Bayesian probability represents a level of certainty relating to a potential outcome or idea. This is in contrast to a frequentist probability that represents the frequency with which a particular outcome will occur over any number of trials.

An event with Bayesian probability of .6 (or 60%) should be interpreted as stating "With confidence 60%, this event contains the true outcome", whereas a frequentist interpretation would view it as stating "Over 100 trials, we should observe event X approximately 60 times."

The difference is more apparent when discussing ideas. A frequentist will not assign probability to an idea; either it is true or false and it cannot be true 6 times out of 10.

Blog posts

What is Bayesianism?
Probability is Subjectively Objective
Probability is in the Mind
When (Not) To Use Probabilities
Against NHST
All Less Wrong posts tagged "Probability"

See also

Priors
Bayesian
Bayes' theorem
Mind projection fallacy

External links

BIPS: Bayesian Inference for the Physical Sciences
Maximum entropy thermodynamics
What is Bayesian statistics?