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Re: [Phys-l] Basic statistics



Ludwik Kowalski wrote:
I suppose that the concept of a "population" versus a "samples from a population" were formulated to deal with problems in fields like sociology, medicine or advertising.


What should be called a population when students measure gravitational acceleration?


I would refer everyone on this thread to the wonderful article "From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics" by Tom Loredo, located at http://www.astro.cornell.edu/staff/loredo/bayes/tjl.html

From my personal experience trying to learn basic statistics, I always got hung up on the notion of a population, and of the standard deviation of the mean. I found the Bayesian approach to be both more intuitive, easier to apply to real data, and more mathematically sound (there is a great article by E.T. Jaynes at http://bayes.wustl.edu/etj/articles/confidence.pdf where he outlines several pathologies in standard stats).

Bottom line: there is no population in the Bayesian approach. Probability is a measure of ones state of knowledge, not a property of the system. In doing so, all of the strained attempts at creating a fictitious population out of measurements vanish (such as, say, analyzing measurements of the mass of the moon by imagining many hypothetical universes of "identical" measurements). On instead is quantifying your state of knowledge.

In almost all easy cases, the Bayesian approach yields the *exact same* numerical result as the standard approach. The interpretation is a lot easier, and a lot easier to communicate to students.




Brian Blais

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bblais@bryant.edu
http://web.bryant.edu/~bblais