Qf3 Qd6 25.b3 Rbe8 26.Rae1 b5 27.axb5 axb5
28.Rxe8 Bxe8 29.Ne3 Nxe3 30.Qxe3 Kg7 31.d4 c4 32.bxc4 bxc4 33.Qe5+ Qxe5
34.dxe5 Bd7 35.Rf4 Rc8 36.Bf1 Bb5 37.Rd4 Kf8 38.d6 Ke8 39.Kf2 Kd8 40.Ke3 Rc5
41.Re4 Bc6 42.Kd4 Rd5+ 43.Kxc4 Rxd6 44.Rd4 Rd7 45.Kc5 Rxd4 46.cxd4 Ba4
47.Kd6 Bb3 48.d5 Ba2 49.e6 0-1
Nasser
Richard Ulrich
wrote:
>
> "Richard Ulrich" <Rich....@comcast.net> wrote in message
> news:kqm7j355u5esbdgn0...@4ax.com...
>
> >
> > Like some other repliers, I suspect that your teacher is not
> > a thoroughly "good statistician", or you would not feel this way.
> >
>
> Actually my professor is distinguished in the field of probability and
> statistics. He is a known expert in this field with many scientific
> publications. < break. snip the rest >
I just want to toss out one opinion about "expertise" versus
being "thoroughly good." I wish I had a better phrase for
the latter, but maybe this will explain what I meant.
Your professor may be a fine expert in an area by knowing
all the *right* answers. He will be a better expert, and a
good teacher, if he also knows all the *wrong* answers that
people can come up with, or will listen to them to learn them,
in order to explain them. Some experts can't (or won't) do that.
The best of scientific "teachers" that I have read about seem to
have the ability to reach just about everybody in the class.
By the way, you mentioned, somewhere, "too many books to read."
I sympathize. By "browse", I meant that you may experience
great gain by a quick scanning -- look for the topics that seem
problematic, and read the sections, and immediately before them.
Libraries are nice. I've gone to a relevant shelf; found 3
or 4 books on my Question of the day; leafed through all
the books for an hour or two (that usually helps, already); and
then, maybe, decided to take the most useful one home to
read some more.
Good luck.
Scott Hemphill
> ps. here is our famous chess game, I digged it up from my chess book. I see
> that you beat me in this game. So you are good in chess and statistics also
> :)
>
> London Congress, England. July 30 1976
> Round 2, Board 75
> W: Nasser Abbasi, Black Shaw,J.E.H
> 1.e4 c5 2.Nf3 d6 3.g3 Nc6 4.Bg2 g6 5.0-0 Bg7 6.d3 Qc7 7.Nc3 e6 8.Nb5
> Qb8 9.Bf4 e5 10.Bg5 a6 11.Nc3 h6 12.Be3 Nge7 13.a4 b6 14.Ne1 0-0 15.f4 Qc7
> 16.Nd5 Nxd5 17.exd5 Nd4 18.fxe5 Rb8 19.exd6 Qxd6 20.Bf4 Be5 21.c3 Nf5
> 22.Bxe5 Qxe5 23.Nc2 Bd7 24.Qf3 Qd6 25.b3 Rbe8 26.Rae1 b5 27.axb5 axb5
> 28.Rxe8 Bxe8 29.Ne3 Nxe3 30.Qxe3 Kg7 31.d4 c4 32.bxc4 bxc4 33.Qe5+ Qxe5
> 34.dxe5 Bd7 35.Rf4 Rc8 36.Bf1 Bb5 37.Rd4 Kf8 38.d6 Ke8 39.Kf2 Kd8 40.Ke3 Rc5
> 41.Re4 Bc6 42.Kd4 Rd5+ 43.Kxc4 Rxd6 44.Rd4 Rd7 45.Kc5 Rxd4 46.cxd4 Ba4
> 47.Kd6 Bb3 48.d5 Ba2 49.e6 0-1
The 0-1 doesn't make any sense. White has a completely won game.
Scott
--
Scott Hemphill hemp...@alumni.caltech.edu
"This isn't flying. This is falling, with style." -- Buzz Lightyear
Nasser Abbasi
"Scott Hemphill" <hemp...@hemphills.net> wrote in message
news:m33ave5...@jade.local...
Sorry, cut/past problems from my Latex file where I keep my games.
It is 1-0 allright, and White was Dr Shaw and I was black.
Nasser
Robert Dodier
> I am taking a course in probability and statistics now. It is at
> the level of upper division / first year graduate.
>
> This is the hardest course I have ever taken so far, Yet, I am
> not sure why it is hard.
>
> Looking at the math on its own, it is hard, but manageable,
> upper level calculus I would say. But for some reason, I find the
> whole subject hard to do well at.
Belief and decision analysis is greatly simplified by adopting
Bayesian probability to represent beliefs, and utility theory to
represent values. Combining the two yields what is typically
called decision theory.
Conventional statistical hypothesis testing (either Fisher's or
the Neyman-Pearson variety) is essentially an attempt to formulate
a decision theory without introducing the probability of hypotheses
and without taking value (utility) of actions into consideration.
This leads to quite needless, and quite useless circumlocutions.
Naturally it is very difficult for students.
My advice to you, Nasser, is to drop whatever class you are taking,
and if there are no proper decision theory classes at your school,
then just study on your own. As I was saying, it is quite simple and
a bright person like yourself doesn't need professor to explain it.
FWIW
Robert Dodier
PS. Here are some readings for you. Some of these were
recommended to me but I haven't looked at all of them.
Probability theory: the logic of science, by E.T. Jaynes
(now published, maybe still on the web somewhere)
Probability, frequency, and reasonable expectation, by R.T. Cox
American J. Physics, 14(1):1--13, 1946.
(reprinted in Shafer & Pearl, Readings in Uncertain Reasoning)
Making Hard Decisions, by Robert Clemen
Bayesian Data Analysis, by Gelman, Carlin, Stern, & Rubin
Decision Analysis for Management Judgment
by P. Goodwin, G. Wright
Thinking and Deciding, by J. Baron
Probabilistic Methods for Financial and Marketing Informatics
by Richard Neapolitan
Decision Analysis, by Howard Raiffa
Smart Choices: A Practical Guide to Making Better Decisions
by John Hammond, Ralph Keeney, Howard Raiffa
http://www.amazon.com/Smart-Choices-Practical-Making-Decisions/dp/0767908864
Decision Tree Primer, by Craig Kirkwood
http://www.public.asu.edu/~kirkwood/DAStuff/decisiontrees/index.html