A priori, a posteriori
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
A bit more practically
Statistics
In probability and statistics, particularly statistical inference, a priori is the prior knowledge of a population. Basically, it is anything factual that we can use to improve our model. It 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.
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.
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)
Linguistics
In linguistics, a priori constructed languages are those that are created from scratch.
A posteriori constructed languages are those that mix and match from existing ones.
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