Wikipedia does IMO an excellent job explaining the notion of a confidence interval. On the other hand, I find the idea of being "73% certain" that something will happen much harder to understand. A percentage implies a ratio, but Bayesians never explain what the numerator and denominator are.
The interpretation of the probability is the same as in frequentist statistics, except you're making statements about the model resulting from your assumptions and data, instead of some hypothetical experiment. I suppose the Bayesian approach is more about building the model whereas the frequentist approach is more about selecting the best model out of several.
>The interpretation of the probability is the same as in frequentist statistics
Not at all. Frequentists cannot define a probability on whether it will rain in a location on a given day. They will respond that such a probability is meaningless. Bayesians can, however, give a meaning to it.
True, but the way a Bayesianist (?) will assign meaning to it involves creating a model, based on some assumptions, which will return a probability. The Bayesian notion of probability is equivalent to the frequentist notion of probability for experiments done on that model. In that sense they are the same.
One way to think of it is in terms of the expected value of betting on being correct. Even if the bet only happens once ever, I still need a way to map how confident I am to how much I think the bet is worth. If I am willing to pay up to $0.73 for a bet that pays out $1 when I'm correct then I am 73% certain.
