Methoden vergleichen

	Bayesianische Inferenz	Bradley-Terry-Modell	Elo Rating
Fachgebiet	Statistik	Entscheidungsfindung	Entscheidungsfindung
Familie	Bayesian methods	Regression model	Regression model
Entstehungsjahr	1763	1952	1978
Urheber	Thomas Bayes; Pierre-Simon Laplace	Ralph Bradley & Milton Terry	Arpad Elo
Typ	Probabilistic inference paradigm	Probabilistic paired comparison model	Pairwise comparison ranking model
Wegweisende Quelle	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.	Bradley, R. A., & Terry, M. E. (1952). Rank analysis of incomplete block designs: I. The method of paired comparisons. Biometrika, 39(3/4), 324–345.	Elo, A. E. (1978). The Rating of Chessplayers, Past and Present. Arco Publishing. ISBN: 978-0-668-04721-0
Aliasnamen	Bayes inference, Bayesian statistics, Bayesian updating, posterior inference	BT Model, Bradley-Terry-Luce Model, Paired Comparison Model, İkili Karşılaştırma Modeli	Elo Rating System, Elo Chess Rating, Elo Skill Rating, Elo Derecelendirme Sistemi
Verwandt	3	3	2
Zusammenfassung	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.	The Bradley-Terry model is a probabilistic model for paired comparisons that assigns a latent strength parameter to each item and predicts the probability that one item beats another in a head-to-head contest. Introduced by Ralph A. Bradley and Milton E. Terry in 1952, it provides a principled statistical framework for ranking items from pairwise preference data, including incomplete comparison designs where not every pair is directly observed.	The Elo Rating System is a pairwise comparison-based ranking method developed by Hungarian-American physicist and chess master Arpad Elo and formally published in 1978. Originally designed to assess the relative skill levels of chess players, it assigns each competitor a numerical rating that rises or falls after each encounter based on the expected versus actual outcome. The system assumes that player performance follows a logistic distribution, enabling probabilistic predictions of match results and continuous rating refinement over time.