Re: why is probability and statistics a hard subject?

Nasser Abbasi 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.

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

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