bay bâhé Fr.: baie A body of water forming an indentation of the shoreline, larger than a cove but smaller than a → gulf (Dictionary.com). M.E. baye, from M.Fr. baie, from L.L. bâia, perhaps ultimately from Iberian bahia. Bâhé, loan from Sp. bahia. |
Bayer designation nâmgozini-ye bayer Fr.: designation de Bayer A stellar designation system in which a specific star is identified by a Greek letter, followed by the genitive form of its hosting → constellation's Latin name. For example, Alpha Eridani, Delta Cephei, Lambda Bootis. The Greek alphabet has only 24 letters. In case a single constellation contained a larger number of stars, Bayer amended with Latin letters: upper case A, followed by lower case b through z (omitting j and v), for a total of another 24 letters. Bayer did not go beyond z, but later astronomers added more designations using both upper and lower case Latin letters, the upper case letters following the lower case ones in general. Examples include, for Vela: a Vel (Velorum), z Vel, A Vel, Q Vel; for Scorpius: d Sco (Scorpii), A Sco; for Leo: b Leo (Leonis), o Leo, A Leo, → c Orionis. Compare with the → Flamsteed designation. First introduced by Johann Bayer (1572-1625) in his atlas Uranometria, published in 1603 at Augsburg, Germany; → designation. |
Bayes' theorem farbin-e Bayes Fr.: théorème de Bayes A theorem in probability theory concerned with determining the → conditional probability of an event when another event has occurred. Bayes' theorem allows revision of the original probability with new information. Its simplest form is: P(A|B) = P(B|A) P(A)/P(B), where P(A): independent probability of A, also called prior probability; P(B): independent probability of B; P(B|A): conditional probability of B given A has occurred; P(A|B): conditional probability of A given B has occurred, also called posterior probability. Same as Bayes' rule. Named after its proponent, the British mathematician Reverend Thomas Bayes (1702-1761). However, Bayes did not publish the theorem during his lifetime; instead, it was presented two years after his death to the Royal Society of London. |
Bayesian Bayesi Fr.: bayésien Being, relating to, or denoting statistical methods based on → Bayes' theorem. Referring to → Bayes' theorem. |
Bayesian inference darbord-e Bayesi Fr.: inférence bayésienne An approach to → statistical analysis in which → unknowns to be estimated have a prior → probability distribution which combined with the information from data produces a posterior probability distribution for the target quantities. |
Bayesian model model-e Bayesi Fr.: modèle bayésien A mathematical framework described by the prior distribution of a random parameter and by the likelihood of the observations. In this framework, all information on the random parameter based on the observations is included in the posterior distribution which can be obtained using → Bayes' theorem (see, e.g., Andrieu et al., 2001, "An Introduction to Monte Carlo Methods for Bayesian Data Analysis," in Nonlinear Dynamics and Statistics, ed. A. I. Mees, Boston: Birkhäuser). |
Bayesian model averaging (BMA) miyângin-giri-ye Bayesi-e model Fr.: An approach to model selection in which one bases inference on an average of all possible models instead of a single best model. The BMA is largely used in various branches of knowledge to properly account for model uncertainty in performing predictions. |