The essential different between Bayesian probability and Frequentist probability is the difference between 2 interpretations of what probability means.
| Bayesian statistics | frequentist statistics | |
|---|---|---|
| what probability means ? | certainty and belief reasonable expectation or quantification of a personal belief. | long-run relative frequency relative frequency that long-run samples would approach given large amounts of data. |
| use of unknown parameters | typically considered fixed, rather than being random variables | ==allows probabilities to be associated with unknow parameters== (these probabilities can sometime have a frequentist interpretation as well as a Bayesian one) |
| allows these probabilities to have an interpretation representing the scientist's belief that given values of the parameter are true | ||
| the result | can be a probability distribution for what is known about the parameters given the results of the experiment. | either - a decision from a significant test - or a confidence interval |