Bayesian [bey-zee-uhn] probability is the likelihood that something will happen based on all available evidence. The more commonly understood concept of frequency probability is the chance that something will happen based only on past occurrences. Rather than interpreting probability as merely the propensity of some phenomenon, Bayesian probability is a quantity assigned for the purpose of representing a state of knowledge, or a state of belief. This allows the application of probability to all sorts of propositions rather than just ones that come with a reference class (historical data).
‘Prior probability’ is information about a hypothesis known before the experiment is undertaken (e.g. a flipped coin has a 50% chance of landing on heads), information learned afterwards is called ‘Posterior probability’ (e.g. if a coin lands on heads many times in a row it is probably improperly weighted). The term ‘Bayesian’ refers to 18th century mathematician and theologian Thomas Bayes, who summarized the theory thusly: ‘The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon its happening.’ (i.e. Likelihood equals Prior probability over Posterior probability.)
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The Daily Omnivore 