Methoden vergleichen

	Dirichlet-Prozess-Mischmodell	Bayes'sche Regression	Markov-Kette Monte Carlo (MCMC)
Fachgebiet	Bayes-Statistik	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods	Bayesian methods
Entstehungsjahr	1973	—	—
Urheber	Ferguson (1973); mixture model formulation by Lo (1984)	—	—
Typ	Nonparametric Bayesian mixture model	Bayesian linear model	Posterior sampling algorithm
Wegweisende Quelle	Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. The Annals of Statistics, 1(2), 209–230.	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955
Aliasnamen	DPMM, DP mixture model, infinite mixture model, Dirichlet process mixture	bayesian linear regression, probabilistic regression, bayesian regresyon	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
Verwandt	3	2	3
Zusammenfassung	The Dirichlet Process Mixture Model (DPMM) is a nonparametric Bayesian clustering method introduced through Ferguson's (1973) Dirichlet process prior that places a probability distribution over distributions. Unlike finite mixture models, the DPMM does not require the analyst to specify the number of clusters in advance; instead it infers the number of components from the data, allowing an effectively unbounded mixture that grows as more observations arrive.	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.