Bayesian Thinking

Bayesian Thinking

Bayesian thinking considers not only what the data have to say, but what your expertise tells you as well.

If you’re the sort of person who reads data science blogs (well hello there!) then you probably already know about Bayes’ Law. Heck, you’ve probably even used it yourself. Unfortunately, in my experience, many people only know Bayes’ Law in a technical, academic context, and don’t actually _understand _it in a way that’s useful in daily life. And that’s a shame, because Bayes’ Law is a beautiful, powerful, rational way of organizing your beliefs. Here’s the thing, though: you already use it in daily life, you just might not know it. In this article I’m going to show you how to consciously use Bayes’ Law with a topical and non-technical example: the (potential) discovery of life on Venus.

Excuse me, what?

If you somehow missed the news, a recent paper by Dr. Jane S. Greaves et al. has sparked a lot of interest in the possibility of life on Venus. Unfortunately, with COVID travel bans in effect, Dr. Greaves wasn’t able to take her team to the balmy planet for a field trip, so instead they used telescopes. In very short, the research team found evidence of phosphine gas in Venus’ atmosphere.

Okay, so what does this have to do with Bayes’ Law?

Bayes’ Law is is a tool for updating your existing beliefs given new information, rather than outright discarding your old beliefs. Brace yourself, because I’m about to show you an equation:

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Bayes’ Law in all its glory

What does this have to do with beliefs and information? Well, it looks a little complex but it’s really quite simple. Let’s break it down:

  • For starters, “P” is read as “the probability of” and “|” is read as “given”. So “P(A|B)” is read as “the probability of A given B”.
  • A is the belief in question; in our case, A is the statement “there is life on Venus”.
  • B is the evidence; in our case, “there is phosphine gas on Venus”.

bayes-theorem venus life statistics data-science

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