Vertaile menetelmiä

	Epäselvä todennäköisyys	Bayesiläinen päättely	Mahdollisuusteoria
Tieteenala	Pehmeä laskenta	Tilastotiede	Pehmeä laskenta
Menetelmäperhe	Bayesian methods	Bayesian methods	Machine learning
Syntyvuosi	1991	1763	1988
Kehittäjä	Peter Walley	Thomas Bayes; Pierre-Simon Laplace	Lotfi Zadeh; Didier Dubois & Henri Prade
Tyyppi	Set-valued probability model	Probabilistic inference paradigm	Uncertainty quantification framework
Alkuperäislähde	Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities. Chapman & Hall. ISBN: 978-0-412-28660-5	Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370–418.	Dubois, D., & Prade, H. (1988). Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press. ISBN: 978-0-306-42520-2
Rinnakkaisnimet	Lower-Upper Probability, Robust Bayesian Analysis, Credal Set Theory, Belirsiz Olasılık	Bayes inference, Bayesian statistics, Bayesian updating, posterior inference	Fuzzy Possibility Theory, Possibilistic Reasoning, Olasılık Teorisi (Bulanık), Possibility Distribution Theory
Liittyvät	3	3	3
Tiivistelmä	Imprecise probability is a generalization of standard probability theory that represents epistemic uncertainty through sets of probability measures, called credal sets, rather than a single precise distribution. Introduced systematically by Peter Walley in his 1991 monograph, the framework characterizes beliefs via lower and upper probabilities (or previsions), bracketing the range of plausible probability assignments when available information is insufficient to determine a unique measure.	Bayesian inference is a statistical paradigm in which probability represents degrees of belief rather than long-run frequencies. It encodes prior knowledge about parameters in a prior distribution, combines that prior with the likelihood of observed data via Bayes' theorem, and produces a posterior distribution that quantifies updated uncertainty. The foundational theorem was published posthumously by Thomas Bayes in 1763 and subsequently systematized by Pierre-Simon Laplace in his 1812 Théorie analytique des probabilités.	Possibility Theory is a mathematical framework for representing and reasoning under uncertainty, introduced by Lotfi Zadeh in 1978 and systematically developed by Didier Dubois and Henri Prade in their 1988 monograph. It uses possibility distributions — functions assigning a degree in [0,1] to each element of a universe — to encode what is plausible or consistent with available information, complementing probability theory for situations where data is scarce or knowledge is imprecise.