A priori, a posteriori

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Most generally

A priori roughly means something like "(from) that which goes before".

Often used in a "prior to experience/measurement".

A posteriori roughly means "(from) that which comes after".

Often meaning after experience, often using said experience

Statistics

In probability and statistics, particularly (statistical) inference, a priori is the prior knowledge of a population.

Basically, it is anything we consider already known, that we can use to improve our model, that is more than just estimations or limited recent measurements. (verify)

A priori probability http://en.wikipedia.org/wiki/A_priori_probability

Posterior probability http://en.wikipedia.org/wiki/Posterior_probability

Modelling

In machine learning and pattern recognition, and the models and math that backs it, a priori refers to factual/good/positive examples that make for supervised learning.

(and a posteriori often short for 'a posteriori estimation' based on it)

Without such a priori examples, the patterns would depend on data behaviour, clustering and such. (verify)

Knowledge (philosophically)

Note that while a priori in the general sense can be translated as 'pre-existing', once you start saying 'a priori knowledge' you trip yourself into epistemology (a.k.a. 'what can we know'), and a bit of metaphysics ('what is there?'), so philosophy's answers try to be a little wider - could be known answers rather than a person currently knows answers.

A priori knowledge: are things that can be knowable independently of experience/evidence (pedantry: ...aside from the experience of the language to communicate it).

say, anything that follows from logic alone.

e.g. regardless of observation, we can say "all bachelors are unmarried", whereas for other things we need observation.

A posteriori knowledge are things that can only be knowable, or verifiable, from empirical evidence.

that which is (or must necessarily be) deduced from epirical evidence, from experience, observation, or personal decision.

The distinction is related to objective versus subjective observation.(verify)

Law

In law, a priori refers to being based on hypothesis or deduction, rather than experimentation.

It can still refer to subjective, semantic details: testimonials are automatically subject to a priori plausability - personal back knowledge. (verify)