I'm teaching myself Bayesian statistics.

The basic idea is to update your beliefs about the world as you gather new evidence. Mathematically, we're solving for P(H|D,X) - the probability (P) of your hypothesis (H) being true, given some data (D) and your background knowledge (X).

Example:

I see bright lights outside my window at night. What's going on?

Initial Hypothesis (H1)

• H1: Those lights are from UFOs. My prior belief the probability (P) of the light being from UFOs (H1) is very low based on my experience (X).

• After looking outside, I see police cars. I update my belief: The probability (P) of UFOs (H1) given the police lights (D) and my experience (X)drops to nearly zero.

New Hypothesis (H2)

• H2: There's crime in my neighborhood. The probability (P) of crime in my neighborhood (H2) given the police lights (D) my experience (X) seems moderate to low. But wait! I spot a fire truck too. New data therefore an update.

• The probability (P) of crime in my neighborhood (H2) given the police car and the fire truck (D) and my experience (X) decreases.

And now there’s a new hypothesis — there’s a fire.

Through each observation, my beliefs evolve. That’s Bayesian updating at work.

The Shift

However, a subtle shift in reasoning can lead you astray. You’ve seen this before. You might know someone who might think: "I see police cars outside, and I read about rising crime on social media, therefore P(rampant crime in my neighborhood) is high." While I never hear someone say assert “P”, I hear people make conclusions and seeking confirming evidence rather than objectively update beliefs based on what’s available.

Simple Ideas

What you see is not all there is.

Life is emergent, not all at once.

Better to let life get ahead of you.

Don’t fool yourself.