6 thoughts on “Natural frequencies instead of Bayes

  1. I am a bit ticked by this column. I think that using the formula for conditional probability or computing frequencies as explained in the column are exactly the same thing. The difference is that the former applies a memorized formula without understanding it whereas the latter basically “derives” that formula every time a computation is needed. To claim that those are intrinsically different methods, or to discuss whether one is more valid than the other, shows a lack of understanding of what mathematics is.

    • I don’t think it’s a question of *mathematical* validity — you get the same number at the end. As a student, it may be more valuable to rederive the formula each time until you develop the intuition as to why it is true.

      I remember learning how to square numbers by playing with grids of squares (10×10, 1×10, etc) and developing a geometric feeling for why (a + b)^2 = a^2 + 2ab + b^2. It’s not a more or less valid way for learning that formula, but the abstraction was easier to understand moving from physical manipulations to mental manipulations rather than the reverse.

      • I entirely agree that as a student is is more valuable to rederive the formula each time (which is what the “method of natural frequencies” is). I was taking issue with the article’s implicit statement that the two “methods” are not the same. To me, that means that they do not understand the formula for conditional probability.

    • This psychology article discusses reasons why using the formula and computing frequencies aren’t exactly the same thing. Here’s one passage from it:

      It turns out that human performance in probabilistic reasoning tasks is remarkably sensitive to the format in which information is presented and answers asked for. Most experiments that elicited “non-normative” performance asked subjects to judge the probability of a single event (e.g., “What is the chance that a person who tests positive for the disease actually has it?”). However, many purported biases and fallacies disappear when people are asked to judge a frequency instead (e.g., “How many people who test positive for the disease will actually have it?”).

      • One of them may be easier to understand for a person, or “make more sense”, or what-have-you, but mathematically they are exactly the same thing. After all, probability means frequency.

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