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Saturday, February 10, 2024

How to think like a Bayesian

Michael Titelbaum
Originally posted 10 Jan 24

You’re often asked what you believe. Do you believe in God? Do you believe in global warming? Do you believe in life after love? And you’re often told that your beliefs are central to who you are, and what you should do: ‘Do what you believe is right.’

These belief-questions demand all-or-nothing answers. But much of life is more complicated than that. You might not believe in God, but also might not be willing to rule out the existence of a deity. That’s what agnosticism is for.

For many important questions, even three options aren’t enough. Right now, I’m trying to figure out what kinds of colleges my family will be able to afford for my children. My kids’ options will depend on lots of variables: what kinds of schools will they be able to get into? What kinds of schools might be a good fit for them? If we invest our money in various ways, what kinds of return will it earn over the next two, five, or 10 years?

Suppose someone tried to help me solve this problem by saying: ‘Look, it’s really simple. Just tell me, do you believe your oldest daughter will get into the local state school, or do you believe that she won’t?’ I wouldn’t know what to say to that question. I don’t believe that she will get into the school, but I also don’t believe that she won’t. I’m perhaps slightly more confident than 50-50 that she will, but nowhere near certain.

One of the most important conceptual developments of the past few decades is the realisation that belief comes in degrees. We don’t just believe something or not: much of our thinking, and decision-making, is driven by varying levels of confidence. These confidence levels can be measured as probabilities, on a scale from zero to 100 per cent. When I invest the money I’ve saved for my children’s education, it’s an oversimplification to focus on questions like: ‘Do I believe that stocks will outperform bonds over the next decade, or not?’ I can’t possibly know that. But I can try to assign educated probability estimates to each of those possible outcomes, and balance my portfolio in light of those estimates.


Key points – How to think like a Bayesian
  1. Embrace the margins. It’s rarely rational to be certain of anything. Don’t confuse the improbable with the impossible. When thinking about extremely rare events, try thinking in odds instead of percentages.
  2. Evidence supports what makes it probable. Evidence supports the hypotheses that make the evidence likely. Increase your confidence in whichever hypothesis makes the evidence you’re seeing most probable.
  3. Attend to all your evidence. Consider all the evidence you possess that might be relevant to a hypothesis. Be sure to take into account how you learned what you learned.
  4. Don’t forget your prior opinions. Your confidence after learning some evidence should depend both on what that evidence supports and on how you saw things before it came in. If a hypothesis is improbable enough, strong evidence in its favour can still leave it unlikely.
  5. Subgroups don’t always reflect the whole. Even if a trend obtains in every subpopulation, it might not hold true for the entire population. Consider how traits are distributed across subgroups as well.