3 ms·

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 wi

by lottin 10y ago

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.

paulddraper 10y ago
They are prior observations: successes and trials.
contravariant 10y ago
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.
- BeetleB 10y ago
  >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.
  - contravariant 10y ago
    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.
jamii 10y ago
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.
- smallnamespace 10y ago
  Technically that's true only if you're risk neutral, but we define risk aversion in terms of probabilities, so you can't avoid a circular argument.

by lottin 10y ago

paulddraper 10y ago

They are prior observations: successes and trials.

contravariant 10y ago

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.

BeetleB 10y ago
>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.
- contravariant 10y ago
  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.

jamii 10y ago

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.

smallnamespace 10y ago
Technically that's true only if you're risk neutral, but we define risk aversion in terms of probabilities, so you can't avoid a circular argument.