Wednesday, January 4, 2012

Practical Statistics Tend To Be Local: the Bayesian specifics.

edited 11/4/19
A little learning is a dangerous thing;
drink deep, or taste not the Pierian spring:
there shallow draughts intoxicate the brain,
and drinking largely sobers us again. -- Alexander Pope (1709)
There are all sorts of ways to waste time, money and other resources in the struggle to make a living. Consider these:
a. putting a new den into a house you want to sell;
b. betting on the “fastest” horse when the weather is uncertain;
c. getting a Ph.D. in French when your dad owns a plumbing business;
d. investing in stocks based on the size of the company.
There is a superstition that some people acquire from studying introductory probability theory. The problem is that they try to apply context-free, universal patterns (axioms) to day-to-day specifics. This superstition can be shown in a variety of examples: the beliefs that
a. members of a larger group are more likely encountered; or
b. the average person is easiest to find; or
c. more is better; or
d. specifics reduce frequency.
But why is it that real estate agents chant, “Location, location, location” and not “New den, new den, new den”?

And does it matter that the horse race is being run in the mud? (If you don’t know, find out what a “mudder” is.)

After twenty-five years, who will have the most money on hand: the French scholar or the plumber? (But don’t “the statistics” tell us that those with more education earn more money?)

If you’re going to study probability and statistics, don’t stop before you get through Bayesian statistics. Adjusting general probability theory to the specific conditions you will be dealing with is a skill that many professionals have difficulty with. (You might be surprised how much unexamined cultural ideology underlies the choosing of "gold standards" or "priors".)

For references and to examine these issues further, see Is The Notion of Conjunctive Fallacy ("Conjunction Fallacy") Based on Fallacy?

 Cordially --- EGR

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