What if I told you that I can show you the difference between Bayesian and Frequentist statistics with one single coin toss?

Before we go any further, the demonstration works best in video form, so don’t read the summary and spoilers below until you’ve seen it. In case some terms are unfamiliar, I’ve linked to friendly explanations to help you out.

In the video, there’s a moment where I ask you, “What is the probability that the coin in my palm is up heads?” The coin has already landed, I’m looking at it, but you can’t see it yet. The answer you give in that moment is a strong hint about whether you’re inclined towards Bayesian or Frequentist thinking.

Frequentist: “There’s no probability about it. I may not know the answer, but that doesn’t change the fact that if the coin is heads up, the probability is 100%, and if the coin is tails up, the probability is 0%.”

Bayesian: “For me, the probability is 50%! For you, it’s whatever it is for you.”

It is only by insisting that the parameter is not a random variable (Frequentist) that it makes any kind of sense to talk about your method’s ability to deliver the right answer. As soon as you let the parameter be a random variable (Bayesian), there’s no longer any notion of right and wrong. There’s only your personal perspective.

Frequentist: The parameter is not a random variable.
Bayesian: The parameter is a random variable.

One word, huge difference. Let’s take a closer look.

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