4 ms·
When does the author talk about double sided coins? The example is based on the premise that the coin is fair and each toss is independent of the others.
by dvvarf 17y ago
When does the author talk about double sided coins? The example is based on the premise that the coin is fair and each toss is independent of the others.
- yummyfajitas 17y agoI'm disputing the premise. The author has a prior, namely "fair coin". I'm suggesting that it's likely that the prior is wrong.
- jerf 17y agoSo, what's the alternative? Give up the concept of "fair coin" when trying to teach statistics? This seems unlikely to be a useful pedagogical move! How is anyone supposed to understand Bayes Theorum before they even understand probability? Mathematicians have to be able to specify priors. Insisting they are unrealistic rather misses the point that the entire reason the phrase "fair coin" appears in the first place is an explicit acknowledgment of the unreality of the situation. If you want to more rapidly move to a Bayesian system when teaching, I'd understand completely, but we still have to start with "fair coins" before we can get around to considering how to prove they aren't fair. (I will be first in line to say many school teachers, being generally poorly trained in mathematics, completely fail to understand this point, and correspondingly ask the "gotcha" question about "what's after 29 heads?" without fully understanding the issue themselves.)
- bravura 17y agoThe point is that common sense forms the basis of our prior knowledge. If your priors are poor, then your probability estimates are going to be inaccurate, even if you know probability theory perfectly.