Sunday, January 24, 2016

trying to be more precise, less ignorant and less vague

​My friends were discussing numerical estimates, especially subjective ratings.  The physician asks, "On a scale from 0 to 10, h​ow bad is your pain?"  Some people find such questions irritating or off-putting or scary.  How can I know what the correct rating is?  What if I say "5" when I should have said "7.2"? Lynn suggests that those who have difficulty with such questions ask the physician "On a scale of 0 to 10, how much do you want an answer?"

I wrote my dissertation in 1968. Back then, there was a big change going on and it is still happening.  The change more or less started with Bruno de Finetti (1906-1985) and Leonard Savage (1917-1971).  These men and Howard Raiffa and others sought to make much greater use of information in people's minds.  The idea is that it could be useful.  In fact, it is already being used in many fields.  Anglo-American statistical methods of analysis of experiments began back with the publication of an anonymous article by an employee of the Guinness Brewing Company using as a foundation a "null hypothesis" of no difference between two groups.  W.S. Gosset published his article in 1908, relying on work done since the mid-1800's on what errors could probably be expected in readings in astronomy.  

The big change just beginning in the mid-1960's was movement away from null hypothesis testing and into Bayesian statistics.  The men mentioned above urged more use of what is called a Bayesian approach, after a British cleric Thomas Bayes (1702-1761).  He published after death on the adjustment of a probability in the light of additional evidence, the way to modify conditional probability. Often a Bayesian approach is much assisted by some initial guess, such my guess that there is a 10% chance there is oil underground right about here.  That figure from my head, 10%, will get corrected over time and experience.

Today, we are in the midst of a push to use computers better and more intelligently in all walks of life and in another push to computerize medical records and communications.  As soon as you have data collected, statisticians want to analyze it for patterns.  

I was interested in this ad I saw this morning as it shows the increased use of math, statistics and precise (although sometimes misleading) definitions:

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