"Beliefs are knobs, not switches!"

Just remember:

• 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 information as it arrives. If a new observation is surprising, make a big adjustment; if it's ho-hum just-as-expected, make little or no adjustment.

Note the two key components:

• 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 relevant 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., maybe one crash every few years = roughly ~0.1% daily?)
• Adjustment: Are you at more, or less, risk tomorrow than the average in that pool of similar people? (Do you rarely drive? Live in a dense urban area with bad traffic? Plan to take a long trip tomorrow? Tend to get a lot of tickets? Anticipate that tonight will be a night of partying and little sleep? And is the weather forecast bad? Will tomorrow be a holiday? ...)

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

And finally: don't be too sure! 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.

_{(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 - 2025-01-01}