Methoden vergleichen

	Dirichlet-Prozess-Mischmodell	Markov-Kette Monte Carlo (MCMC)
Fachgebiet	Bayes-Statistik	Bayes-Statistik
Familie	Bayesian methods	Bayesian methods
Entstehungsjahr	1973	—
Urheber	Ferguson (1973); mixture model formulation by Lo (1984)	—
Typ	Nonparametric Bayesian mixture 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
Aliasnamen	DPMM, DP mixture model, infinite mixture model, Dirichlet process mixture	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
Verwandt	3	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.	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.