Linganisha mbinu

	Uwezekano Usio sahihi	Uthibitisho wa Kibayes
Nyanja	Ukokotoaji Laini	Takwimu
Familia	Bayesian methods	Bayesian methods
Mwaka wa asili	1991	1763
Mwanzilishi	Peter Walley	Thomas Bayes; Pierre-Simon Laplace
Aina	Set-valued probability model	Probabilistic inference paradigm
Chanzo asilia	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.
Majina mbadala	Lower-Upper Probability, Robust Bayesian Analysis, Credal Set Theory, Belirsiz Olasılık	Bayes inference, Bayesian statistics, Bayesian updating, posterior inference
Zinazohusiana	3	3
Muhtasari	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.