手法を比較

	ベイズ非パラメトリック法	ガウス過程	マルコフ連鎖モンテカルロ法 (MCMC)
分野	ベイズ	機械学習	ベイズ
系統	Bayesian methods	Machine learning	Bayesian methods
提唱年	1973 (DP); 2006 (GP canonical text)	2006 (book); roots in Kriging, 1951)	—
提唱者	Ferguson (Dirichlet Process, 1973); Rasmussen & Williams (GP, 2006)	Rasmussen, C. E. & Williams, C. K. I.	—
種類	Bayesian nonparametric model	Probabilistic non-parametric model	Posterior sampling algorithm
原典	Rasmussen, C.E. & Williams, C.K.I. (2006). Gaussian Processes for Machine Learning. MIT Press. ISBN: 978-0262182539	Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press. ISBN: 978-0-262-18253-9	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
別名	BNP, Dirichlet process mixture, DPM, Gaussian process regression	GP, Gaussian Process Regression, GPR, Kriging	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
関連	3	3	3
概要	Bayesian nonparametric methods are a family of flexible Bayesian models in which model complexity is not fixed in advance but grows automatically with the data. The two most widely used members are the Dirichlet Process Mixture (DPM), which clusters observations without pre-specifying the number of clusters, and Gaussian Process (GP) regression, which places a prior directly over functions and performs regression or classification without committing to a parametric form. Both frameworks were formalised in the Bayesian nonparametric literature, with the canonical GP treatment given by Rasmussen and Williams (2006).	A Gaussian Process (GP) is a non-parametric, fully probabilistic machine learning model that places a prior distribution directly over functions. Rather than predicting a single value, it returns a predictive mean and a calibrated uncertainty estimate at every test point, making it especially valuable for regression on small to medium datasets and for Bayesian optimization tasks.	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.