draft notes for a one-page quick-start "Think Better" module:

"Beliefs are knobs, not switches!"

• Estimate prior odds for each outcome
• Adjust the odds as new evidence comes in

Bayes in a Nutshell

How likely is it that the enemy will attack at dawn, that the next card is an ace, that you will catch the flu, or that you will get married next year? To answer any probabilistic question "Bayes Rule" says to start with your best guess of the chance for each possible result, then adjust those guesses based on observations. If an observation is surprising, make a big adjustment proportional to its likelihood; if it's as expected, make little or no adjustment.

Note the two key components of Bayes Rule:

• Baseline: prior chances of events
• Adjustment: updates based on evidence

For simple well-defined cases, like rolling dice or winning a lottery, precise baseline odds and the size of updates can be computed with a little math. Complex real-world situations, in contrast, demand experience and good judgment — but the same principles apply. For example, to estimate your chance of being in a traffic accident tomorrow:

• Baseline: What's the average accident rate for people like you? (e.g., one crash every few years?)
• Adjustment: Are you at more or less risk tomorrow than the average? (Do you drive? Live in an urban area? Need to take a big trip? Tend to get a lot of tickets? Is the weather forecast bad? Will it be a holiday? ...)

And most important: continue to adjust as new evidence arrives. If your sports team is evenly-matched with the opponent before the big game, the odds of winning are about 50%. If your team falls far behind in the final minutes, the odds become a lot worse. If a nice slice of cake awaits you in the refrigerator at home, the likelihood of an enjoyable dessert is high. If when you arrive you find unexpected visitors and a party underway, chances fall for finding that food uneaten.

And finally: don't be too sure. The most common cognitive fallacies involve anchoring on old beliefs, under-adjusting for new evidence, overlooking alternative outcomes, and seeking evidence to confirm rather than refute judgments. Stay open to surprise!

(cf Statistics - A Bayesian Perspective (2010-08-13), Introduction to Bayesian Statistics (2010-11-20), Mantra - Beliefs Are Knobs, Not Switches (2017-07-03), Think Better - Three Keys (2019-06-05), ...) - ^z - 2020-01-26