A priori, a posteriori: Difference between revisions
m (→Statistics) |
m (→Linguistics) |
||
(7 intermediate revisions by the same user not shown) | |||
Line 2: | Line 2: | ||
==Most generally== | |||
'''A priori''' roughly means something like '''"(from) that which goes before"'''. | '''A priori''' roughly means something like '''"(from) that which goes before"'''. | ||
Line 13: | Line 13: | ||
==A bit more practically== | |||
Line 19: | Line 19: | ||
In probability and statistics, particularly (statistical) [[inference]], a priori is the prior knowledge of a population. | In probability and statistics, particularly (statistical) [[inference]], a priori is the prior knowledge of a population. | ||
Basically, it is anything | |||
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}} | |||
Line 27: | Line 28: | ||
Posterior probability | Posterior probability | ||
http://en.wikipedia.org/wiki/Posterior_probability | http://en.wikipedia.org/wiki/Posterior_probability | ||
Also in statistics, the [https://en.wikipedia.org/wiki/Prior_probability prior probability] | |||
typically refers to the probability distribution before some evidence is taken into account. | |||
===Modelling=== | ===Modelling=== | ||
Line 41: | Line 47: | ||
Note that while a priori in the general sense can be translated as 'pre-existing', | 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]]. | 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 {{comment|(pedantry: ...aside from the experience of the language to communicate it)}}. | '''A priori knowledge''': are things that ''can'' be knowable independently of experience/evidence {{comment|(pedantry: ...aside from the experience of the language to communicate it)}}. | ||
: say, anything that follows from logic ''alone''. | : 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. | ::: e.g. regardless of observation, we can say "all bachelors are unmarried", whereas for other things we need observation. | ||
Line 89: | Line 95: | ||
It can still refer to subjective, semantic details: | It can still refer to subjective, semantic details: | ||
testimonials are automatically subject to a priori plausability - personal back knowledge. {{verify}} | testimonials are automatically subject to a priori plausability - personal back knowledge. {{verify}} | ||
===Linguistics=== | ===Linguistics=== | ||
<!-- | <!-- | ||
In linguistics, a priori [[constructed language]] | In linguistics, an "a priori [[constructed language]]" is one created from scratch. | ||
A posteriori constructed languages are those that mix and match from existing ones. | A posteriori constructed languages are those that mix and match from existing ones. | ||
Line 100: | Line 105: | ||
--> | --> | ||
==Why the terms are fuzzier than we pretend they are== | |||
<!-- | <!-- | ||
Revision as of 13:50, 4 March 2024
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 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
Also in statistics, the prior probability typically refers to the probability distribution before some evidence is taken into account.
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)