Roughly speaking, we can divide Bayesianism into two, maybe three or more, separate but related meanings:
1. Adherence to a form of Bayesian epistemology. You think that knowledge comes in degrees of belief, and the correct way to update your beliefs on seeing new information is to use Bayes theorem. It's usually done informally.
2. Adherence to Bayesian statistics. You believe that frequentist inference is invalid and that frequentist measures of an estimator's quality should not be used. Instead, you prefer to use precisely defined priors and likelihoods, derive their posteriors, and report a quantity based solely on that. Moreover, you would often espouse some form of Bayesian decision theory - i.e., you have... (read more)
Roughly speaking, we can divide Bayesianism into two, maybe three or more, separate but related meanings:
1. Adherence to a form of Bayesian epistemology. You think that knowledge comes in degrees of belief, and the correct way to update your beliefs on seeing new information is to use Bayes theorem. It's usually done informally.
2. Adherence to Bayesian statistics. You believe that frequentist inference is invalid and that frequentist measures of an estimator's quality should not be used. Instead, you prefer to use precisely defined priors and likelihoods, derive their posteriors, and report a quantity based solely on that. Moreover, you would often espouse some form of Bayesian decision theory - i.e., you have... (read more)