手法を比較

	ベイズ非パラメトリック法	ベイズ回帰	ガウス過程
分野	ベイズ	ベイズ	機械学習
系統	Bayesian methods	Bayesian methods	Machine learning
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	Bayesian linear model	Probabilistic non-parametric model
原典	Rasmussen, C.E. & Williams, C.K.I. (2006). Gaussian Processes for Machine Learning. MIT Press. ISBN: 978-0262182539	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	Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press. ISBN: 978-0-262-18253-9
別名	BNP, Dirichlet process mixture, DPM, Gaussian process regression	bayesian linear regression, probabilistic regression, bayesian regresyon	GP, Gaussian Process Regression, GPR, Kriging
関連	3	2	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).	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.	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.