Thursday, September 24, 2020

Guessing and Bayes


In my posting prior to this one, I gave an example of two probabilities influencing yet a third. To do that, I assumed a probability for "A" and I assumed a probability for "B", both of which jointly influence "C". But, I gave no evidence that either of these assumptions was "calibrated" by prior experience.

I just guessed
What if I just guessed about "A" and "B" without any calibrated evidence to back up my guess? What if my guess was off the mark? What if I was wrong about each of the two probabilities? 
Answer: Being wrong about my guess would throw off all the subsequent analysis for "C".

Guessing is what drives a lot of analysts to apoplexy -- "statisticians don't guess! Statistics are data, not guesses."
Actually, guessing -- wrong or otherwise -- sets up the opportunity to guess again, and be less wrong, or closer to correct.  With the evidence from initial trials that I guessed incorrectly, I can go back and rerun the trials with "A" and "B" using "adjusted" assumptions or better guesses.

Oh, that's Bayes!
Guessing to get started, and then adjusting the "guess" based on evidence so that the analysis or forecast can be run again with better insight is the essence of Bayesian methodology for handling probabilities.
 
And, what should that first guess be?
  • If it's a green field -- no experience, no history -- then guess 50/50, 1 chance in 2, a flip of the coin
  • Else: use your experience and history to guess other than 1 chance in 2
According to conditions
Of course, there's a bit more to Bayes' methodology: the good Dr Bayes -- in the 18th century -- was actually interested in probabilities conditioned on other probable circumstances, context, or events. His insight was: 
  • There is "X" and there is "Y", but "X" in the presence of "Y" may influence outcomes differently. 
  • In order to get started, one has to make an initial guesses in the form of a hypothesis about not only the probabilistic performance of "X" and "Y", but also about the the influence of "Y" on "X"
  • Then the hypothesis is tested by observing outcomes, all according to the parameters one guessed, and 
  • Finally, follow-up with adjustments until the probabilities better fit the observed variations. 
Always think Bayesian!
  • To get off the dime, make an assumption, and test it against observations
  • Adjust, correct, and move on!



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